The tension in the rope at the 57. 6° angle is 48.58 N, and the tension in the rope at the 33. 8° angle is 36.28 N.
What is meant by angle?
An angle is a figure in plane geometry that is created by two rays or lines that have a shared endpoint. The Latin word "angulus," which meaning "corner," is the source of the English term "angle." The shared terminus of two rays is known as the vertex, and the two rays are referred to as sides of an angle.A pair of rays (half-lines) with a shared terminal are combined to form an angle. The latter is referred to as the angle's vertex, and the rays are sometimes referred to as the angle's legs and other times as its arms.Angles with a measurement of zero degrees or zero radians are referred to as zero angles. No of the unit of measurement, the zero angle has a measure of.The tension force exerted by the first rope, T1
The tension force exerted by the second rope, T2
and the force of gravity, mg
T1x = −T1 cos 57.6°
T2x = T2 cos 33.8°
mgx = 0
T1y = T1 sin 57.6°
T2y = T2 sin 33.8°
mgy = −mg
Thus, the x and y components of the resultant force will be:
x:
Rx = T1x + T2x + mgx
Rx = −T1 cos 57.6° + T2 cos 33.8° + 0
Rx = T2 cos 33.8° − T1 cos 57.6° (1)
y:
Ry = T1y + T2y + mgy
Ry = T1 sin57.6°+ T2 sin 33.8° + (−mg)
Ry = T1 sin 57.6° + T2 sin33.8° − mg (2)
The next step is to substitute Rx and Ry in Eq. (1) and Eq. (2) with 0:
Rx = T2 cos 33.8° − T1 cos 57.6°
Ry = T1 sin57.6° + T2 sin 33.8° − mg
↓
0 = T2 cos33.8°− T1 cos 57.6° (3)
0 = T1 sin57.6°+ T2 sin 33.8°− mg (4)
Using these two equations we can easily find T1 and T2.
There are multiple ways in which we can do this. One way would be to first solve Eq. (3) for T2:
0 = T2 cos33.8°− T1 cos 57.6°
T2 cos 33.8° − T1 cos 57.6° = 0
T2 cos 33.8° = T1 cos 57.6°
T2 = T1 cos57.6°/ cos 33.8°
T2 = 0.747T1 (5)
hen, we substitute T2 with 0.735T1 in Eq. (4):
0 = T1 sin 57.6°+ T2 sin 33.8° − mg
0 = T1 sin 57.6° + 0.735T1 sin 33.8°− mg
And we solve it for T1:
0 = T1 (sin 57.6° + 0.747 sin 33.8°) − mg
0 = T1 (0.848) − mg
mg = 0.848T1
0.848T1 = mg
T1 = mg /0.848
T1 = (4.2kg) (9.81 N/kg) / 0.848T
T1 = 48.58 N
Finally, we substitute the value of T1 in Eq. (5) to find T2:
T2 = 0.747T1
T2 = (0.747) (48.58 N)
T2 = 36.28 N
Therefore, the tension in the rope at the 57. 6°angle is 48.58 N, and the tension in the rope at the 33. 8°angle is 36.28 N.
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a spring has a force constant of 100 n/m and an unstretched length of 0.07 m. one end is attached to a post that is free to rotate in the center of a smooth table, as shown in the top view above. the other end is attached to a 1 kg disc moving in uniform circular motion on the table, which stretches the spring by 0.03 m. friction is negligible. 10. what is the centripetal force on the disc? (a) 0.3 n (b) 3n (c) 10 n (d) 300 n (e) 1,000 n 11. what is the work done on the disc by the spring during one full circle?
In a circle at constant speed, the work done is zero since the Force is always perpendicular to the distance moved as you move incrementally around the circle.
What is uniform circular motion?An object moves in a circle at a consistent speed in a motion known as uniform circular motion. Any point on a propeller, for instance, that is rotating continuously, is moving uniformly in circles. The second, minute, and hour hands on a watch are some further examples. It is amazing that despite the constant rotation rate, points on these revolving objects are actually speeding. We must consider the motion in terms of vectors in order to see this.
A centripetal motion is an Objects having a constant speed have zero acceleration in one-dimensional kinematics. In two- and three-dimensional kinematics, a particle can experience acceleration even if its speed is constant if it follows a curved trajectory, like a circle.
