Question

# A cart of mass m1(pictured) is free to move nearly frictionless up a ramp at angle...

A cart of mass m1(pictured) is free to move nearly frictionless up a ramp at angle θ. A small mass m2 hangs from a string that runs over a pulley and connects to m1. We will determine the acceleration of the cart m1 over a known distance x,then plot the acceleration of m1 as a function of the hanging mass m2.

a) The hanging mass will create a constant pulling force to accelerate the cart up the ramp. Using Newton’s Second Law of Motion, derive an expression for the acceleration of the system in terms of g, θ, m1 and m2. Show your work and explain your reasoning below.

Step 1: Free Body Diagram for each object

b) Step 2: Apply Newton’s 2nd Law to obtain dependence of acceleration on other variables

c) Step 3: Prediction of Relationship between Acceleration and Pulling Force If the pulling force is doubled(i.e. the hanging mass is doubled), will the acceleration also double? Why or why not?Justify your answer.

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