Answer:
If people did not have the rights established in Miranda v. Arizona, they could be subjected to police coercion and forced confessions without a lawyer present. This could lead to wrongful convictions and denial of due process, which are essential components of the American justice system
A box slides on a level floor. It is slowing with a constant
acceleration of magnitude 2.0 m/s2
. What is the coefficient of
kinetic friction between the box and the floor?
Answer:
Explanation:
We can use the following equations of motion to solve the problem:
v^2 = u^2 + 2as
where v is the final velocity, u is the initial velocity, a is the acceleration, s is the distance travelled.
In this case, the box is slowing down, so the initial velocity u is greater than the final velocity v. We can use a negative sign to indicate that the acceleration is opposite to the initial velocity.
Let us assume that the mass of the box is m and the coefficient of kinetic friction is μ. The force of friction acting on the box is given by f = μmg, where g is the acceleration due to gravity.
Since the acceleration of the box is 2.0 m/s^2, we have
f = ma
μmg = m(-2.0)
μg = -2.0
μ = -2.0/g
Substituting g = 9.8 m/s^2, we get
μ = -0.204
Since the coefficient of friction cannot be negative, we take the absolute value and obtain:
μ = 0.204
Therefore, the coefficient of kinetic friction between the box and the floor is approximately 0.204.
You leave Fort worth ,Texas,at 2:41 p.m. and arrive in Dallas at 3:23 p.m. , covering a distance of 58km. what is your average speed in metres per second ?
Answer:
Explanation:
The time taken to travel from Fort Worth to Dallas is:
t = 3:23 pm - 2:41 pm = 42 minutes = 0.7 hours
The distance covered is:
d = 58 km
The average speed is:
v = d/t = 58 km / 0.7 hours = 82.86 km/h
To convert km/h to m/s, we can use the conversion factor:
1 km/h = 0.2778 m/s
Therefore, the average speed in m/s is:
v = 82.86 km/h × 0.2778 m/s/km = 23.06 m/s (rounded to two decimal places)
So the average speed is 23.06 m/s.
Dish Network sent a satellite into orbit around 36000 km above the Earth's surface. What is the speed of the Satellite in miles per hour?
G=6.67 x 10^-11
M Earth = 5.98 x 10^24 kg
R Earth = 6.37 x 10^6 m
A. 306889 mi/hr
B. 6,864.38 mi/hr
C. 6.86491 mi/hr
D. 9.8mi/hr
Answer:
Explanation:
First, we need to use the formula for the speed of an object in circular orbit:
v = sqrt(GM/R)
where G is the gravitational constant, M is the mass of the Earth, R is the distance between the center of the Earth and the satellite.
Converting the units to meters and kilograms:
G = 6.67 × 10^-11 m^3/kg s^2
M = 5.98 × 10^24 kg
R = (36000 + 6.37 × 10^6) × 1000 = 4.23 × 10^7 m
Plugging in the values:
v = sqrt((6.67 × 10^-11) × (5.98 × 10^24) / (4.23 × 10^7))
v ≈ 3075.58 m/s
Finally, we can convert this to miles per hour:
v = 3075.58 m/s x (3600 s/hr) / (1609.34 m/mi) = 6873.18 mi/hr
Therefore, the answer is option A. 306889 mi/hr is incorrect.
A 65 kg-mass person stands at the end of a diving board, 1.5 m from the board's pivot point. Determine the torque the person is exerting on the board with respect to the pivot point. Show your work.
Answer:
Explanation:
The torque is given by the formula:
τ = F × r × sin(θ)
where τ is the torque, F is the force applied, r is the distance between the force and the pivot point, and θ is the angle between the force and the lever arm.
In this case, the person's weight is the force being applied, and it can be calculated as:
F = m × g
where m is the mass of the person and g is the acceleration due to gravity (9.81 m/s^2).
F = 65 kg × 9.81 m/s^2 = 637.65 N
The distance between the person and the pivot point is 1.5 m, so r = 1.5 m.
The angle between the person's weight and the lever arm is 90 degrees, so sin(θ) = 1.
Therefore, the torque the person is exerting on the board is:
τ = F × r × sin(θ) = 637.65 N × 1.5 m × 1 = 956.475 N·m
So the person is exerting a torque of 956.475 N·m on the diving board with respect to the pivot point.
