AP Phys I - Atwood & Inclined Planes Review

AP Phys I
Atwood Machines &Pulley Problems

Coupled Forces

What are coupled forces?

A couple, in mechanics, are a pair of equal forces that are parallel but opposite in direction.

One key example of a coupled force problem is one involving a pulley system.

The Atwood Machine

In 1784, George Atwood created a device to calculate force and tension and to verify the laws of motion of objects under constant acceleration. His device, now known as an Atwood's Machine, consisted of two masses connected by a tight string that passes over a pulley. When the masses are equal, the pulley system is in equilibrium, i.e. balanced. When the masses are not equal, both masses will experience an acceleration (indicated with red arrows). For simplification, we will assume the ideal pulley scenario, where the mass of the string is negligible and we ignore any frictional effects acting on the pulley. With these assumptions, the accelerations a1 and a2 are equal.

The Atwood Machine

When m1>m2, the sign convention used is such that m1 accelerates int he downwards y direction and m2 moves upward. Here, we let the acceleration be positive. On the other hand, if m1< m2, we will set the acceleration as negative. With this convention, we can derive a system of equations describing the acceleration of each mass:

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Fill in the Blanks

Calculate the acceleration of the system.

Round to appropriate significant figures.

Do no include units

Fill in the Blanks

Calculate the tension force.

Round to appropriate significant figures.

Include a single space between the number and the unit.

Fill in the Blanks

Calculate the acceleration of the system.

Do not include units.

Round to appropriate significant figures.

Fill in the Blanks

Calculate the tension in the string.

Round to appropriate significant figures.

Include a single space between the number and the unit.

Multiple Choice

What does a pulley system do?

• Forces two objects so split the applied force

• Changes an object's velocity

• Changes an object's speed

• Changes the direction of a force

Multiple Choice

A pulley is used to lift an object with a mass of 24.5kg. How much force must a person apply to the opposite side in order to lift the object?

• 24.5 kg

• 240 N

• 25 N

• 360 N

Multiple Choice

What would the acceleration of m2 be if m1 was 4 kg and m2 is 5kg?

• 1.1 m/s/s, 270 degrees

• 1.1 m/s/s, 90 degrees

• .92 m/s/s, 270 degrees

• .92 m/s/s, 0 degrees

Multiple Choice

What is the acceleration of the cart on the table if the cart and mass has a combined mass of 8kg with a coefficient of friction of 0.15 and the hanging mass is 5.5kg?

• 15 m/s/s, 0 degrees

• 15 m/s/s 90 degrees

• 3.1 m/s/s 0 degrees

• 3.1 m/s/s 270 degrees

Multiple Choice

The students double the mass that hangs from the string. They also replace the original cart with a new cart that has double the mass. By doubling both masses, how will the tension in the string and the acceleration of the cart change?

• The tension and the acceleration will double.

• The tension will double, but the acceleration will stay the same.

• The tension will stay the same, but the acceleration will double.

• The tension and the acceleration will stay the same.

Multiple Choice

An Atwood’s machine is set up by suspending two blocks connected by a string of negligible mass over a pulley, as shown above. The blocks are initially held at rest and then released at time t =0 s. The speed of the 3 kg block at time t = 2.0 s is most nearly

• 2.0 m/s

• 4.0 m/s

• 7.0 m/s

• 10.0 m/s

Multiple Choice

A 0.30 kg ball is in a cup of negligible mass attached to a block of mass M that is on a table. A string passing over a light pulley connects the block to a 2.5 kg object, as shown above. The system is released from rest, the block accelerates to the right, and after moving 0.95 m the block collides with a bumper near the end of the table. The ball continues to move and lands on the floor at a position 2.4 m below and 1.8 m horizontally from where it leaves the cup. Assume all friction is negligible.

Calculate the speed of the ball just after the block hits the bumper and the ball leaves the cup. (Hint: Find time using T-chart first.)

• 2.6 m/s

• 6.2 m/s

• 1.2 m/s

• 9.2 m/s

Multiple Choice

A 0.30 kg ball is in a cup of negligible mass attached to a block of mass M that is on a table. A string passing over a light pulley connects the block to a 2.5 kg object, as shown above. The system is released from rest, the block accelerates to the right, and after moving 0.95 m the block collides with a bumper near the end of the table. The ball continues to move and lands on the floor at a position 2.4 m below and 1.8 m horizontally from where it leaves the cup. Assume all friction is negligible.