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suppose a 3000 cm3 container holds 7.0 g of nitrogen gas at a pressure of 200 kpa . the gas can be heated at constant pressure if a piston moves outward to let the gas expand as it's heated. alternatively, the gas can be heated at constant volume if the piston is locked in place to prevent expansion. how does the heat required for one of these processes compare to the heat required for the other process? how much heat is required to double the volume and temperature at constant pressure?
The heat required would be Q = 7.0 g/28 g/mol * 20.8 J/molK * (2T - T) = 544 J.
What is heat?Heat is the transfer of energy from one body or system to another due to the difference in their temperatures. Heat is commonly transferred through thermal conduction, convection, radiation, or when two bodies with different temperatures come into direct contact.
The heat required for a process at constant pressure is greater than the heat required for a process at constant volume. This is because when a gas is heated at constant pressure, work is done to push the piston outward, so more energy is required.
To double the volume and temperature at constant pressure, the heat required would be equal to the change in internal energy of the system,
which can be calculated using the equation Q = nCvΔT,
where n is the number of moles of gas,
Cv is the molar heat capacity,
and ΔT is the change in temperature.
In this case, the molar heat capacity of nitrogen gas is 20.8 J/molK,
So the heat required would be Q = 7.0 g/28 g/mol * 20.8 J/molK * (2T - T) = 544 J.
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a 6.5 kg object is suspended by a string from the ceiling of an elevator. the acceleration of gravity is 9.8 m/s 2 . determine the tension in the string if it is accelerating upward at a rate of 2.6 m/s 2 . answer in units of n. answer in units of n.
The rightward directions she gives are as follows: 1. Move 400 meters to the northwest. 3. The wealth is hidden there, 700 meters to the east-southeast.
What else do u mean by 9.8m s2 of acceleration caused by gravity?This means that anything is pushed toward the center of the earth, which causes the pulled object to accelerate by 9.8 meters per second as it "falls" to the earth. As a result, each second that such a body is dragged towards the earth, its velocity (speed with direction) increases by around 9.8 meters per second.
Is the gravity always 9.8 inches?It should be remembered that gravitation is not a continuous force; gravity weakens the more you are from the center of the Earth. Since it fluctuates from 9.83 at the poles to 9.78 at the equator, it isn't even a consistent at the surface. Due to this, we utilize an average value of 9.8.
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if a ball is thrown into the air with a velocity of 40 fts, its height in feet t seconds later is given by y 40t 16t2. (a) find the average velocity for the time period beginning when t 2 and lasting (i) 0.5 second (ii) 0.1 second (iii) 0.05 second (iv) 0.01 second
The change in position or displacement (Δx) divided by the time intervals (Δt) in which the displacement occurs yields the average velocity.
What is the average velocities of ball?Depending on the sign of the displacement, the average velocity can be positive or negative.
To begin, in order to calculate average velocities, we need the position for each instant mentioned:
Y(2) = 2 ft
Y(2.5) = 0 ft
Y(2.1) = 13.44 ft
Y(2.05) = 14.76 ft
Y(2.01) = 15.7584 ft
Let us now compute the average velocities:
V(2 - 2.5) = Y(2.5) - Y(2) / 2.5 - 2
= -32 ft/s
V(2 - 2.1) = Y(2.1) - Y(2) / 2.1 - 2
= -25.6 ft/s
V(2 - 2.05) = Y(2.05) - Y(2) / 2.05 - 2
= -24.8 ft/s
V(2 - 2.01) = Y(2.01) - Y(2) / 2.01 - 2
= -24.16 ft/s
Now, we can derive the expression for y for the instantaneous velocity:
For t=2s, V(t) = 40 - 32t V(2) = -24ft/s
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Joiya grabs a cold bottle of water from the refrigerator and carries it across her dining room. The dining room is at room temperature.
Which of the following describe possible ways heat would be transferred in this system?
The possible ways that heat can be transferred in this system are:
Radiation Conduction How can heat be transferred in this system ?The most typical method of heat transfer is conduction, which involves the direct exchange of heat between two things.
Heat waves are created during the radiation heat transfer process and may be absorbed, reflected, or transmitted through a cooler substance. Earth is warmed by the sun using electromagnetic radiation. Heat waves come from warm bodies.
When Joiya sets the bottle of water down on a table or chair, then by conduction, heat ( or the loss of it ) would move around the table. Radiation would allow for the cold temperature to move into the air around the cold bottle.