A uniformly charged insulating sphere with radius r and charge +Q
lies at the center of a thin-walled hollow cylinder with radius R>r
and length L>2r. The cylinder is non-conducting and carries no net charge.
1:Determine the outward electric flux through the rounded "side" of the cylinder, excluding the circular end caps. (Hint: Choose a cylindrical coordinate system with the axis of the cylinder as its z -axis and the center of the charged sphere as its origin. Note that an area element on the cylinder has magnitude dA=2πRdz
2:Determine the electric flux upward through the circular cap at the top of the cylinder.
3:Determine the electric flux downward through the circular cap at the bottom of the cylinder.
4:Add the results from parts A - C to determine the outward electric flux through the closed cylinder.
5:What result is expected according to Gauss's law?
Note:Express your answers in terms of electric constant ϵ0
and some or all of the variables r, R , L , Q .
According to Gauss' equation, the total flux of an electric field in a confined surface is directly proportional to the charge enclosed.
State Gauss’s law.1)To determine the outward electric flux through the rounded "side" of the cylinder, we can use Gauss's law. We choose a cylindrical Gaussian surface with radius r and length L, centered at the origin (where the charged sphere is located). The electric field due to the sphere is spherically symmetric, so the electric field lines are parallel to the cylinder's axis and perpendicular to its sides.
E = (1/4πϵ0) (Q/r^2)
where r is the distance from the origin (center of the sphere) to the point on the Gaussian surface.
The area element of the Gaussian surface is dA = 2πRdz, where dz is an element of length along the cylinder's axis. The electric flux through the top and bottom surfaces of the Gaussian surface is then given by:
Φ = ∫E⋅dA = E ∫dA = E(2πR)L
Substituting the expression for the electric field, we have:
Φ = (Q/2ϵ0r^2)(2πRL)
Therefore, the outward electric flux through the rounded "side" of the cylinder is:
Φ = (Q/ϵ0)(R/Lr^2)
2)To determine the electric flux upward through the circular cap at the top of the cylinder, we use a flat Gaussian surface with radius R and height r, centered at the top of the cylinder. The electric field due to the charged sphere is perpendicular to the Gaussian surface, so the electric flux through the top cap is simply the flux through the flat Gaussian surface. The electric field at any point on the Gaussian surface is given by Coulomb's law as:
E = (1/4πϵ0) (Q/R^2)
The area element of the Gaussian surface is dA = πR^2, so the electric flux through the top cap is given by:
Φ = ∫E⋅dA = E ∫dA = EπR^2
Substituting the expression for the electric field, we have:
Φ = (Q/ϵ0)(R/r^2)
3)To determine the electric flux downward through the circular cap at the bottom of the cylinder, we use a similar flat Gaussian surface with radius R and height r, centered at the bottom of the cylinder. The electric flux through the bottom cap is also given by:
Φ = (Q/ϵ0)(R/r^2)
4)Adding the results from parts 1-3, we have the total outward electric flux through the closed cylinder as:
Φ_total = Φ_side + Φ_top + Φ_bottom
= (Q/ϵ0)(R/Lr^2) + 2(Q/ϵ0)(R/r^2)
Simplifying this expression, we have:
Φ_total = (Q/ϵ0) [(2R/r^2) + (R/Lr^2)]
5)According to Gauss's law, the total outward electric flux through a closed surface is proportional to the total charge enclosed within that surface. In this case, the closed surface is the cylindrical Gaussian surface with radius r and length L, centered at the origin (where the charged sphere is located). The charge enclosed within this surface is simply the charge of the sphere, which is +Q. Therefore, we expect the total outward electric flux through the closed cylinder to be:
Φ_total = Q/
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How could you use the game of baseball to explain the difference between
inertia and momentum?
Explanation:
Inertia refers to the tendency of an object to resist changes in its motion. In baseball terms, a baseball that is at rest on the ground has a high level of inertia because it is resistant to moving until an external force, such as a player's bat, acts on it.
Momentum, on the other hand, is the product of an object's mass and velocity and refers to the quantity of motion that an object possesses. In baseball terms, a baseball that is moving at a high velocity, such as when it is hit by a bat, has a high level of momentum.
To illustrate the difference between inertia and momentum in baseball, consider the scenario of a baseball that is hit by a bat. Before the bat hits the ball, the ball is at rest and has a high level of inertia. However, once the bat hits the ball, the ball gains momentum and begins to move. As the ball moves, it continues to possess momentum, but its inertia gradually decreases as it encounters external forces, such as air resistance and friction from the ground, which act to slow it down.
