The speed (in revolutions per minute) at which resonance vibrations will occur is 273.91 RPM.
The front-loading washing machine is mounted on a thick rubber pad that acts as a spring. When the rotor spins at radians per second, the rotor exerts a vertical force of newtons on the machine.
Resonance vibrations occur when the natural frequency of the machine matches the frequency of the external force applied to it. This can cause the machine to vibrate excessively and even damage it.
In this scenario, the natural frequency of the washing machine is related to its spring constant and the mass of the machine. Neglecting friction, resonance vibrations occur at RPMs.
Given,
The weight (with m/s) of the machine depresses the pad exactly 0.89 cm.
The rotor exerts a vertical force of N on the machine.
The natural frequency of a machine is given by:
f = 1/2π x √(k/m)
where f is the frequency of oscillation,
k is the spring constant of the spring,
m is the mass of the machine.
In this case, the weight of the machine depresses the spring by 0.89 cm.
So, the effective spring constant is given by,
k = F/x = (mg)/x
where F is the weight of the machine,
m is its mass,
g is the acceleration due to gravity,
and x is the amount by which the spring is compressed.
Substituting the given values,
k = (m x g) / x = (m x 9.8) / 0.0089 = 1101.12m N/m
Substituting the given values,
f = 1/2π x √(k/m) = 1/2π x √(1101.12m/m) = 4.9448 √m Hz
The frequency of oscillation is given in Hz.
To convert it to RPMs, we need to divide it by 60 (the number of seconds in a minute) and multiply it by 2π (the number of radians in a circle).
f = 4.9448 √m Hz = (4.9448 √m x 2π)/60 RPM
At resonance, the frequency of oscillation should match the frequency of the rotor.
So, the frequency of the rotor is given by,
f = ω/2π
where ω is the angular velocity of the rotor in radians per second.
Substituting the given values,
N = mg = F,
ω = N/(m x r) = 94.4912/r rads/s
where r is the radius of the rotor in meters.
Substituting these values in the equation for frequency,
f = ω/2π = (94.4912/r) / 2π = 15.0415 / r Hz
At resonance, the frequency of oscillation should match the frequency of the rotor.
Therefore,4.9448 √m = 15.0415 / r
Squaring both sides,19.4542 m = (15.0415/r)^2
Solving for r, r = 0.0275 m = 2.75 cm
Therefore, the radius of the rotor is 2.75 cm.
The speed (in revolutions per minute) at which resonance vibrations will occur is 273.91 RPM.
To know more about resonance:https://brainly.com/question/15337338
#SPJ11
The position of a particle moving along the x axis with a constant acceleration may be determined from the expression x(t) = b + c(t - 2 s), where b = 2.00 m, c = 9.00 m/s, and x will be in meters when t is in seconds. Determine the following. (Where applicable, indicated direction with the sign of your answer.) (a) position, velocity, and speed of the particle at the time t = 0 s (Enter your answers to at least one decimal place.) position x(t = 0 ) = ____ m/svelocity v(t = 0 ) = ____ m/s peed v(t = 0 s) = ____ m/s
The speed of the particle at t = 0 s is 9.00 m/s. The position of the particle at t = 0 s is -16.00 m.
The position, velocity, and speed of the particle at the time t = 0 s can be determined by substituting t = 0 into the given expression for x(t) and taking the first and second derivatives of x(t) with respect to time.
(a) Position at t = 0 s:
x(t) = b + c(t - 2 s)
x(t = 0) = 2.00 m + 9.00 m/s(0 - 2 s)
x(t = 0) = 2.00 m - 18.00 m
x(t = 0) = -16.00 m
(b) Velocity at t = 0 s:
v(t) = dx/dt = c
v(t = 0) = 9.00 m/s
The velocity of the particle at t = 0 s is 9.00 m/s.
(c) Speed at t = 0 s:
The speed of the particle is the absolute value of the velocity, so:
v(t = 0) = |9.00 m/s| = 9.00 m/s
To learn more about Speed :
https://brainly.com/question/13943409
#SPJ11
What do we call a push or pull on an object?
Answer:
a force
Explanation:
b) A hammer of weight 100 N falls freely on a nail from height 1.25 m. Find the impulse and average force of blow if impact last for 10-² S.
An alpha particle is a nucleus of doubly ionized helium . It has mass of 6.68×10^- 27 kg and charge of 3.2 ×10^- 19 C. Compare the force of electrostatic repulsion between the two Alpha particles with the force of gravitational attraction between them.
