5. You are playing a game where the goal is to slide a small block up a ramp with inclination a so that it reaches a target at a vertical distance h above the bottom of the incline. There is friction between the block and the incline, with kinetic friction coefficient Mk. Use the work-kinetic energy theorem to calculate the initial speed you must give the block at the bottom of the incline so that it will come to rest at the target. Express your answer in terms of g, h, pk, and a. α h

College Physics
11th Edition
ISBN:9781305952300
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Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
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Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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Please include explanations and work for the problems. Please write it out to make it easy to understand.

**Problem Statement:**

You are playing a game where the goal is to slide a small block up a ramp with inclination \( \alpha \) so that it reaches a target at a vertical distance \( h \) above the bottom of the incline. There is friction between the block and the incline, with kinetic friction coefficient \( \mu_k \). Use the work-kinetic energy theorem to calculate the initial speed you must give the block at the bottom of the incline so that it will come to rest at the target. Express your answer in terms of \( g \), \( h \), \( \mu_k \), and \( \alpha \).

---

**Diagram Description:**

The diagram accompanying the problem shows a small block on an inclined ramp. 

- The ramp is inclined at an angle \( \alpha \).
- An initial velocity \( \vec{v_i} \) is directed up the ramp.
- The block moves up to reach a target, which is a distance \( h \) vertically from the starting point. 

The ramp and the block illustrate the path the block needs to follow in order to reach the height \( h \). The diagram helps visualize the problem of calculating the necessary initial speed given the effects of gravity and friction on the block as it ascends the incline.
Transcribed Image Text:**Problem Statement:** You are playing a game where the goal is to slide a small block up a ramp with inclination \( \alpha \) so that it reaches a target at a vertical distance \( h \) above the bottom of the incline. There is friction between the block and the incline, with kinetic friction coefficient \( \mu_k \). Use the work-kinetic energy theorem to calculate the initial speed you must give the block at the bottom of the incline so that it will come to rest at the target. Express your answer in terms of \( g \), \( h \), \( \mu_k \), and \( \alpha \). --- **Diagram Description:** The diagram accompanying the problem shows a small block on an inclined ramp. - The ramp is inclined at an angle \( \alpha \). - An initial velocity \( \vec{v_i} \) is directed up the ramp. - The block moves up to reach a target, which is a distance \( h \) vertically from the starting point. The ramp and the block illustrate the path the block needs to follow in order to reach the height \( h \). The diagram helps visualize the problem of calculating the necessary initial speed given the effects of gravity and friction on the block as it ascends the incline.
Expert Solution
Step 1

Draw the free-body diagram of the block.

Physics homework question answer, step 1, image 1

Determine the inclined distance of the block.

sinα=hdd=hsinα

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