Box Up Ramp

On moving day, Santiago pushes a box weighing 170.0 \(\rm{N}\) at constant speed up a ramp. They push parallel to the ramp with a force of magnitude \(F\_{\textit{A on B}}\) (see the figure below). The ramp makes an angle of \(\theta = {{params_ang}}^{\circ}\) with the horizontal direction. The coefficients of static and kinetic friction friction between the box and the ramp are \(\mu_s = {{params_s}}\) and \(\mu_k = {{params_k}}\), respectively.

Question Text

Draw a free body diagram for this problem using the labelled axes provided in the figure. Label each force with subscripts indicating the agent of the force and the force on which it acts. Use R for ramp, A for Santiago, E for earth, and B for box. Be sure to consider the force Santiago exerts on the box \(F\_{\textit{A on B}}\), the force of kinetic friction \(f\_{\textit{k, R on B}}\), the force of static friction \(f\_{\textit{s, R on B}}\), the weight of the box \(W\_{\textit{E on B}}\), the normal force \(N\_{\textit{R on B}}\), and any other forces that may be acting on the box.

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Part 2

Is this an example of static or dynamic equilibrium?

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Part 3

From your free body diagram, write Newton’s second law equation for the x-components.

Note that it may not be necessary to use every variable and for angles, use their numeric value in degrees. Use the following table as a reference for each variable:

For	Use
\(F\_{\textit{A on B}}\)	F_ab
\(f\_{\textit{k, R on B}}\)	F_krb
\(f\_{\textit{s, R on B}}\)	F_srb
\(W\_{\textit{E on B}}\)	W_eb
\(N\_{\textit{R on B}}\)	N_rb
\(\theta\)	theta

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Part 4

From your free body diagram, write Newton’s second law equation for the y-components.

Note that it may not be necessary to use every variable and for angles, use their numeric value in degrees. Use the following table as a reference for each variable:

For	Use
\(F\_{\textit{A on B}}\)	F_ab
\(f\_{\textit{k, R on B}}\)	F_krb
\(f\_{\textit{s, R on B}}\)	F_srb
\(W\_{\textit{E on B}}\)	W_eb
\(N\_{\textit{R on B}}\)	N_rb
\(\theta\)	theta

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Part 5

Solve your equations to find \(F\_{\textit{A on B}}\).

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Please enter in a numeric value

Part 6

If the box started at rest on the ramp, how hard would Santiago have to initially push the box to just overcome the static force of friction?

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Part 7

Once the box started moving, if Santiago maintained the force you found in Part 6, what would happen to the box?

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Attribution

Problem is licensed under the CC-BY-NC-SA 4.0 license.