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Options for this question include:
Convection Conduction Radiationwhich of the following statements about forces is false? group of answer choices forces change the momentum of a body forces always occur in equal and opposite pairs where there is no force, objects continue to move the way they were moving there are places on earth where all forces are absent forces cause an acceleration to take place
The statement that is false is "there are places on earth where all forces are absent." Forces, such as gravity, are always present on Earth.
All the given statements are true except the statement "there are places on earth where all forces are absent." is false.
Forces change the momentum of a body,forces always occur in equal and opposite pairs (Newton's third law), where there is no force, objects continue to move the way they were moving, and forces cause an acceleration to take place are all true statements about forces.
Newton's third law simply states that there is an equal and opposite reaction to every action. So, if object A exerts a force on object B, object B will exert an equal but opposite force on object A.
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how many times more intense is the least intense perceptible sound at 100 hz compared to the least intense perceptible sound at 1000 hz ? specifically, you are looking for the ratio i100hz/i1000hz .
The ratio i100hz/i1000hz is 1000, meaning that the least intense perceptible sound at 100 Hz is 1000 times more intense than the least intense perceptible sound at 1000 Hz.
What is intense?Intense is an adjective describing something that is extreme or powerful, either in terms of strength, emotion, or concentration. It can refer to a feeling, such as intense emotion, or a physical sensation, such as intense pain.
The least intense perceptible sound at 100 Hz is about one millionth of a Pascal, while the least intense perceptible sound at 1000 Hz is about one billionth of a Pascal. Therefore, the ratio i100hz/i1000hz is 1000, meaning that the least intense perceptible sound at 100 Hz is 1000 times more intense than the least intense perceptible sound at 1000 Hz.
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a ping-pong ball has a diameter of 4.18 cm and average density of 0.0348 g/cm3 . what force would be required to hold it completely submerged under water? the acceleration of gravity is 9.8 m/s 2 . answer in units of n.
The force required to hold the ping pong ball completely under the water is 36,189.98 dyne.
Given:Diameter of ball = 4.18 cm
The radius of the ball = 2.09 cm
The volume of the ball can be calculated as V= [tex]\frac{4}{3}[/tex]π r³
Therefore, the volume of the ball = 38.26 cm³
The net force required to completely submerge a ball under water = (Buoyant force) - (the weight of the ball)
If ρ₁ is used for the density of water. Then, the value of ρ₁ is 1 g cm⁻³.
Buoyant force = ρ₁gV
= 1 × 980 × 38.26
= 37494.80 dyne
Here, ρ₂ = density of ball = 0.0348 1 g cm⁻³.
Weight of ball = ρ₂gV
= 0.0348 × 980 × 38.26
= 1304.82 dyne
Therefore, the net force required to completely submerge a ball under water = 37494.80 - 1304.82 = 36,189.98 dyne or 0.362 N
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what charge q should be placed at the center of the square to keep the other four charges in equilibriumn
Answer:
To keep the other four charges in equilibrium, the charge q that should be placed at the center of the square is equal in magnitude but opposite in sign to the total charge of the other four charges.
technically a geosynchronous satellite is one that orbits the earth once per sidereal day, which is 23.93 hours, not 24 hours. why is this? and how much difference will it make to the altitude of the satellite
Geosynchronous satellite makes a round around the earth in 29.93 hours. It makes a difference of 36000 km difference in the altitude.
Geosynchronous satellites are those that remains stationery with respect to a place. This is because their time period to complete a cycle is 23.93 hours, that is exactly the same as the rotation period of the earth. So the satellite appears stationery. The velocity of the geosynchronous satellite around the earth is 3.07 km/s or 3070 m/s.
GMm/(R+h)² = mv²/(R+h)
GM/v² = (R+h)²
Where R is the radius of the earth = 6.37 × 10⁶ m, h is the altitude of the satellite above the earth, and M is the mass of the earth that is 6 × 10²⁴ kg, G = 6.67 × 10⁻¹¹ Nm²/kg²
(6.67 × 10⁻¹¹ ×6 × 10²⁴)/(3070)² = (R+h)
(R+h) = 42461989 m
6.37 × 10⁶ + h = 42461989
h = 42461989 - 6.37 × 10⁶
h = 36.09 × 10⁶ m
h = 36000 km.
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2. A 38kg child is at the top of a slide that is 2. 1m tall.
(a) If there is no friction, how fast will they be moving when they reach the bottom of the slide?
(b) If they lose 250. 0J of energy to sound, heat, and friction, how fast will they be moving when they reach the bottom?