[ where the Universe of gravitational constant = 6.67×10^-11 Nm²/kg² and permittivity of free space=8.85×10^-12 F/m ]
show with steps:'(
Answer: To compare the force of electrostatic repulsion and gravitational attraction between two alpha particles, we need to calculate both forces using the given information:
Electrostatic force of repulsion between two alpha particles:
Coulomb's law states that the force of electrostatic repulsion between two charged particles is given by:
F = (kq1q2)/r^2
where k is Coulomb's constant, q1 and q2 are the charges of the two particles, and r is the distance between them.
Here, q1 = q2 = 3.2×10^-19 C (charge of alpha particle), and r = distance between two alpha particles.
We know that two alpha particles are doubly ionized helium nuclei, so they each contain two protons. Thus, their separation distance will be approximately equal to the sum of their radii, which is about 4 fm (4 × 10^-15 m).
Plugging in these values, we get:
F_elec = (8.85×10^-12 * (3.2×10^-19)^2) / (4×10^-15)^2
F_elec = 8.17×10^-28 N
Gravitational force of attraction between two alpha particles:
The force of gravitational attraction between two particles is given by:
F = G*(m1*m2)/r^2
where G is the gravitational constant, m1 and m2 are the masses of the two particles, and r is the distance between them.
Here, m1 = m2 = 6.68×10^-27 kg (mass of alpha particle), and r = distance between two alpha particles.
Plugging in these values, we get:
F_grav = (6.67×10^-11 * (6.68×10^-27)^2) / (4×10^-15)^2
F_grav = 3.71×10^-57 N
Therefore, we can see that the force of electrostatic repulsion between two alpha particles is much greater than the force of gravitational attraction between them.
F_elec/F_grav = (8.17×10^-28 N) / (3.71×10^-57 N) ≈ 2.2×10^29
Explanation:
Answer: The electrostatic force of repulsion between the two alpha particles is about 5.5 × 10^48 times stronger than the gravitational force of attraction between them.
Explanation:
The force of electrostatic repulsion between two alpha particles can be calculated using Coulomb's law:
F_e = k * (q1 * q2) / r^2
where k is the Coulomb constant (1/4πε0), q1 and q2 are the charges of the particles (in coulombs), and r is the distance between them (in meters).
For alpha particles, the charge is 3.2 × 10^-19 C and the distance between them can be assumed to be the sum of their radii, which is approximately 2 x 10^-15 m. Using the given value of the Coulomb constant and the values for charge and distance, we can calculate the force of electrostatic repulsion:
F_e = (9 × 10^9 Nm²/C²) * [(3.2 × 10^-19 C)^2 / (2 × 10^-15 m)^2]
= 1.15 × 10^-28 N
The force of gravitational attraction between two alpha particles can be calculated using Newton's law of gravitation:
F_g = G * (m1 * m2) / r^2
where G is the gravitational constant (6.67×10^-11 Nm²/kg²), m1 and m2 are the masses of the particles (in kg), and r is the distance between them (in meters).
For alpha particles, the mass is 6.68 × 10^-27 kg, and the distance between them can be assumed to be the sum of their radii, which is approximately 2 x 10^-15 m. Using the given value of the gravitational constant and the values for mass and distance, we can calculate the force of gravitational attraction:
F_g = (6.67 × 10^-11 Nm²/kg²) * [(6.68 × 10^-27 kg)^2 / (2 × 10^-15 m)^2]
= 2.1 × 10^-77 N
Comparing the two forces, we see that the electrostatic force of repulsion is much stronger than the gravitational force of attraction:
F_e / F_g = (1.15 × 10^-28 N) / (2.1 × 10^-77 N) = 5.5 × 10^48
Therefore, the electrostatic force of repulsion between the two alpha particles is about 5.5 × 10^48 times stronger than the gravitational force of attraction between them.
Read more about Electrostatic Repulsion:
https://brainly.com/question/25307761
1. What represents the building blocks for all living things?
Cells represents the building blocks for all living things.
Cells are called "the building blocks of life" because they are the basic structural and functional elements of human life. Cells are the basic units of all stages of biological organization. This suggests that cells of different species create tissues, organs, and organ systems.
The cornerstone of all living beings is the cell. There are billions of cells in the human body, each serving a specific purpose.
Your DNA contains information that tells our cells how to make proteins. Vital bodily processes including digestion, cell growth and muscle movement are fueled by protein.
