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# SolutionsSet03 - Homework Solutions Set 03 Physics 121...

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Homework Solutions Physics 121 Set 03 Spring 2008 - 1 - Problem 1 The solution to this problem is similar to the solution to problem 4 on set # 2, except that in addition to the pulling force T 3 we have to include the friction force. The first step is to calculate he acceleration of the system. Assume the acceleration is a then we know that the net force on the blocks must be F net = m 1 + m 2 + m 3 ( ) a The net force can also be expressed in terms of the pulling and friction forces: F net = T 3 ! μ k m 1 + m 2 + m 3 ( ) g where μ k m i g is the friction force on mass m i . By combining these two equations we can determine the acceleration a : a = T 3 ! μ k m 1 + m 2 + m 3 ( ) g m 1 + m 2 + m 3 ( ) = T 3 m 1 + m 2 + m 3 ( ) ! μ k g The net force on block m 1 is equal to F 1 = m 1 a = m 1 T 3 m 1 + m 2 + m 3 ( ) ! μ k m 1 g The net force on block m 1 can also be expressed in terms of the tension T 1 and the friction force acting on block 1: F 1 = T 1 ! μ k m 1 g By combining these two expressions we see that T 1 = m 1 T 3 m 1 + m 2 + m 3 ( ) We can follow the same procedure for block 2 where we find that the net force must be equal to F 2 = m 2 a = m 2 T 3 m 1 + m 2 + m 3 ( ) ! μ k m 2 g The second expression for the net force on block 2, expressed in terms of the tension in the strings and the friction force, is equal to

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Homework Solutions Physics 121 Set 03 Spring 2008 - 2 - F 2 = T 2 ! T 1 ! μ k m 2 g By combining these two expressions, and using the expression for T 1 , we can obtain the following expression for T 2 : T 2 = m 2 T 3 m 1 + m 2 + m 3 ( ) ! μ k m 2 g " # \$ % & + T 1 + μ k m 2 g ( ) = m 1 + m 2 ( ) T 3 m 1 + m 2 + m 3 ( )
Homework Solutions Physics 121 Set 03 Spring 2008 - 3 - Problem 2 There are three forces acting on each rider: The gravitational force, which is directed in the negative vertical direction and has a magnitude of mg . The friction force, which is directed in the positive vertical direction and must have a magnitude of mg if the riders do not slip down the wall.

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SolutionsSet03 - Homework Solutions Set 03 Physics 121...

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