Problem: A 42.6-kg crate of tools rests on a horizontal floor. You exert a gradually increasing horizontal push on it and observe that the crate just begins to move when your force exceeds 326 N. After that you must reduce your push to 226 N to keep it moving at a steady 25.1 cm/s.(a) What is the coefficient of static friction between the crate and the floor?(b) What is the coefficient of kinetic friction between the crate and the floor?(c) What push must you exert to give it an acceleration of 1.26 m/s2?(d) Suppose you were performing the same experiment on this crate but were doing it on the moon instead, where the acceleration due to gravity is 1.62  m/s2. What magnitude push would cause it to move?(e) What would its acceleration be (on the moon) if you maintained the push in part (c)?

FREE Expert Solution

We're asked about static and kinetic friction in a horizontal surface, and the applied forces related to it.

For forces problems in general, we have a series of steps to follow:

1. Draw a free body diagram (FBD), making sure to include and label coordinate axes
2. Set up Newton's Second Law equation ( ma )
3. Solve for the target variable

Remember that the magnitude of a friction force is calculated using

$\overline{){{\mathbit{f}}}_{{\mathbit{s}}{\mathbf{,}}{\mathbit{m}}{\mathbit{a}}{\mathbit{x}}}{\mathbf{=}}{{\mathbit{\mu }}}_{{\mathbit{s}}}{\mathbit{N}}}$ (maximum static friction)

or

$\overline{){{\mathbit{f}}}_{{\mathbit{k}}}{\mathbf{=}}{{\mathbit{\mu }}}_{{\mathbit{k}}}{\mathbit{N}}}$ (kinetic friction

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Problem Details

A 42.6-kg crate of tools rests on a horizontal floor. You exert a gradually increasing horizontal push on it and observe that the crate just begins to move when your force exceeds 326 N. After that you must reduce your push to 226 N to keep it moving at a steady 25.1 cm/s.

(a) What is the coefficient of static friction between the crate and the floor?

(b) What is the coefficient of kinetic friction between the crate and the floor?

(c) What push must you exert to give it an acceleration of 1.26 m/s2?

(d) Suppose you were performing the same experiment on this crate but were doing it on the moon instead, where the acceleration due to gravity is 1.62  m/s2. What magnitude push would cause it to move?

(e) What would its acceleration be (on the moon) if you maintained the push in part (c)?