To know more about Cell, visit,
https://brainly.com/question/13920046
#SPJ4
In the circuit, the lamp is rated at 4 volts and 0. 5 watts. What size resistor must r1 be in order to supply the correct current to this lamp?
For the 4-volt, 0.5-watt lamp to receive the proper power, R1 should be 48 ohms.
To find the required resistance of R1, we need to use Ohm's law, which states that the current (I) flowing through a circuit is equal to the voltage (V) divided by the resistance (R), i.e., I = V/R.
First, we need to determine the current that the lamp requires. The power (P) of the lamp is given by P = IV, where I is the current flowing through it, and V is its voltage rating. We know that the power of the lamp is 0.5 watts and its voltage rating is 4 volts. Substituting these values, we get:
0.5 = I * 4
Solving for I, we get:
I = 0.5/4 = 0.125 amps
Now, we can use the current value to determine the resistance of R1 using Ohm's law. We know that the voltage drop across R1 is 6 volts (the total voltage of the battery minus the voltage of the lamp). Substituting the values of I and V into the formula, we get:
R1 = V/I = 6/0.125 = 48 ohms
Therefore, R1 should be 48 ohms to supply the correct current to the 4-volt, 0.5-watt lamp.
To learn more about circuit refer to:
brainly.com/question/12608491
#SPJ4
A man of mass 50kg ascends a flight of stairs 5m high in 5 seconds.If acceleration due to gravity is 10m/s the power expended is
Answer:
490 W
Explanation:
F = ma = (50 kg)(9.8 m/s²) = 490 N (Weight = W = mg)
Work = W = Fd = (490 N)(5 m) = 2450 J
Power = W/t = 2450 J / 5 s = 490 J/s = 490 W (watts)
How long would it take a roller skater to travel 25 km if his/her speed is 8 km/hr?
At a pace of 8 km/hr, it would take the roller skater 3.125 hours to complete 25 km.
To determine how long it would take a roller skater to travel 25 km if their speed is 8 km/hr, we can use the formula:
time = distance / speed
In this case, the distance is 25 km and the speed is 8 km/hr. Substituting these values into the formula, we get:
time = 25 km / 8 km/hr
Simplifying, we get:
time = 3.125 hours
Therefore, it would take the roller skater 3.125 hours to travel 25 km at a speed of 8 km/hr. It's important to note that this is assuming a constant speed throughout the journey, and not taking into account any breaks or rest stops the skater may need to take.
To learn more about speed refer to:
brainly.com/question/17661499
#SPJ4
Determining the distance to stars can be challenging. The parallax method is one way of finding the distance to many stars around us. Your research team measures the parallax of two stars that have a distance of 5 degrees from each other in the night sky: The first star has a parallax of 0.11 arcsec, and the second has a parallax of 0.13 arcsec. How far apart are the two stars from each other? Express your answer in light-years
Answer:
The parallax method relies on measuring the apparent shift in position of a star against the background of more distant stars as the Earth orbits the Sun. The angle of this shift is called the parallax angle, and it can be used to calculate the distance to the star.
To determine the distance between the two stars in the problem, we need to use some trigonometry. Since the stars are 5 degrees apart in the night sky, we can use the formula:
distance = (angular separation / 2) x (1 / parallax)
Plugging in the values for the first star, we get:
distance1 = (5 / 2) x (1 / 0.11) = 22.7 light-years
And for the second star:
distance2 = (5 / 2) x (1 / 0.13) = 19.2 light-years
Now, we can use the Pythagorean theorem to find the distance between the two stars:
distance between stars = √(distance1^2 + distance2^2) = √(22.7^2 + 19.2^2) = 29.4 light-years
Therefore, the two stars are about 29.4 light-years apart from each other.
After an unfortunate accident occurred at a local warehouse, you were contracted to determine the cause. A jib crane collapsed and injured a worker. The horizontal steel beam had a mass of 85. 10 kg per meter of length, and the tension in the cable was =12040 N. The crane was rated for a maximum load of 500 kg. If =5. 000 m, =0. 450 m, =2. 000 m, and ℎ=2. 250 m, what was the magnitude of L (the load on the crane) before the collapse? The acceleration due to gravity is =9. 810 m/s2
The magnitude of the load on the crane before the collapse was 7871.48 N, which is well below the maximum load rating of 500 kg.To determine the load on the crane, we need to use the principles of static equilibrium.
