Problem Statement: An object of mass M is connected to an object of mass m by a massless string resting over a massless, frictionless pulley. Mass M accelerates on the frictionless surface to the right. a. Choose an appropriate coordinate system (s) and draw free body diagram(s). Make a table of known/given information and unknown/wanted information. List any physical assumptions you are using to solve the problem. M ti h Write down Newton's Second Law for both block m and bl

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Chapter4: Dynamics: Force And Newton's Laws Of Motion
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Problem Statement: An object of mass M is
connected to an object of mass m by a massless string
resting over a massless, frictionless pulley. Mass M
accelerates on the frictionless surface to the right.
M
a. Choose an appropriate coordinate system (s) and draw
free body diagram(s). Make a table of known/given
information and unknown/wanted information. List any
physical assumptions you are using to solve the problem.
b. Write down Newton's Second Law for both block m and block M.
c. What is the acceleration constraint for the two blocks?
Massless string
Massless, fric-
tionless pulley
m
d. Find a symbolic expression for the acceleration of both blocks M and m.
e. Assess the validity of your solutions in the following ways:
1) Check the physical units of your expression for the acceleration for the two blocks.
2) Consider the situation where m = 0. What do you expect the acceleration of block
M to be? Does your solution from part d match your expectations in this situation?
Consider the situation where m >> M (mass m is many orders of magnitude greater
than mass M). Does the resulting acceleration result make sense? Explain in words.
Transcribed Image Text:Problem Statement: An object of mass M is connected to an object of mass m by a massless string resting over a massless, frictionless pulley. Mass M accelerates on the frictionless surface to the right. M a. Choose an appropriate coordinate system (s) and draw free body diagram(s). Make a table of known/given information and unknown/wanted information. List any physical assumptions you are using to solve the problem. b. Write down Newton's Second Law for both block m and block M. c. What is the acceleration constraint for the two blocks? Massless string Massless, fric- tionless pulley m d. Find a symbolic expression for the acceleration of both blocks M and m. e. Assess the validity of your solutions in the following ways: 1) Check the physical units of your expression for the acceleration for the two blocks. 2) Consider the situation where m = 0. What do you expect the acceleration of block M to be? Does your solution from part d match your expectations in this situation? Consider the situation where m >> M (mass m is many orders of magnitude greater than mass M). Does the resulting acceleration result make sense? Explain in words.
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