Answer:
3. A 0. 850 kg air-track glider moving at 1. 75 m/s bumps into a 1. 45 kg glider initially at rest.
(a) If the collision is elastic, find the total kinetic energy after collision.
(b) If the collision is completely inelastic, find the total kinetic energy after collision.
Show all your work
Part a: Velocity with no friction: v = 6.41 m/s.
Part b: velocity of the moving object when it reached at the bottom is found as 5.29 m/s.
Explain the term kinetic energy?Kinetic energy, which may be seen in the movement of an item or subatomic particle, is indeed the energy of motion. Kinetic energy is present in every particle and moving object.Potential energy P.E
P.E = mgh
P.E = 38 x 9.8 x 2.1 J
This all transforms to kinetic energy just at bottom = 0.5 mv² if there is no energy loss.
So,
0.5 x 38 x v² = 38 x 9.8 x 2.1,
v = 6.41 m/s
Part b: If friction results in a loss of energy of 250 J
0.5 x 38 x v² = 38 x 9.8 x 2.1 - 250
v² = 532.04/ (0.5 x 38)
v = 5.29 m/s
Thus, the velocity of the moving object when it reached at the bottom is found as 5.29 m/s.
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The correct question is-
2. A 38kg child is at the top of a slide that is 2. 1m tall.
(a) If there is no friction, how fast will they be moving when they reach the bottom of the slide?
(b) If they lose 250. 0J of energy to sound, heat, and friction, how fast will they be moving when they reach the bottom?
the building block of all elements and the smallest component into which an element can be divided?
a. building blocks
b. element
c. A molecule
d. atom
The building block of all elements and the smallest component into which an element can be divided d. atom
What is the smallest energy building block?
Quarks, the universe's tiniest particles, are significantly smaller and have far greater energy levels than the protons and neutrons in which they are found.
An atom is the smallest unit of an element that retains all of its characteristics.
However, atoms include several subatomic particles, the most significant of which are protons, neutrons, and electrons.
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(c) what is the minimum thickness of a soap bubble film (air-soap-air) with refractive index 1.38 that results in a constructive interference in the reflected light if this film is illuminated by a beam of light of wavelength 610 nm?
The minimum thickness of a soap bubble film (air-soap-air) with refractive index 1.38 that results in a constructive interference in the reflected light if this film is illuminated by a beam of light of wavelength 610 nm is 150
nm.
What is refractive index ?The refractive index of an optical medium is described as a dimensionless number that gives the indication of the light bending ability of that medium.
Condition for constructive interference is given as ,
2μt = (2n + 1) λ/2
t = (2n + 1) x 900 / 4x 1.5
where n = 0(for minimum thickness)
Therefore t= 150nm
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what tool uses sound waves to measure the distance of an object
A tool that uses sound waves to measure the distance of an object is called a sonar device.
What do you mean by Sonar Device?A sonar device is a tool that uses sound waves to measure the distance or detect the presence of objects underwater. The device sends out a high-frequency sound pulse that travels through the water and bounces back to the device after hitting an object. By measuring the time it takes for the sound wave to return, the device can determine the distance to the object and generate an image of the underwater environment. Sonar technology is widely used in applications such as navigation, fishing, and search and rescue operations.
Sound waves are a type of mechanical wave that travels through a medium, such as air, water, or solids, and is generated by the vibration of an object. The vibration creates a compression and rarefaction of the medium, which then spreads out as a wave. When these waves reach the ear, they are interpreted by the brain as sound. The speed of sound in a given medium depends on the properties of that medium, such as density and temperature.
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When a potential difference of 125V is applied to two parallel plates, the field between them is 4. 25 x 103N/C. How far apart are the plates?
The distance between the two parallel plates can be found using the equation E = V/d where E is the electric field, V is the potential difference and d is the distance between the plates. Thus, d = V/E = 125V / 4.25 x 103N/C = 29.41cm
What is the relationship between electric field, potential difference, and distance in parallel plates?
The relationship between electric field, potential difference and distance in parallel plates is inversely proportional. As the potential difference increases, the electric field between the plates increases and the distance between the plates decreases. And as the distance between the plates increases, the electric field between the plates decreases and the potential difference applied to the plates decreases.
It can be mathematically represented by the formula E = V / d, where E is the electric field, V is the potential difference, and d is the distance between the plates.
