SolutionsSet03

SolutionsSet03 - Homework Solutions Physics 121 Set 03...

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Unformatted text preview: 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 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 ....
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SolutionsSet03 - Homework Solutions Physics 121 Set 03...

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