At 5220J, a temperature increase occurs from 10 degrees Celsius to 60 degrees Celsius. What is the mass of the water?
The mass of water that undergoes a change in temperature from 10 degrees celsius to 60 degrees celsius is 24.9 g.
What is mass?Mass is the quantity of matter a body contained.
To calculate the mass of the water, we use the formula below
Formula:
m = Q/cΔt................... Equation 1Where:
m = Mass of waterQ = Amount of heatc = Specific heat capacity of waterΔt = Change in temperatureFrom the question,
Given:
Q = 5220 Jc = 4200 J/kg.KΔt = 60-10 = 50 degree celsiusSubstitute these values into equation 1
Q = 5220/(4200×50)Q = 0.0249 kgQ = 24.9 gHence, the mass of water is 24.9 g.
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Mary walked north from her home to Sheila's home, which is 4.0 kilometers away. Then she turned right and walked another 3.0 kilometers to the supermarket, which is 5.0 kilometers from her own home. She walked the total distance in 1.5 hours. What were her average speed and average velocity?
A.
Her average speed was about 4.6 km/hr, and her average velocity was about 3.3 km/hr.
B.
Her average speed was about 3.3 km/hr, and her average velocity was about 4.6 km/hr.
C.
Her average speed was about 3.3 km/hr, and her average velocity was 0 km/hr.
D.
Her average speed was 0 km/hr, and her average velocity was about 4.6 km/hr.
Her average speed was about 4.6 km/hr, and her average velocity was about 3.3 km/hr.
The entire distance travelled divided by the total time taken is the definition of average speed. In this case, the total distance travelled was 7.0 km, and the total time taken was 1.5 hours. Hence, the average speed can be determined as follows:
Average Speed = [tex]\frac{7.0 km }{ 1.5 \ hours }= 4.6 km/hr[/tex]
The displacement divided by the whole time travelled is the average velocity. In this case, the displacement was 3.0 km (from Mary's home to Sheila's home), and the total time taken was 1.5 hours.The average velocity can therefore be determined as follows:
Average Velocity = [tex]\frac{3.0 km }{1.5 \ hours} = 3.3 km/hr[/tex]
Therefore,Her average velocity was roughly 3.3 km/hr, and her average speed was roughly 4.6 km/hr.
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Why would theoretical muzzle velocity be lower than measured muzzle velocity?
Answer:
Explanation:
Theoretical muzzle velocity is calculated based on various physical models and assumptions, such as the conservation of energy and momentum, the properties of the propellant and barrel, and other factors that can affect the velocity of the projectile as it exits the muzzle of the firearm. However, in practice, there can be many factors that can influence the actual velocity of the projectile, which can result in a measured muzzle velocity that is higher than the theoretical value. Some possible reasons for this discrepancy include:
Variation in propellant burn rate: Theoretical models assume a constant burn rate for the propellant, but in practice, there can be variations in the rate at which the propellant burns due to differences in temperature, humidity, and other factors. This can affect the velocity of the projectile as it exits the muzzle.
Barrel condition: Theoretical models assume a perfectly smooth, straight barrel, but in practice, barrels can have imperfections such as rough spots or bends that can affect the velocity of the projectile as it travels through the barrel.
Environmental factors: Theoretical models assume ideal conditions, but in practice, there can be factors such as wind, temperature, and humidity that can affect the velocity of the projectile as it travels through the air.
Measurement errors: Measuring the muzzle velocity of a projectile can be challenging, and errors in measurement can result in a measured velocity that is higher than the actual value.
Human error: Human factors such as shooter error, inconsistency in handling and loading the firearm, and other factors can also contribute to discrepancies between theoretical and measured muzzle velocities.
Overall, while theoretical muzzle velocity can provide a useful estimate of the velocity of a projectile exiting a firearm, there are many factors that can influence the actual velocity in practice, leading to measured velocities that are higher than the theoretical value.
an object is launched at a velocity of 40m/s in a direction making an angle of 50°upward with the horizontal
a)what is the maximum height reached by the object
b) what is the object total flight time between launch and touching the ground
c) what's the object horizontal range(maximum ×above ground)
When heal flows between systems Entropy
Answer: increases
Explanation:
13 Which of these fitness events happened LAST? OA. PE becomes part of American school curriculum. OB. Title IX forbids gender discrimination in sports. O C. The YMCA opens a gym in America. O D. The adjustable plate-loaded barbell is invented.