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The distance between the two parallel plates can be found using the equation E = V/d , 29.41cm far apart are the plates .
Evaluating :E = V/d
where E is the electric field,
V is the potential difference and
d is the distance between the plates.
Thus, d = V/E
= 125V / 4.25 x 103N/C
= 29.41cm
Potential difference :The relationship between electric field, potential difference and distance in parallel plates is inversely proportional. As the potential difference increases, the electric field between the plates increases and the distance between the plates decreases. And as the distance between the plates increases, the electric field between the plates decreases and the potential difference applied to the plates decreases.
It can be mathematically represented by the formula E = V / d, where E is the electric field, V is the potential difference, and d is the distance between the plates.
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a ball thrown at a brick wall bounces directly back with the same speed it had when it struck the wall. has the velocity of the ball changed? explain.
Yes, the velocity of the ball has changed as it changed its direction from hitting the wall and after it struck the wall.
Speed is a scalar which means it has magnitude but not the direction. Velocity, on the other hand, is a vector with both magnitude and a direction. As the speed of two cars may be the same, if they are heading to different directions, then their velocity are not identical.
The velocity of he ball has changed. Let's call that the initial direction positive, when the ball was going towards the wall, its velocity is positive +V. But when it bounces directly back, the direction is now is negative -V. The direction of the velocity has changed, even though the magnitude has not.
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Electromagnetic waves transfer energy from one ____ to ____ ?
If a current of 16A flows through a wire with a resistance of 0.6 Ohms, calculate the voltage.
If a current of 16A flows through a wire with a resistance of 0.6 Ohms, the voltage is: 9.6V.
How to find the voltage?Using this formula to determine the voltage
V = I × R
Where:
V = voltage = ?
I = current = 16A
R = resistance = 0.6 Ohms
Let plug in the formula
V = 16A × 0.6 Ohms
V = 9.6V
Therefore the voltage is 9.6V
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A heat engine has a thermal efficiency of 0. 46. During each cycle, it absorbs 780 J of heat from a high-temperature reservoir. How much waste heat does it discard each cycle.
A) 420 J
B) 200J
C) 780 J
D) 360 J
There is a thermal efficiency of 0.46 for a heat engine. With each cycle, it absorbs 780 J of heat from the high-temperature storage. B) 200 J waste heat it discard each cycle.
The thermal efficiency of a heat engine is defined as the ratio of the work output to the heat input, so in this case, the thermal efficiency is 0.46. Therefore, the work output is 0.46 * 780 J = 360 J.
The waste heat discarded each cycle is the difference between the heat input and the work output, so 780 J - 360 J = 200 J.
How much useful work does the heat engine perform in each cycle?
The useful work that the heat engine performs in each cycle can be determined by using the formula: thermal efficiency * heat absorbed = useful work. In this case, the thermal efficiency is 0.46, and the heat absorbed is 780 J.
Therefore, the useful work done by the engine is 0.46 * 780 J = 360 J.
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If the work required to speed a car up from 10km/h to 20km/h is 5.0 x 10^3 J, what would be the work required to increase the cars speed from 20km/h to 30km/h?
If the work required to speed a car up from 10km/h to 20km/h is 5.0 x 10^3 J, the work required to increase the cars speed from 20km/h to 30km/h is: 8.33 × 10³J.
How to find the work required?Using this formula to determine the work required to increase the cars speed from 20km/h to 30km/h
[tex]Wii = Wi (V^2_2- V^2_1) /v^2_2 - v^2_1[/tex]
Let plug in the formula
Work required = (5 × 10³) (30² -20²) / (20² -10²)
Work required = (5 × 10³) ( 900 - 400) /(400 - 100)
Work required = (5 × 10³) ( 500) / 300
Work required = 8.33 × 10³J
Therefore the Work required is 8.33 × 10³J.
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A sailor is walking on an aircraft carrier and is observed by a stationary barge. The sailor's velocity according to the barge is 36 m/s. At the same time, the barge observed the aircraft carrier moving at 43 m/s. What is the velocity of the sailor relative to the aircraft carrier?
The velocity of the sailor relative to the aircraft carrier is - 7 m/s.
What is the velocity of the sailor relative to the aircraft carrier?
The velocity of the sailor relative to the aircraft carrier is calculated by applying the principle of relative velocity as shown below.
