The 115 kg crate is subjected to the forces shown. If it is originally at rest, determine the distance it slides in order to reach a speed of [tex]v = 8.5 \, \text{m/s}[/tex].

Question

16-02-2025
Physics

High School

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The 115 kg crate is subjected to the forces shown. If it is originally at rest, determine the distance it slides in order to reach a speed of [tex]v = 8.5 \, \text{m/s}[/tex].

Answer :

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mmrizvi034 mmrizvi034 · Answer 1 · 2024-08-11T03:24:56-04:00

Final answer:

The crate slides a distance of approximately 31.8 meters to obtain a speed of v=8.5 m/sv=8.5m/s.

Explanation:

To determine the distance the crate slides to obtain a speed of v=8.5 m/sv=8.5m/s, we can use the work-energy principle. According to this principle, the work done on an object is equal to the change in its kinetic energy.

The work done on the crate is the sum of the work done by the applied force and the work done by friction. The work done by the applied force can be calculated using the formula W=F⋅dW=F⋅d, where FF is the magnitude of the force and dd is the distance over which the force acts.

Given that the crate starts from rest, the initial kinetic energy is zero. Therefore, the work done by the applied force is equal to the change in kinetic energy, which is 12mv221mv2, where mm is the mass of the crate and vv is the final velocity.

We rearrange the formula to solve for dd and substitute the given values to find the distance the crate slides. After performing the calculations, we find that the crate slides approximately 31.8 meters to obtain a speed of v=8.5 m/sv=8.5m/s.