In this example we will add friction to an inclined ramp. Of course, friction does work and we will need to determine its contribution to WotherWother. A crate full of machine parts sits on the floor; the total mass is 8.0 kg. The crate must be raised to the floor of a truck by sliding it up a ramp 2.5 m long, inclined at 30∘. The shop foreman, giving no thought to the force of friction, calculates that he can get the crate up the ramp by giving it an initial speed of 5.0 m/S at the bottom and letting it go. Unfortunately, friction is not negligible; the crate slides 1.6 mm up the ramp, stops, and slides back down. (Figure 1) shows the situation. (a) Assuming that the friction force acting on the crate is constant, find its magnitude. (b) How fast is the crate moving when it reaches the bottom of the ramp?PART BSuppose the foreman had released the box from rest at a height of 0.25 m above the ground. What would the crate's speed be when it reaches the bottom of the ramp? ### Illustration DescriptionThe image consists of two diagrams, labeled (a) and (b), depicting a person pushing a box up a ramp. Both diagrams illustrate various physical parameters related to the motion of the box.#### Diagram (a)- **Scenario**: A person is pushing an orange box with mass \( m = 8.0 \, \text{kg} \) up a ramp. - **Ramp and Motion Details**: - The inclined ramp forms an angle of \( 30^\circ \) with the horizontal. - Initial velocity (\( v_1 \)) of the box is \( 5.0 \, \text{m/s} \) at Point 1. - The box travels from Point 1 to Point 2, a distance of \( 2.5 \, \text{m} \). - The horizontal distance is marked as \( 1.6 \, \text{m} \). - The vertical height from the end of the ramp to its start at Point 2 is \( 0.80 \, \text{m} \). - At Point 2, the final velocity (\( v_2 \)) of the box is \( 0 \, \text{m/s} \).#### Diagram (b)- **Scenario**: Similar to diagram (a), the person is at the bottom of the ramp, but the orientation of the box's motion is different.- **Ramp and Motion Details**: - The box approaches the person with a velocity indicated as \( v_3 \). - The box initially starts at rest at the top of the ramp (\( v_2 = 0 \, \text{m/s} \)) before approaching the person.- **Point 3**: This point marks the beginning of the person's interaction with the box on the ramp.### ExplanationThese diagrams are often used in physics to illustrate the concepts of mechanics, specifically involving motion on inclined planes. Key ideas include calculating work done, energy conservation (potential and kinetic energy), and understanding the forces acting on an object on an incline.Students may be asked to compute:- The acceleration of the box as it moves along the incline.- The net force exerted by the person on the box.- Energy transformations as the box moves from Point 1 to Point 2 in Diagram (a), and vice versa in Diagram (b

Given data: Mass of the car, m=8.0 kg Inclined angle, θ=30o Initial speed of the crate, u=5.0 m/s…

Answered: In this example we will add friction to…

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

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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In this example we will add friction to an inclined ramp. Of course, friction does work and we will need to determine its contribution to WotherWother. A crate full of machine parts sits on the floor; the total mass is 8.0 kg. The crate must be raised to the floor of a truck by sliding it up a ramp 2.5 m long, inclined at 30∘. The shop foreman, giving no thought to the force of friction, calculates that he can get the crate up the ramp by giving it an initial speed of 5.0 m/S at the bottom and letting it go. Unfortunately, friction is not negligible; the crate slides 1.6 mm up the ramp, stops, and slides back down. (Figure 1) shows the situation. (a) Assuming that the friction force acting on the crate is constant, find its magnitude. (b) How fast is the crate moving when it reaches the bottom of the ramp?

PART B

Suppose the foreman had released the box from rest at a height of 0.25 m above the ground. What would the crate's speed be when it reaches the bottom of the ramp?

### Illustration Description

The image consists of two diagrams, labeled (a) and (b), depicting a person pushing a box up a ramp. Both diagrams illustrate various physical parameters related to the motion of the box.

#### Diagram (a)

- **Scenario**: A person is pushing an orange box with mass \( m = 8.0 \, \text{kg} \) up a ramp.
- **Ramp and Motion Details**:
- The inclined ramp forms an angle of \( 30^\circ \) with the horizontal.
- Initial velocity (\( v_1 \)) of the box is \( 5.0 \, \text{m/s} \) at Point 1.
- The box travels from Point 1 to Point 2, a distance of \( 2.5 \, \text{m} \).
- The horizontal distance is marked as \( 1.6 \, \text{m} \).
- The vertical height from the end of the ramp to its start at Point 2 is \( 0.80 \, \text{m} \).
- At Point 2, the final velocity (\( v_2 \)) of the box is \( 0 \, \text{m/s} \).

#### Diagram (b)

- **Scenario**: Similar to diagram (a), the person is at the bottom of the ramp, but the orientation of the box's motion is different.
- **Ramp and Motion Details**:
- The box approaches the person with a velocity indicated as \( v_3 \).
- The box initially starts at rest at the top of the ramp (\( v_2 = 0 \, \text{m/s} \)) before approaching the person.
- **Point 3**: This point marks the beginning of the person's interaction with the box on the ramp.

### Explanation

These diagrams are often used in physics to illustrate the concepts of mechanics, specifically involving motion on inclined planes. Key ideas include calculating work done, energy conservation (potential and kinetic energy), and understanding the forces acting on an object on an incline.

Students may be asked to compute:
- The acceleration of the box as it moves along the incline.
- The net force exerted by the person on the box.
- Energy transformations as the box moves from Point 1 to Point 2 in Diagram (a), and vice versa in Diagram (b

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