The crane is in equilibrium when the sum of the forces acting on it is zero and the sum of the torques is also zero.The forces acting on the crane are tension in the cable and the weight of the horizontal beam. the torque is due to the weight of the horizontal beam.First, calculate the weight of the horizontal beam:
W = mgL = 85.105.0009.810 = 4168.52 N, where m is the mass per meter of length, g is the acceleration due to gravity, and L is the length of the beam.Now calculating the torque due to the weight of the beam :
τ = W*(h/2) = 4168.52*(2.250/2) = 4686.03 Nm, where h is the height of the horizontal beam. since the crane is equilibrium, the tension in the cable must balance the weight of the beam which is T = W. now substituting the values we get :
=>12040 N = 4168.52 N + L=> 12040 N - 4168.52 N = 7871.48 N
To know more about torque refer to the link brainly.com/question/29024338
#SPJ4
Gino is teaching his partner a dance by using eight counts.
He has included quarter-turns at the end of each eight count for a total of 32 counts.
When Gino's dance partner finishes the dance, she has faced a total of three walls.
What does Gino need to tell his partner through constructive feedback?
she performed too many quarter-turns.
She danced for longer than 32 counts.
She used bad technique for the dance.
She forgot an eight count or a quarter-turn.
Answer:
uhhh
Explanation:
Gino should tell his partner that she should have only done four quarter turns and should have finished the dance after 32 counts. This would have resulted in her facing only two walls at the end.
What is quarter?Quarter is a term used to describe the amount of rotation an object has undergone when it does a full turn. A quarter-turn is the equivalent of 90 degrees. Quarter are commonly used to measure the rotation of a wheel, a lever, a bolt, or any other object that can be rotated. It is also used in architecture to describe the amount of rotation of a staircase or other structure. In engineering, quarter-turns are used to measure the amount of torque that is being applied to a mechanism or device. Quarter are also used to measure the amount of rotation when adjusting the settings of a device.
To learn more about quarter
https://brainly.com/question/30628942
#SPJ1
A bullet is fired with a speed of 50 m/s into a block of wood of mass 0. 5kg and becomes embedded in it. If it gives block a speed of 15m/s. Find the mass of the bullet correct to 2sf
The mass of the bullet is approximately 0.21 kg (to 2 significant figures).
We can use the principle of conservation of momentum to solve this problem. The total amount of momentum prior to and following the impact are equal.
Let the mass of the bullet be "m" kg.
The momentum of the bullet before the collision is:
p1 = m × 50 m/s = 50m
The momentum of the bullet and block after the collision is:
p2 = (m + 0.5 kg) × 15 m/s = 15(m + 0.5)
According to the principle of conservation of momentum:
p1 = p2
50m = 15(m + 0.5)
50m = 15m + 7.5
35m = 7.5
m = 7.5/35 = 0.2143 kg (rounded to 2 significant figures)
Therefore, the mass of the bullet is approximately 0.21 kg (to 2 significant figures).
for such more question on mass
https://brainly.com/question/19385703
#SPJ4
A figure skater spins at 2 revolutions per second with her arms outward, a position in which her moment of inertia about her axis of rotation is 0. 4 kg m2. By pulling her arms inward, she is able to increase her rate of spinning to 12 revolutions per second. Calculate her rotational kinetic energy after she has pulled her arms inward
The figure skater increases the speed of her spin to 10 revolutions per second by drawing her arms inside.
The speed of the skater's spin drops by a factor of two as she spreads her arms out in front of her, doubling the moment of inertia. She dramatically reduces her inertia moment while folding her wrists in, resulting in a considerable increase in rotational velocity.
When does a speedskater reach a point of inertia?
During skating, the skater's mass is measured in terms of how far it extends from the axis around the direction that he or herself is spinning. This is known as the inertia moment, or moment of inertia The magnitude of its moment of inertia increases with distance from the axis. The force required to halt a moving item is measured by momentum.
To know more about direction click here
brainly.com/question/30098658
#SPJ4
The kinetic energy of a bullet fired from a gun is 40j. If the mass of the bullet is 0.1kg, calculate the initial speed of the bullet
Answer:
KE = 1/2 M V^2
V = (2 KE / M)^1/2 = (2 * 40 / .1)^1/2 = 28.3 m/s
calculate the minimum power density measurable if the detectable photogenerated current is 10% of the dark current.
The minimum power density measurable is 0.1 times the dark current density divided by the elementary charge and the external quantum efficiency of the detector.
The minimum power density measurable can be calculated using the following formula:
P = Jsc / (q * η)
where P is the power density, Jsc is the short-circuit current density, q is the elementary charge, and η is the external quantum efficiency of the detector.
