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An **Atwood machine** uses a cable drawn over a **pulley** to connect two or more masses. One of the masses acts as a counterbalance or counterweight to reduce acceleration because of gravity. Elevators in multi-level buildings are examples of Atwood machines. The counterweight in an elevator is typically the mass of the elevator plus about half of the mass of the allowable load.

One block sits on a frictionless table. It is connected by a massless rope to a second box that is hanging off the side of the table. The acceleration of the blocks is

a. zero

b. g/2

c. g

d. a value between zero and g

e. greater than g

ANSWER: d. a value between zero and g

b. is only true for equal masses.

1. In an **Atwood's machine**, the larger mass is 1.8 kg and the smaller mass is 1.2 kg.

a. Ignoring friction, what is the acceleration of the masses?

b. What is the tension in the string?

2. A 10.0 kg mass, m_{1}, on a frictionless table is accelerated by a 5.0 kg mass, m_{2}, hanging over the edge of the table. What is the acceleration of the mass along the table?

3. Two identical blocks are tied together with a string which passes over a **pulley** at the crest of the inclined planes, one of which makes an angle ø_{1} = 28° to the horizontal, the other makes the complementary angle ø_{2} = 62°. If there is no friction anywhere, with what acceleration do the blocks move?

4.

A 2.00-kg and a 6.00-kg block are connected by a light string over a frictionless pulley. The two blocks are allowed to move on a fixed s wedge inclined 30º. µ = 0.18 Determine the acceleration of the two blocks and the tension in the string.

5. Two blocks are moving down a ramp that is inclined at 30º. Box 1(of mass 1.55 kg) is above box 2(of 3.1 kg) and they are connected by a rod having negligible mass. Find the tension of the rod if the coefficient of kinetic friction for box 1 is .226 and box 2 is .113.

6.

Two blocks, one 0.8 kg and the other 2.0 kg are connected by a massless string over a frictionless pulley. The coefficient of kinetic friction is 0.14, and the downward ramp angle is 60 degrees.

a) Determine the acceleration of the blocks.

b) Calculate the tension of the string.

7.

A 5.0kg mass is accelerated from rest at the bottom of the 4.0 m long ramp by a falling 20.0kg mass suspended over a frictionless pulley. The ramp is inclined 30º ramp from the horizontal, and the coefficient of kinetic friction = .26.

a. Determine the acceleration of the 5.0 kg mass along the ramp.

b. Determine the tension in the rope during the acceleration on the 5.0 kg mass along the ramp.

8.

A box of mass m_{1} sits on a table. It is connected, by a rope drawn through a pulley, to a box m_{2} = 2.10 kg that is hanging off the side of the table. The coefficient of static friction between mass m_{1} and the table is 0.400, whereas the coefficient of kinetic friction is 0.295.

a. What minimum value of m_{1} will keep the boxes from starting to move?

b. What value of m_{1} will keep the boxes moving at constant speed?

9.

A 20 kg block, m_{1}, is sliding on a 10 kg block, m_{2}. The blocks are on a 20º slope and are connected by a light string looped over a pulley. All surfaces are frictionless. Find the acceleration of each block and the tension in the sting that connects the blocks.

10.

A 20 kg weight on a table is attached by a string to another 20 kg weight that is hanging over the edge of the table. Assuming that the coefficient of friction is 0.2, what is the acceleration and what is the tension in the string?

Selected solutions are printed below.

For solutions to all the problems on this page click here.

1.

a. The net force on each mass is given in the two equations (g = 9.8 m/s/s):

1.8a = 1.8g -T

1.2a = T - 1.2g

Since a and T are the same for both masses, add the two equations:

3.0a = .6g

Therefore,

a = .2g = 1.96 m/s/s

b. Substituting for a in the first equation:

1.8(1.96) = 1.8(9.8) - T

T = 14.1 N

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