Vs/c = Vs - Vc
where;
Vs is the velocity of the sailorVc is the velocity of the aircraftThe velocity of the sailor relative to the aircraft carrier is calculated as;
Vs/c = 36 m/s - 43 m/s
Vs/c = -7 m/s
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if the distance between atoms in a solid is 175 pm, what velocity must an electron have so that its de broglie wavelength is equal to that distance? what velocity must an ar atom have so that its de broglie wavelength is equal to that distance?
When this problem is solved, we will arrive at the value 72741 to 4 meters per second.
In simple terms, what would you call distance?An object's total, directionless motion is measured in terms of distance. Distance may also be referred to as the amount of ground covered by an element, depending on the starting or finishing point.
Distance calculations' objectiveBy calculating its distance, we can determine an object's actual size. One can measure the space that an object takes up above us. Its true size can be determined after we know how far away it is. As you get further away, something gets smaller.
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Find the distance and displacement of Greyhound bus traveling 90km north and 15km south
here is ur answer
MARK BRAIN PLease
if these objects roll without slipping down a ramp, which one will reach the bottom of the ramp first? multiplechoice : 1) there is not enough information to determine 2) object b 3) object a 4) they will reach the bottom at the same time.
There is not enough information to determine which object will reach the bottom of the ramp first. So option 1 is correct.
Without knowing the mass, radius, and coefficient of friction of the objects and the angle of the ramp, we can't determine which object will have the greater acceleration and thus reach the bottom of the ramp first.
To determine which object will reach the bottom of the ramp first, we need to know the acceleration of each object. The acceleration of an object is determined by the net force acting on it.
Which in turn is determined by the gravitational force acting on the object and the frictional force acting on it.
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two objects are thrown from the top of a tall building and experience no appreciable air resistance. one is thrown up, and the other is thrown down, both with the same initial speed. what are their speeds when they hit the street?two objects are thrown from the top of a tall building and experience no appreciable air resistance. one is thrown up, and the other is thrown down, both with the same initial speed. what are their speeds when they hit the street?they are traveling at the same speed.the one thrown down is traveling faster.the one thrown up is traveling faster.
The speed when they hit the street will be equal to each other.
What is Air resistance?Air resistance and gravity are the two fixed forces of nature which move on any object on Earth. For example, when a plane flies through the air, the air particles are pressing against the aeroplane, making it harder for the aircraft to move. When you see a feather fall, it is greatly affected by air resistance.
What is Gravity ?A force applied to all bodies on Earth is Weight ( W ), which is caused by Earth's gravity. If a body is free falling, its only acceleration is g , gravity. So gravity increases velocity. Both objects will show a change in their velocities because of gravity.
The velocity for both objects if one is thrown up and other is thrown down is same which is given by this formula:
where,
v= final velocity,
v₀= initial velocity,
h is the difference in height between building and street and g= acceleration due to gravity.
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A penny is dropped off the top of the Statue of Liberty, 93 m tall. What is the speed of the penny after 2.5 seconds (assuming no air resistance)?
The speed of the penny after 2.5 seconds is 24.5 m/s.
What is speed?
Speed is a scalar quantity that refers to "how fast an object is moving." It is the rate at which an object changes its position, and it is measured in units of distance per unit of time (such as meters per second or miles per hour). Speed is related to the distance traveled by an object and the time it takes to travel that distance, and it can be calculated by dividing the distance traveled by the time it took to travel that distance.
The speed of an object in free fall can be calculated using the equation:
v = g * t
where v is the velocity, g is the acceleration due to gravity (approximately 9.8 m/s^2 on the Earth's surface) and t is the time elapsed.
In this scenario, the penny is dropped off the top of the Statue of Liberty, which is 93 m tall, and we want to find the speed of the penny after 2.5 seconds.
So, we can substitute the values in the equation:
v = 9.8 m/s^2 * 2.5 s = 24.5 m/s
Therefore, the speed of the penny after 2.5 seconds is 24.5 m/s (assuming no air resistance).
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if a simple pendulum oscillates with small amplitude and its length is doubled, what happens to the frequency of its motion? (a) it doubles. (b) it becomes times as large. (c) it becomes half as large. (d) it becomes 1/ vc times as large. (e) it remains the same.
Option E - it remains the same , if a simple pendulum oscillates with small amplitude and its length is doubled .
The greatest displacement or distance that a point on a wave or vibrating body may travel in relation to its equilibrium position
A wave's amplitude is the difference between its starting position and its maximum displacement. Frequency is the amount of waves which pass past the certain place each second. Period is the length of time it takes for a wave cycle to finish.