Assuming that the photogenerated current is 10% of the dark current, the total current density (J) can be expressed as:
J = Jdark + Jph
where Jdark is the dark current density and Jph is the photogenerated current density.
Since Jph is 10% of Jdark, we can express Jph as:
Jph = 0.1 * Jdark
The short-circuit current density (Jsc) can be approximated as Jph because the detector is operated under short-circuit conditions.
Thus, Jsc ≈ Jph = 0.1 * Jdark
Substituting this into the formula for P, we get:
P = Jsc / (q * η) ≈ Jph / (q * η) = 0.1 * Jdark / (q * η)
Therefore, the minimum power density measurable is 0.1 times the dark current density divided by the elementary charge and the external quantum efficiency of the detector.
Know more about power density
https://brainly.com/question/16016898
#SPJ11
Three point charges have equal magnitudes and are located on the same line. The separation d between A and B is the same as the separation between B and C. One of the charges is positive and two are negative, as the drawing shows. Consider the net electrostatic force that each charge experiences due to the other two charges. Rank the net forces in descending order (greatest first) according to magnitude. A. A, B, C b. B, C, A c. A, C, B d. C, A, B e. B, A, C
The proper order of the net forces is A, B, and C in decreasing order of magnitude.
Let's consider the net electrostatic force that each charge experiences due to the other two charges:
Charge A experiences a force towards the right due to the repulsion with Charge B, and towards the left due to the attraction with Charge C. As both charges are of the same magnitude, these two forces cancel each other out, and there is no net force on Charge A.
Charge B experiences an attraction towards the left due to Charge A, and a repulsion towards the right due to Charge C. As both charges are of the same magnitude, these two forces cancel each other out, and there is no net force on Charge B.
Charge C experiences a force towards the left due to the attraction with Charge B, and towards the right due to the repulsion with Charge A. As both charges are of the same magnitude, these two forces cancel each other out, and there is no net force on Charge C.
Therefore, the correct ranking of the net forces in descending order of magnitude is: A, B, C.
To learn more about electrostatic force refer to:
brainly.com/question/9774180
#SPJ4
Explain the forces acting on the skateboard and how the forces affect the motion of the skateboard.
The forces acting on a skateboard include gravity, friction, air resistance, and applied force, and they all affect the motion of the skateboard in different ways.
When a skateboard is in motion, several forces act on it that affect its movement. The main forces acting on a skateboard are:
Gravity: This is a force that pulls the skateboard downwards towards the ground. The weight of the skateboard and the rider are also affected by gravity.
Friction: This is a force that opposes the motion of the skateboard. Friction is caused by the skateboard's wheels rolling on the ground or surface, and it can slow down the skateboard's speed.
Air resistance: This is a force that opposes the motion of the skateboard as it moves through the air. The faster the skateboard moves, the more air resistance it experiences.
Applied force: This is the force applied by the rider to propel the skateboard forward or to perform tricks. The amount of applied force determines how fast or slow the skateboard moves.
The combination of these forces affects the motion of the skateboard. If the applied force is greater than the forces of friction, air resistance, and gravity, the skateboard will accelerate. If the forces of friction, air resistance, and gravity are greater than the applied force, the skateboard will slow down or come to a stop.
Learn more about force here
brainly.com/question/19584436
#SPJ4
Rank the electric potential energy of the charged particles from highest to lowest.
Answer: 1234 is correct
hope that helps
Explanation:
An object is placed in front of a convex mirror at infinity. According to the New Cartesian Sign Convention, the sign of the focal length and the sign of the image distance in this case are respectively:
(a) +, -
(b) -,+
(c) -, -
(d) +,+
Answer:
the correct answer is (c) -, -.
Explanation:
When an object is placed in front of a convex mirror at infinity, the image formed is a virtual image located at the focal point of the mirror.
According to the New Cartesian Sign Convention, the focal length of a convex mirror is negative. Therefore, the sign of the focal length in this case is "-".
Since the image is formed behind the mirror and is a virtual image, its distance from the mirror is negative. Therefore, the sign of the image distance in this case is also "-".
Therefore, the correct answer is (c) -, -.
which graph best represents the relationship between the between the strength of an electric field and distance from a point charge?
The fourth option best represents the proper graph, which resembles a branch of a hyperbola.
What is the Coulomb's law?From Coulomb's Law.
F = k · (q₁ · q₂) / r²
where
Q1 and Q2 are the charges of the two particles, F is the electrostatic force separating them, k is the Coulomb's constant, and r is the separation between them.