The answer is A. PE becomes part of American school curriculum.
Title IX, which forbids gender discrimination in sports, was enacted in 1972.
The YMCA opened its first gym in America in Boston in 1851.
The adjustable plate-loaded barbell was invented in the late 1940s by a man named George Snyder.
Physical Education (PE) has been a part of American school curriculums for well over a century, with the first school gymnasiums being built in the 1800s.
What is an american school curriculum?
The American school curriculum is the set of educational standards and guidelines used by schools in the United States to structure their academic programs. The curriculum typically includes courses in core academic subjects such as English, math, science, and social studies, as well as elective courses in areas such as the arts, foreign languages, and physical education.
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A 1.20 kg copper rod resting on two horizontal rails 0.90 m apart carries a
current I = 55.0 A from one rail to the other. The coefficient of static friction
between the rod and rails is μs= 0.60.
(a) What is the smallest vertical magnetic field B that would cause the rod to
slide?
(b) Suppose a B field is directed at some angle to the vertical φ, with the current
along the rod directed into the page, as shown. Find an expression for B as a
function of φ for the case when the rod is just on the verge of beginning to slide.
(c) Find the value of φ which yields the smallest value of B that would cause
the rod to slide, together with the corresponding value of B.
(a) The smallest vertical magnetic field B that would cause the rod to
slide is 0.145 Tesla for given The coefficient of static friction
between the rod and rails is μs= 0.60
What is magnetic field ?A magnetic field is a vector field that describes the magnetic influence on moving charges, currents, and magnetic materials. A moving charge in a magnetic field is subjected to a force that is perpendicular to both its own velocity and the magnetic field.
(a) using formula
μs × m × g = I × L × B
μs= 0.60
M= 1.2 kg
I = current = 55.0 A
L = Length = 0.9 m
magnetic field (B) = 0.145 Tesla
(b) expression
force (f) = I × L × B × sinФ
(c) given B = 0.145 Tesla
μs × m × g= I × L × B × sinФ
Ф = 90°
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what component of fitness does tennis not fall under?
Answer:
Play tennis, nothing can train you better for the sport than the sport itself. However, tennis is one of those unique sports that combine nearly all components of fitness including power, agility, speed, flexibility, reaction time, balance, coordination, cardiovascular endurance and muscular endurance.
Explanation:
Explain how a balloon is able to keep its shape?
Answer:
It depends on how they are made.
Explanation:
Rubber balloons are not always spherical in shape. When filled with air, the inflation forms a balance between the balloon material, including its shape and thickness and its elasticity and the pressure of the air. That’s what determines its shape. Although a sphere is often the shape, it could be tubular, offset, and most other shapes.
a mass of 20kg is held stationary by a rope passing over a frictionless pally. what is the tension T in the rope?
The tension in the rope is 196.2 N. The rope is exerting a force of 196.2 N on the object to keep it stationary.
Assuming that the mass is not accelerating, the tension in the rope must be equal to the weight of the mass. The weight of the mass can be found using the formula:
weight = mass x acceleration due to gravity
where acceleration due to gravity is approximately 9.81 m/s².
Therefore, the weight of the mass is:
weight = 20 kg x 9.81 m/s² = 196.2 N
Since the mass is held stationary, the tension in the rope must be equal to the weight of the mass, which is 196.2 N. So the tension T in the rope is 196.2 N.
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QUESTION 7
Which of the following statements best summarizes the energy conversion taking place in the every day item shown below? (a flashlight)
a. Chemical energy from the battery is converted to electrical energy in the flashlight.
b. Nuclear energy from the battery is converted to thermal energy that heats up the light.
c. Thermal energy from the battery is converted to electrical energy in the flashlight.
d. Electrical energy from the battery is converted to potential energy.
Answer:
a. Chemical energy from the battery is converted to electrical energy in the flashlight.
A rocket takes off from a space station, where there is no gravity other than the negligible gravity due to the space station, and reaches a speed of 110 m/s in 10.0 s. If the exhaust speed is 1,600 m/s and the mass of fuel burned is 118 kg, what was the initial mass (in kg) of the rocket?
The initial mass of the rocket was 106 kg.
What is the initial mass of the rocket?We can use the principle of conservation of momentum to solve this problem.