Given,length of a simple pendulum is doubled .
To find, frequency of motion.
we have Time period T before doubling the length,
T = 2π[tex]\sqrt{\frac{L}{g} }[/tex] L- length,g-acceleration due to gravity
T/2π = [tex]\sqrt{\frac{L}{g} }[/tex]
g = L(2π/T[tex])^{2}[/tex] → 1
when length is doubled,Time period [tex]T^{'}[/tex]
[tex]T^{'}[/tex] = 2π [tex]\sqrt{\frac{2L}{g} }[/tex]
( [tex]T^{'}[/tex] /2π[tex])^{2}[/tex] = [tex]\frac{2L}{g}[/tex]
g=2L( 2π/T[tex])^{2}[/tex] → 2
from equation 1 and 2
L( 2π/T[tex])^{2}[/tex] = 2L( 2π/T[tex])^{2}[/tex]
2π/T=[tex]\sqrt{2}[/tex](2π/T)
1/T =[tex]\sqrt{2}[/tex](1/T)
we know,frequency γ = 1/T
γ =[tex]\sqrt{2}[/tex] γ '
γ ' =[tex]\frac{1}{\sqrt{2} }[/tex] γ
Therefore option E is correct.
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a net force of 5.0 x 102 n causes an object to accelerate at a rate of 5.0 m/s2. what is the mass of the object?
The mass of the object is: 100 kg
What is force?It is the physical magnitude that expresses the effort necessary to move the mass of one kilogram with an acceleration of one meter per second squared, this is expressed in units of the international system in Newton.
To solve this exercise, the formula and procedure to be applied is:
F = m * a
Where:
m = massF = Forcea = accelerationInformation about the problem:
m = ?F= 5.0x 10^2 n1 N = kg * m/s²a= 5.0 m/s²Applying the force formula and isolating the mass, we get:
F = m * a
m= F/a
m= 5.0x 10^2 n /5.0 m/s²
m= 100 kg
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a metal object is suspended from a spring scale. the scale reads 936 n when the object is suspended in air, and 769 n when the object is completely submerged in water. find the volume of the object. the acceleration of gravity is 9.8 m/s 2 . answer in units of m3 .
The volume of object will be equal to the volume of water displaced so the object's volume is also 17.04 dm⁻³.
What is volume?In water, the object appears lighter than in air.
That is,
936 - 769 = 167N.
Water provided the167N buoyant force.
The buoyant force on an object in water is equal to the weight of water displaced by the object. The buoyant force acting on the metal object in this case is 167N. The object must have displaced the same weight of water.
Given g = 9.8m/s²
Water displacement mass:
Mass = weight /g
= 167/9.8
. = 17.04 kg
Water displacement volume:
At room temperature, the density of water is 1.000 kg.dm⁻³. Each kilogram of water has a volume of 1 dm³ (one cubic decimeter), which is equal to 1 L. (one liter).
V = Mass / Density
= m/ρ
= 17.04/1.000 kg.dm⁻³
= 17.04dm⁻³
The object is completely submerged. As a result, the object's volume will remain constant. The object is completely submerged. As a result, the object's volume will be equal to the volume of water displaced. The object's volume is also 17.04 dm⁻³.
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in a thundercloud there may be electric charges of 35.0 c near the top of the cloud and -35.0 c near the bottom of the cloud. these charges are separated by 2.20 km. what is the electric force on the top charge? magnitude
The magnitude of electric force is [tex]2.27 * 10^{6} N[/tex] (downwards)
We know that electric force between two charges is given by equation:
F = [tex]\frac{k.q_{1} .q_{2} }{r^{2} }[/tex]
Where,
k = constant = [tex]9 * 10^{9} Nm^{2} /C^{2}[/tex]
q1 = first charge =35 C
q2 = second charge = -35 C
r = distance between them = 2.2 km = 2200m
Putting these values in above equation we get:
F = -[tex]2.27 * 10^{6} N[/tex] , where negative sign denotes the direction.
So, the magnitude of electric force is [tex]2.27 * 10^{6} N[/tex] (downwards)
According to Coulomb’s law, the force of attraction or repulsion between two charged bodies is directly proportional to the product of their charges and inversely proportional to the square of the distance between them. It acts along the line joining the two charges considered to be point charges. The law is applicable only for the point charges at rest.To know more about electrostatics visit:
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