The force becomes weaker as the two particles move apart.
Moreover, as r approaches zero, F approaches 1 / 0 =. F is endlessly powerful when there's no separation between the two particles. As a result, the force axis will never be touched by the force about distance graph.
Learn more about Coulomb's law:https://brainly.com/question/506926
#SPJ1
What is the minimum diameter at section (1) to avoid cavitation at that point? take d2 = 12 cm, the maximum water temperature as 30°c, and the density of water as 1000 kg/m3. (round the final answer to three decimal places. )?
The minimum diameter at section (1) to avoid cavitation at that point is 5.057 cm (rounded to three decimal places).
How to determine the minimum diameter at section (1) to avoid cavitation at that point?To determine the minimum diameter at section (1) to avoid cavitation at that point, we can use the following formula:
d1 = √((4q)/((πv)),
where
q = the flow rate (m³/s)v = the velocity of water (m/s)
To avoid cavitation, the velocity of water at section (1) should not exceed the critical velocity, which can be calculated using the following formula:
vc = √((p2-pv)/(0.5*density)),
where
p2 = the pressure at section (2) (Pa)
pv = the vapor pressure of water at the maximum temperature (Pa)
density = the density of water (kg/m³)
Assuming that the pressure at section (2) is atmospheric (101325 Pa), the vapor pressure of water at 30°C is 4243.7 Pa.
Thus,
vc = √((101325-4243.7)/(0.5*1000)) = 14.697 m/s
To determine the flow rate, we can use the continuity equation:
q = ((π/4)d2²v
where d2 is given as 12 cm, or 0.12 m. If we assume that the flow is steady and incompressible, the flow rate is constant throughout the pipe.
Thus,
q = ((π/4)(0.12)²v
Combining these equations, we get:
d1 = √((4*((π/4)(0.12)²v)/((πvc))
d1 = √((0.0144v)/14.697)
d1 = 0.003762 × [tex]v^{0.5[/tex]
To avoid cavitation, d1 must be greater than or equal to the minimum diameter required at section (1). Therefore, we can set d1 equal to the critical diameter, which is given by:
dc = √((4q)/((πvc))
Substituting the values for q and vc, we get:
dc = √((π/4)(0.12)² 14.697)
dc = 0.05057 m
Therefore, the minimum diameter at section (1) to avoid cavitation at that point is 5.057 cm (rounded to three decimal places).
To learn more about cavitation, visit:
https://brainly.com/question/29672894
#SPJ1
A transverse wave is observed to be moving along a lengthy rope. Adjacent crests are positioned 2. 4 m apart. Exactly six crests are observed to move past a given point along the medium in 9. 1 seconds. Determine the wavelength, frequency and speed of these waves
The wavelength of the wave is 2.4 m, the frequency of the wave is 0.6593 Hz, and the speed of the wave is 0.2637 m/s.
A transverse wave is observed to be moving along a lengthy rope
Distance between adjacent crests (wavelength) = λ = 2.4 m
Number of crests passing a point = 6
Time taken for these crests to pass = t = 9.1 s
We can use the formula:
Speed = Distance / Time
Speed of the wave (v) = λ / t
Frequency of the wave (f) = Number of crests / Time taken
So, substituting the given values, we get:
Speed of the wave (v) = λ / t
v = 2.4 m / 9.1 s
v = 0.2637 m/s
Frequency of the wave (f) = Number of crests / Time taken
f = 6 / 9.1 s
f = 0.6593 Hz
Learn more about transverse wave here
brainly.com/question/15819487
#SPJ4
An 8kg ball traveling at4m/s collides head on with a 3kg ball traveling at 14m/s. The balls bounce off each other and travel back the way they come. The 8kg ball travels away at 2m/s. Calculate the kinetic energy before and after collision
The kinetic energy before the collision is 358 J and the kinetic energy after the collision is 232 J.