The momentum of the rocket before takeoff is zero, since it is at rest, and the momentum after takeoff is the product of the mass of the rocket and its velocity.
However, during the takeoff, the rocket ejects a mass of fuel at a certain velocity, which creates a backward force (thrust) that propels the rocket forward.
This thrust can be calculated using the equation:
Thrust = (mass flow rate) x (exhaust velocity)
mass flow rate = (mass of fuel burned) / (burn time)
The mass of the rocket at any given time can be calculated using the equation:
mass = (initial mass) - (mass of fuel burned)
Using these equations, we can solve for the initial mass of the rocket:
Calculate the thrust:
Thrust = (118 kg / 10.0 s) x 1600 m/s = 1,888 N
Calculate the mass of the rocket at the end of the burn:
mass(end) = (initial mass) - (mass of fuel burned) = (initial mass) - 118 kg
Use the principle of conservation of momentum to find the initial mass:
momentum before = momentum after
0 = (mass(end) + 118 kg) x 110 m/s
mass(end) = -118 kg / 110 m/s = -1.07 kg/s
mass(end) = (initial mass) - 118 kg
(initial mass) = mass(end) + 118 kg
(initial mass) = (-1.07 kg/s x 10.0 s) + 118 kg
(initial mass) = 106 kg
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a metal block of density 900kg weight 60newton in air find it's weight when it is immersed in paraffin wax of density 800kg
Answer:
We can use the concept of buoyancy to solve this problem.
The weight of the metal block in air is equal to the force of gravity acting on it, which is given as 60 Newtons. When the block is immersed in paraffin wax, it displaces a certain volume of wax equal to its own volume, and experiences an upward force due to buoyancy that partially cancels out the force of gravity acting on it.
The buoyant force acting on the block is given by the formula:
buoyant force = weight of fluid displaced
= density of fluid x volume of fluid displaced x acceleration due to gravity
The weight of the metal block in the paraffin wax is then equal to the difference between the weight of the block in air and the buoyant force acting on it.
Let's calculate the volume of the metal block first:
density of metal block = 900 kg/m³
weight of metal block in air = 60 N
acceleration due to gravity = 9.81 m/s²
weight of metal block = density of metal block x volume of metal block x acceleration due to gravity
volume of metal block = weight of metal block / (density of metal block x acceleration due to gravity)
= 60 N / (900 kg/m³ x 9.81 m/s²)
= 0.006536 m³
Now, let's calculate the weight of the metal block in the paraffin wax:
density of paraffin wax = 800 kg/m³
buoyant force = density of fluid x volume of fluid displaced x acceleration due to gravity
= 800 kg/m³ x 0.006536 m³ x 9.81 m/s²
= 51.02 N
weight of metal block in paraffin wax = weight of metal block in air - buoyant force
= 60 N - 51.02 N
= 8.98 N
Therefore, the weight of the metal block when it is immersed in paraffin wax of density 800 kg/m³ is 8.98 Newtons.
explain using diagram how to burn a paper using concave mirror
Explanation:
B.C.ghmll h ffghklhgfjla Toyota Celica, travelling initially at 26.9 m/s [S], comes to a stop in 2.61 s. The mass of the car with the driver is 1.18 × 103 kg. Calculate the car’s acceleration.
The initial velocity of the car is 26.9 m/s [S], and the final velocity is 0 m/s [S]. The time taken for the car to come to a stop is 2.61 s. Using the formula:
acceleration = (final velocity - initial velocity) / time
we can find the car's acceleration:
acceleration = (0 m/s - 26.9 m/s) / 2.61 s
acceleration = -10.305 m/s^2
The negative sign indicates that the car is decelerating, or slowing down.
To calculate the force acting on the car during the deceleration, we can use Newton's second law:
force = mass x acceleration
force = (1.18 × 10^3 kg) x (-10.305 m/s^2)
force = -12,166.1 N
The force acting on the car during deceleration is -12,166.1 N, or approximately 12.2 kN.
A block of mass m1=3.0kg rests on a frictionless horizontal surface. A second block of m2=2.0kg hangs from an ideal cord of negligible mass that runs over an ideal pulley and then is connected to the first block . the blocks are released from rest . determine the displacement of the velocityA block of mass m1=3.0kg rests on a frictionless horizontal surface. A second block of m2=2.0kg hangs from an ideal cord of negligible mass that runs over an ideal pulley and then is connected to the first block . the blocks are released from rest . Determine how far has block 1 moved during the 1.2-s interval?
