**Physics Problem: Work Done by Forces on an Inclined Track** --- **Scenario:** A cart for hauling ore out of a gold mine has a mass of 439 kg, including its load. The cart runs along a straight stretch of track that climbs a shallow 4.75° incline. A donkey, which is trudging along and to the side of the track, has the unenviable job of pulling the cart up the slope with a 441 N force for a distance of 185 m by means of a rope that is parallel to the slope but makes an angle of 14.5° with the track. **Assumptions:** Model the rolling resistance of the cart as though it were sliding on the track with a coefficient of friction of 0.0163. Use \( g = 9.81 \, \text{m/s}^2 \), and note that angle A in the image is the angle of the incline while angle B is the angle the rope makes with the track. **Tasks:** 1. **Find the work \( W_d \) that the donkey performs on the cart during this process.** \[ W_d = \_\_\_\_ \, \text{J} \] 2. **Find the work \( W_g \) that the force of gravity performs on the cart during this process.** \[ W_g = \_\_\_\_ \, \text{J} \] 3. **Calculate the work \( W_f \) done on the cart by friction during this process.** \[ W_f = \_\_\_\_ \, \text{J} \] --- **Diagram Explanation:** The image includes a diagram of the scenario with a cart on a track, a donkey pulling the cart via a rope, and labels indicating the track incline (4.75°) and the horizontal ground. The angle \( A \) represents the track's incline, while angle \( B \) shows the angle the rope makes with the track.
**Physics Problem: Work Done by Forces on an Inclined Track** --- **Scenario:** A cart for hauling ore out of a gold mine has a mass of 439 kg, including its load. The cart runs along a straight stretch of track that climbs a shallow 4.75° incline. A donkey, which is trudging along and to the side of the track, has the unenviable job of pulling the cart up the slope with a 441 N force for a distance of 185 m by means of a rope that is parallel to the slope but makes an angle of 14.5° with the track. **Assumptions:** Model the rolling resistance of the cart as though it were sliding on the track with a coefficient of friction of 0.0163. Use \( g = 9.81 \, \text{m/s}^2 \), and note that angle A in the image is the angle of the incline while angle B is the angle the rope makes with the track. **Tasks:** 1. **Find the work \( W_d \) that the donkey performs on the cart during this process.** \[ W_d = \_\_\_\_ \, \text{J} \] 2. **Find the work \( W_g \) that the force of gravity performs on the cart during this process.** \[ W_g = \_\_\_\_ \, \text{J} \] 3. **Calculate the work \( W_f \) done on the cart by friction during this process.** \[ W_f = \_\_\_\_ \, \text{J} \] --- **Diagram Explanation:** The image includes a diagram of the scenario with a cart on a track, a donkey pulling the cart via a rope, and labels indicating the track incline (4.75°) and the horizontal ground. The angle \( A \) represents the track's incline, while angle \( B \) shows the angle the rope makes with the track.
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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![**Physics Problem: Work Done by Forces on an Inclined Track**
---
**Scenario:**
A cart for hauling ore out of a gold mine has a mass of 439 kg, including its load. The cart runs along a straight stretch of track that climbs a shallow 4.75° incline. A donkey, which is trudging along and to the side of the track, has the unenviable job of pulling the cart up the slope with a 441 N force for a distance of 185 m by means of a rope that is parallel to the slope but makes an angle of 14.5° with the track.
**Assumptions:**
Model the rolling resistance of the cart as though it were sliding on the track with a coefficient of friction of 0.0163. Use \( g = 9.81 \, \text{m/s}^2 \), and note that angle A in the image is the angle of the incline while angle B is the angle the rope makes with the track.
**Tasks:**
1. **Find the work \( W_d \) that the donkey performs on the cart during this process.**
\[ W_d = \_\_\_\_ \, \text{J} \]
2. **Find the work \( W_g \) that the force of gravity performs on the cart during this process.**
\[ W_g = \_\_\_\_ \, \text{J} \]
3. **Calculate the work \( W_f \) done on the cart by friction during this process.**
\[ W_f = \_\_\_\_ \, \text{J} \]
---
**Diagram Explanation:**
The image includes a diagram of the scenario with a cart on a track, a donkey pulling the cart via a rope, and labels indicating the track incline (4.75°) and the horizontal ground. The angle \( A \) represents the track's incline, while angle \( B \) shows the angle the rope makes with the track.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8e6897f5-0596-4cca-8959-384f442956db%2Ff921d4f2-b511-4e52-b2a2-d95a778d29fa%2Fe6whlq6.jpeg&w=3840&q=75)
Transcribed Image Text:**Physics Problem: Work Done by Forces on an Inclined Track**
---
**Scenario:**
A cart for hauling ore out of a gold mine has a mass of 439 kg, including its load. The cart runs along a straight stretch of track that climbs a shallow 4.75° incline. A donkey, which is trudging along and to the side of the track, has the unenviable job of pulling the cart up the slope with a 441 N force for a distance of 185 m by means of a rope that is parallel to the slope but makes an angle of 14.5° with the track.
**Assumptions:**
Model the rolling resistance of the cart as though it were sliding on the track with a coefficient of friction of 0.0163. Use \( g = 9.81 \, \text{m/s}^2 \), and note that angle A in the image is the angle of the incline while angle B is the angle the rope makes with the track.
**Tasks:**
1. **Find the work \( W_d \) that the donkey performs on the cart during this process.**
\[ W_d = \_\_\_\_ \, \text{J} \]
2. **Find the work \( W_g \) that the force of gravity performs on the cart during this process.**
\[ W_g = \_\_\_\_ \, \text{J} \]
3. **Calculate the work \( W_f \) done on the cart by friction during this process.**
\[ W_f = \_\_\_\_ \, \text{J} \]
---
**Diagram Explanation:**
The image includes a diagram of the scenario with a cart on a track, a donkey pulling the cart via a rope, and labels indicating the track incline (4.75°) and the horizontal ground. The angle \( A \) represents the track's incline, while angle \( B \) shows the angle the rope makes with the track.
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