Calculate the magnitude of the acceleration of the block as it moves across the table. (Hint: Use horizontal velocity to plug into the equation)

• 3.5 m/s²

• 5.3 m/s²

• 15.3 m/s²

• 13.35 m/s²

Multiple Choice

A 0.30 kg ball is in a cup of negligible mass attached to a block of mass M that is on a table. A string passing over a light pulley connects the block to a 2.5 kg object, as shown above. The system is released from rest, the block accelerates to the right, and after moving 0.95 m the block collides with a bumper near the end of the table. The ball continues to move and lands on the floor at a position 2.4 m below and 1.8 m horizontally from where it leaves the cup. Assume all friction is negligible.

(Calculate the mass M of the block.

• 4.24 kg

• 4.6 kg

• 8.64 kg

• 6.84 kg

Multiple Choice

A 0.30 kg ball is in a cup of negligible mass attached to a block of mass M that is on a table. A string passing over a light pulley connects the block to a 2.5 kg object, as shown above. The system is released from rest, the block accelerates to the right, and after moving 0.95 m the block collides with a bumper near the end of the table. The ball continues to move and lands on the floor at a position 2.4 m below and 1.8 m horizontally from where it leaves the cup. Assume all friction is negligible.

If the mass of the ball is increased, the horizontal distance it travels before hitting the floor will...

• decrease.

• increase.

• stay the same.

Multiple Choice

How much is Fnet on the system?

• 40 N

• 50 N

• 10 N

• 4 N

Multiple Choice

Calculate the acceleration of the system.

• 30/4 m/s²

• 10/4 m/s²

• 5 m/s²

• 20 m/s²

Multiple Choice

How much is Fnet on the system?

• 50 N

• 30 N

• 5 N

• 3 N

Multiple Choice

An Atwood’s machine is set up by suspending two blocks connected by a string of negligible mass over a pulley, as shown above. The blocks are initially held at rest and then released at time t =0 s. The speed of the 3 kg block at time t = 2.0 s is most nearly

• 2.0 m/s

• 4.0 m/s

• 7.0 m/s

• 10.0 m/s

Fill in the Blanks

An Atwood machine is a mechanical system consisting of two objects connected via a rope over a pulley. Suppose object A has a mass of 30.0 kg, and object B has a mass of 24.0 kg. Suppose object A is released from rest. Determine the magnitude of the acceleration for both objects. Assume the rope and pulley are massless.

Round to three sig figs, no units.

Fill in the Blanks

1. An Atwood machine is a mechanical system consisting of two objects connected via a rope over a pulley. Suppose object A has a mass of 50.0 kg and object B has a mass of 7.50 kg. Suppose object A is released from rest. Determine the magnitude of the acceleration for both objects. Assume the rope and pulley are massless.

2. Round to three sig figs, no units.

Fill in the Blanks

1. An Atwood machine is a mechanical system consisting of two objects connected via a rope over a pulley. Suppose object A has a mass of 64.0 kg and object B has a mass of 24.0 kg. Suppose object A is released from rest. Determine the magnitude of the acceleration for both objects. Assume the rope and pulley are massless.

   Round to three sig figs, no units.

Multiple Choice

A block of mass M is attached to a modified Atwood Machine and is accelerated upward at 3a by a constant force F_o. What is the weight of the block?

• F_o-Mg

• 3Mg

• 2Mg

• Mg

Multiple Choice

Block A is placed on a rough surface inclined at an angle θ above the horizontal. A taut string connects block A over a pulley to block B, which hangs from the string, as shown. The masses of blocks A and B are M_A and M_B respectively. At time t=0, block A is sliding up the slope as block B falls, and the blocks are both slowing down. Assume that the mass and friction of the pulley are negligible.

The two blocks eventually stop and reverse direction. Which of the following graphs best predicts the acceleration of block A as it moves up and down the rough, inclined surface? Assume that the positive direction points down the slope.