A) 13.4 m
B) 2.1 m
C) 28.2m
D) 7.6m
The answer is:
D. 7.6m
In the arrangement described in Sample Problem B, how much would the water’s internal energy increase if the mass fell 6.69 m?
If a mass fell into water, the water's internal energy would increase due to the conversion of the kinetic energy of the falling mass into thermal energy.
How to explain the informationWhen the mass hits the water, it will experience a force from the water, and this force will cause the mass to decelerate and eventually come to a stop. During this process, the kinetic energy of the mass is converted into thermal energy of the water, which increases the water's internal energy.
The amount by which the water's internal energy increases will depend on several factors, including the mass of the falling object, its velocity, and the properties of the water, such as its specific heat capacity and temperature. Additionally, the temperature of the water may rise due to the energy transfer from the falling object, which would further increase its internal energy.
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How much heat is necessary to change 10 g of ice at -20°C into water at 10°C?
Answer:
Explanation:
The process can be broken down into two steps:
Heat required to raise the temperature of ice from -20°C to 0°C.
Heat required to melt ice at 0°C and raise the temperature of water from 0°C to 10°C.
Step 1:
The heat required to raise the temperature of ice can be calculated using the specific heat capacity of ice, which is 2.09 J/g°C.
Heat required = mass × specific heat capacity × change in temperature
Heat required = 10 g × 2.09 J/g°C × (0°C - (-20°C))
Heat required = 418 J
Step 2:
The heat required to melt ice and raise the temperature of water can be calculated using the heat of fusion of ice and the specific heat capacity of water.
Heat required to melt ice = mass × heat of fusion of ice
Heat required to melt ice = 10 g × 334 J/g
Heat required to melt ice = 3340 J
Heat required to raise the temperature of water can be calculated using the specific heat capacity of water, which is 4.18 J/g°C.
Heat required = mass × specific heat capacity × change in temperature
Heat required = 10 g × 4.18 J/g°C × (10°C - 0°C)
Heat required = 418 J
Total heat required = Heat required in Step 1 + Heat required to melt ice + Heat required in Step 2
Total heat required = 418 J + 3340 J + 418 J
Total heat required = 4176 J
Therefore, 4176 J of heat is required to change 10 g of ice at -20°C into water at 10°C.
A similar device includes a transformer so that an MP3 player can also be charged. The primary coil has 300 turns.
(a) How many turns are needed in the secondary winding if the voltage is stepped up from 6.2 V to 15.5 V?
(b) Given that the current in the primary winding is 10 mA, what power is transmitted to the secondary windings if the transformer is 77% efficient?
The secondary coil needs 120 turns.The power transmitted to the secondary winding is 0.155 W.
How does the voltage change between the primary and secondary coil in a transformer?A transformer works by using electromagnetic induction to transfer electrical energy between two circuits. The voltage changes between the primary and secondary coil based on the ratio of the number of turns in each coil. In a step-up transformer, the voltage is increased from the primary to the secondary coil, while in a step-down transformer, the voltage is decreased.
Transformers are commonly used in electronic devices to convert voltage levels, isolate circuits, and match impedances. They are often used in power supplies to step down the voltage from the wall outlet to a level that can be used by the device. They are also used in audio amplifiers to match the impedance of the output to the speaker, and in radio and television receivers to tune in to different frequencies.
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1. A 8.2 kg mass hanging from a spring scale is slowly lowered onto a vertical spring.
A) What does the spring scale read just before the mass touches the lower spring?
B) The scale reads 14 N when the lower spring has been compressed by 2.4 cm . What is the value of the spring constant for the lower spring?
C) At what compression length will the scale read zero?
The spring scale read just before the mass touches the lower spring is 80.36N, the spring constant for the lower spring is 2765N/m and at 2.9cm length the scale will read zero.
Given the mass of spring = 8.2kg
The force exerted for compressing of spring = 14N
The compression in spring = 2.4cm = 0.024m
(A.) Initially the spring scale reads only the weight of the mass = mg
W = 8.2 * 9.8 = 80.36N
(B) Let the value of spring constant = k
The net force exerted so that the scale reads(F') = 80.36N - 14 = 66.36N
We know that according to Hooke's law the force exerted on spring F = kx such that:
F' = kx then:
66.36 = k * 0.024
k = 66.36/0.024 = 2765N/m
(C) the compression where scale reads zero = x'
The scale reads zero when the restoring force equals to the weight of the mass then the scale reads zero such that:
x' = 80.36/2765 = 0.029m = 2.9cm
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1 Suppose the displacement of particle P from origin at time t is given by x(t)=t²-6t find the average velocity and acceleration of p over the time interval 1 <=t<=3 sec
Answer:
-2 m/s and the average acceleration is 2 m/s².