KE_before = (1/2) * m1 * v1^2 + (1/2) * m2 * v2^2
KE_before = (1/2) * 8 * 4^2 + (1/2) * 3 * 14^2
= 64 + 294
= 358 J
m1 * v1 + m2 * v2 = m1 * v1' + m2 * v2'
Substituting the given values, we get:
8 * 4 + 3 * 14 = 8 * 2 + 3 * v2'
Solving for v2', we get:
v2' = (8 * 4 + 3 * 14 - 3 * v1') / 3
The negative sign indicates that the 3kg ball is moving in the opposite direction after the collision. We also know that the 8kg ball is moving away at 2m/s. Therefore,
v1' = 2 m/s
Substituting this value, we get:
v2' = (8 * 4 + 3 * 14 - 3 * 2) / 3
= 12 m/s
The kinetic energy after the collision is:
KE_after = (1/2) * m1 * v1'^2 + (1/2) * m2 * v2'^2
Substituting the given values, we get:
KE_after = (1/2) * 8 * 2^2 + (1/2) * 3 * 12^2
= 16 + 216
= 232 J
Kinetic energy is the energy an object possesses due to its motion. In physics, it is defined as the energy that an object possesses due to its motion, and it is dependent on the mass and velocity of the object. The formula for kinetic energy is KE = 1/2mv², where KE is the kinetic energy, m is the mass of the object, and v is the velocity of the object.
Kinetic energy is a scalar quantity, meaning that it has only magnitude and no direction. It is a fundamental concept in physics, and it is used to describe many phenomena, including the motion of particles, the motion of objects, and the conversion of energy between different forms. The kinetic energy of an object can be transformed into other forms of energy, such as potential energy or thermal energy, through various processes.
To learn more about Kinetic energy visit here:
brainly.com/question/26472013
#SPJ4
A concave mirror has a focal length of 5.0 cm. A candle is located at a distance of 8.0 cm from the mirror. Calculate the image distance.
Answer:
13 cm
Explanation:
13 cm is the image distance
Find the period ,acceleration and velocity of a body in SHM, whose amplitude is 10cm and frequency 100Hz
i. the period of oscillation: Speed, V=ωr2−y2. ii. the acceleration at the maximum displacement: V=10π×(0.05)2−(0.03)2=10π×0.04=0.4π m/s.
iii. the velocity at the center of motion: V=10π×(0.05)2−02
given = 5 cm = 0.05 m
T = 0.2 s
ω=2π/T=2π/0.2=10πrad/s
At the point when relocation is y, then acceleration, a=−ω2y
Speed, V=ωr2−y2
Case (a) When y=5cm=0.05m
a=−(10π)2×0.05=−5π2m/s2
V=10π×(0.05)2−(0.05)2=0
Case (b) When y=3cm=0.03m
a=−(10π)2×0.03=−3π2m/s2
V=10π×(0.05)2−(0.03)2=10π×0.04=0.4π m/s
Case (c) When y=0
a=−(10π)2×0=0
V=10π×(0.05)2−02
T = 2π√(m/k). By timing the length of one complete oscillation we can decide the period and thus the frequency. Note that on account of the pendulum, the period is free of the mass, while on account of the mass of spring, the period is free of the length of the spring.
to know more about oscillation click here:
https://brainly.com/question/12622728
#SPJ4
the complete question is:
A body moving in simple harmonic motion has an amplitude of 10cm and a frequency of 100 Hz. Find i. the period of oscillation, ii. the acceleration at the maximum displacement, iii. the velocity at the center of motion.
Two point masses are the same distance R from an axis of rotation and have moments of inertia IA and IB. (a) If IB 5 4IA, what is the ratio mB/mA of the two masses? (b) At what distance from the axis of rotation should mass A be placed so that IB 5 IA?
The two masses have a ratio of mB/mA = IB/IA = 4. Mass A must be put at a distance of x = [mB R (2 + sqrt(3))] / 2 for IB to equal IA (mA - mB) are As a result, mass A must be positioned at a distance of x = [mB R (2 + (3))] / [mB R] for IB to equal IA (mA - mB).
What is the equation for the inertial moment of two point masses?The sum of each particle's product of mass and the square of its distance from the axis of rotation is what determines the moment of inertia. The moment of inertia formula is given as I = miri2.
The formula for the total moment of inertia about the axis of rotation is
I = IA + IB
If IB = 4IA, then:
I = IA + 4IA = 5IA
So, the ratio of the two masses is:
mB/ mA = IB/IA = 4
(b)Let x represent the separation between mass A and the rotational axis. Thus, mass A's moment of inertia is:
IA = mA x²
And with respect to the axis of rotation, the moment of inertia of mass B is:
IB = mB (R - x)²
If IB = IA, then:
mA x² = mB (R - x)²
Expanding the right-hand side and simplifying, we get:
mB x² - 2mB Rx + mB R² = mA x²
(mA - mB) x² + 2mB Rx - mB R² = 0
The solutions of this equation are:
x = [ -2mB R ± √((2mB R)² - 4(mA - mB)(-mB R²))] / 2(mA - mB)
Simplifying, we get:
x = [mB R (2 ± √(3))] / (mA - mB)
Since x must be positive, we take the solution with the plus sign:
x = [mB R (2 + √(3))] / (mA - mB)
To know more about inertia visit:-
https://brainly.com/question/3268780
#SPJ1
if an object is orbiting the sun with an orbital period of 15 years, what is its average distance from the sun?
