Question

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.

Answer #1

A block of mass m1 = 3.27 kg on a frictionless plane inclined at
angle θ = 26.2° is connected by a cord over a massless,
frictionless pulley to a second block of mass m2 = 2.60 kg hanging
vertically (see the figure). (a) What is the acceleration of the
hanging block (choose the positive direction down)? (b) What is the
tension in the cord?

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You are pulling a
heavy crate (mass m) up a ramp inclined at an angle
θ to the horizontal. The ramp is not a smooth
surface. The rope that you are pulling with is parallel to the
incline.
What forces are acting
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Group of answer choices
Friction, gravity, normal force and tension
Gravity and tension
Friction, gravity and tension
Friction
Gravity, normal force and tension
Gravity
Normal force
Tension

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A hanging weight, with a mass of m1 = 0.370
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pulley can be modeled as a hollow cylinder with an inner radius of
R1 = 0.0200 m, and an outer radius of
R2 = 0.0300 m; the mass of the spokes is
negligible. As...

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