Explanation:
To find the average velocity of particle P over the time interval 1<=t<=3 sec, we need to use the following formula:
average velocity = (final displacement - initial displacement) / (final time - initial time)
In this case, the initial time is 1 sec and the final time is 3 sec. Therefore, the initial displacement is:
x(1) = 1² - 6(1) = -5
And, the final displacement is:
x(3) = 3² - 6(3) = -9
Now, we can substitute the values in the formula:
average velocity = (-9 - (-5)) / (3 - 1) = -2 m/s
To find the average acceleration of particle P over the time interval, we need to use the following formula:
average acceleration = (final velocity - initial velocity) / (final time - initial time)
We know that the initial time is 1 sec, the final time is 3 sec, and the initial velocity is the velocity at time t=1 sec. Therefore, the initial velocity is:
v(1) = 2t - 6 = 2(1) - 6 = -4 m/s
We also know that the final velocity is the velocity at time t=3 sec. Therefore, the final velocity is:
v(3) = 2t - 6 = 2(3) - 6 = 0 m/s
Now, we can substitute the values in the formula:
average acceleration = (0 - (-4)) / (3 - 1) = 2 m/s²
Therefore, the average velocity of particle P over the time interval 1<=t<=3 sec is -2 m/s and the average acceleration is 2 m/s².
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4. Are the light waves reflecting off a red stop sign longer or shorter than the waves reflecting off a violet-colored jacket? Explain how you know.
The light waves reflecting off a red stop sign would be longer than the light waves reflecting off a violet-colored jacket. This is because red light has a longer wavelength than violet light.
Light waves and reflectionLight waves, like all waves, are characterized by their wavelength. The wavelength of a wave determines its color, with shorter wavelengths appearing as blue and violet, and longer wavelengths appearing as red and orange.
Because the wavelength of red light is longer than the wavelength of violet light, the light waves reflecting off the red stop sign would be longer than the light waves reflecting off the violet-colored jacket.
Learn more about Light waves here:
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A metal filament Lamp rated at 750w, 100v into be connected in series with a capacitor across a 230v, 60hz supply. Calculate the capacitance required
Answer : 0.00885 farads or 8.85 microfarads
Explanation: To calculate the capacitance required, we can use the following formula:
C = 1 / [2 * pi * f * ((V^2 - Vlamp^2)/P)]
where:
C = capacitance in farads (F)
pi = 3.14159...
f = frequency in hertz (Hz)
V = voltage in volts (V)
P = power in watts (W)
Vlamp = voltage of the lamp in volts (V)
Using the given values, we have:
C = 1 / [2 * pi * 60 * ((230^2 - 100^2)/750)]
C = 1 / [2 * 3.14159 * 60 * ((230^2 - 100^2)/750)]
C = 1 / [113.09724]
C = 0.00885 farads (F)
Therefore, the capacitance required is approximately 0.00885 farads or 8.85 microfarads.
Work Energy Theorem Question: You apply 50 N to a 10 kg object to cause it to move from rest to 2.5 m/s. What distance was the object moved?
Answer:
0.625 meters
Explanation:
We can use the work-energy that the work done on an object is equal to the change in its kinetic energy:
Work = ΔK = Kf - Ki
Where:
Work is the work done on the object
ΔK is the change in kinetic energy of the object
Kf is the final kinetic energy of the object
Ki is the initial kinetic energy of the object (which is zero since the object is at rest)
The work done on the object is equal to the force applied to the object multiplied by the distance over which the force is applied:
Work = F × d
Where:
F is the force applied to the object (50 N)
d is the distance over which the force is applied (unknown)
So we can write:
F × d = Kf - Ki
Substituting the given values:
50 N × d = 1/2 × 10 kg × (2.5 m/s)^2 - 0
Simplifying:
50 N × d = 31.25 J
Solving for d:
d = 31.25 J / 50 N = 0.625 m
Therefore, the object was moved a distance of 0.625 meters.
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