Its average separation from of the Sun is 6.1 AU, or (225/3)AU.
What relationship does the orbital period have to the solar distance?When the period (P) is written in years and the orbital radius (a) is represented in light years away (1 AU is the arithmetic mean between the Sun and the planet Earth), Kepler's Third Law states that P2 = a3. where P is measured in Earth years, an is measured in astronomical units, and M is the centre object's mass expressed in Sun-mass units.
How far does an orbit typically travel?As seen from it above Middle Latitudes, the Earth circles the Sun at an arithmetic mean of 149.60 million kilometres (92.96 million miles), anticlockwise. One axial tilt year, or 365.249 days, is needed to complete one orbit, during which duration Earth has travelled 940 million kilometres (584 million mi).
To know more about separation visit:
https://brainly.com/question/17177213
#SPJ1
Determine the voltage dropped across
The voltage dropped across R₃ is 52.68 volts.
How to calculate voltage?To determine the voltage dropped across R₃, we can use the voltage divider formula:
V₃ = ( R₃ / ( R₁ + R₂ + R₃ + R₄ ) ) x ET
Substituting the given values, it can be calculated as:
V₃ = (36 Ω / ( 15 Ω + 18 Ω + 36 Ω + 13 Ω ) ) x 120 V
V₃ = ( 36 Ω / 82 Ω ) x 120 V
V₃ = 52.68 V
Therefore, the voltage dropped across R₃ is approximately 52.68 volts.
Find out more on voltage here: https://brainly.com/question/27861305
#SPJ1
you have a camera with a 35.0-mm-focal-length lens and 36.0-mm-wide film. you wish to take a picture of a 12.0-m-long sailboat but find that the image of the boat fills only of the width of the film. (a) how far are you from the boat? (b) how much closer must the boat be to you for its image to fill the width of the film?
The distance between the boat and the camera is 0.0525 m. The boat must move closer by a distance of 35 mm to fill the width of the film.
you have a camera with a 35.0-mm-focal-length lens and 36.0-mm-wide film. you wish to take a picture of a 12.0-m-long sailboat but find that the image of the boat fills only the width of the film.
(a) Given data:
The focal length of the lens, f = 35.0 mm
Width of the film, w = 36.0 mm
Length of the sailboat, L = 12.0 m
Length of the image of the sailboat on film = Width of the film
Let the distance between the boat and the camera be x.
The object distance, u = ?
Image distance, v = f
Let M be the magnification of the image, then we have:
M = v/u
Width of the image, W' = w
Since the image of the boat fills only half of the width of the film,
W' = w/2.
Now, using the relation,
1/f = 1/u + 1/v
Putting f = 35mm, v = 35mm, and solving for u, we get
u = 52.5 mm = 0.0525 m
Therefore, the distance between the boat and the camera is 0.0525 m.
(b)Width of the image, W = w = 36 mm
Width of the sailboat, L = 12 m
Let the new distance between the boat and the camera be y.
The new image distance, v' = f
The new object distance, u' =?We know that the magnification of the image is given by M = v'/u'.
And the width of the image of the boat is given by:
W = (M)(L)
Using the relation,
1/f = 1/u' + 1/v', we can find the object distance, u'.
Substituting the given values, we get
u' = 0.0175 m = 17.5 mm
Therefore, the boat must move closer by a distance of (52.5 - 17.5) mm = 35 mm to fill the width of the film.
To know more about Distance:https://brainly.com/question/26550516
#SPJ11
Compute the THR of the following
A THR (Total Home Run) is a statistic that measures the total number of home runs a baseball player has hit during a season or career. It is calculated by adding up all of the home runs a player has hit in a season.
What is statistic ?Statistic is a branch of mathematics which deals with the collection, analysis and interpretation of numerical data. It is used to help make inferences and decisions about a population by studying a sample of that population. It is a way to summarize the information and draw conclusions about the population based on the sample data. Statisticians use various techniques such as data mining, hypothesis testing and regression analysis to draw meaningful conclusions from the data.
To learn more about statistic
https://brainly.com/question/7992443
#SPJ9