Dean Fabien exerts a force P on the car at an angle a = 20°. The 1760 kg car has front wheel drive. Prof. Schulz, the driver, spins the front wheels, and the coefficient of kinetic friction uk = 0.02. [Hint: Think about what direction friction should be drawn. The car is in reverse...] The combined effect of friction and a snow pile behind the rear tires exerts a horizontal resting force S. Getting the car to move requires overcoming a resisting force S = 420 N. a. What force P must Dean Fabien exert? b. What value of a will minimize the magnitude of P that Dean Fabien would have to exert to overcome the resisting force S = 420 N? [Hint: Think calculus!] What force must he exert (at this new angle)? C.
Dean Fabien exerts a force P on the car at an angle a = 20°. The 1760 kg car has front wheel drive. Prof. Schulz, the driver, spins the front wheels, and the coefficient of kinetic friction uk = 0.02. [Hint: Think about what direction friction should be drawn. The car is in reverse...] The combined effect of friction and a snow pile behind the rear tires exerts a horizontal resting force S. Getting the car to move requires overcoming a resisting force S = 420 N. a. What force P must Dean Fabien exert? b. What value of a will minimize the magnitude of P that Dean Fabien would have to exert to overcome the resisting force S = 420 N? [Hint: Think calculus!] What force must he exert (at this new angle)? C.
Transcribed Image Text:**Problem Description:**
Dean Fabien exerts a force \( P \) on the car at an angle \( \alpha = 20^\circ \). The 1760 kg car has front-wheel drive. Prof. Schulz, the driver, spins the front wheels, and the coefficient of kinetic friction \( \mu_k = 0.02 \). [Hint: Think about what direction friction should be drawn. The car is in reverse...] The combined effect of friction and a snow pile behind the rear tires exerts a horizontal resisting force \( S \). Getting the car to move requires overcoming a resisting force \( S = 420 \, \text{N} \).
Questions:
a. What force \( P \) must Dean Fabien exert?
b. What value of \( \alpha \) will minimize the magnitude of \( P \) that Dean Fabien would have to exert to overcome the resisting force \( S = 420 \, \text{N} \)? [Hint: Think calculus!]
c. What force must he exert (at this new angle)?
**Visual Explanation:**
1. **Image of a Car:**
- A person is seen pushing a snow-covered car. The car is positioned in front of a snow pile which offers resistance.
2. **Diagram of Forces:**
- A side view of the car is shown with dimensions:
- Distance from the rear to the center of mass: 1.62 m
- Distance from the front to the center of mass: 2.55 m
- Total length from rear to front: 3.40 m
- Height from the ground to the point where force \( P \) is applied: 0.90 m
- Force \( P \) is shown acting at an angle \( \alpha \) from the horizontal.
- The resisting force \( S \) is displayed acting horizontally at the rear.
This exercise involves applying concepts of physics, specifically forces and friction, to solve problems regarding the movement of the car stuck in snow with the application of external force and optimizing that force using basic calculus principles.
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![**Problem Description:**
Dean Fabien exerts a force \( P \) on the car at an angle \( \alpha = 20^\circ \). The 1760 kg car has front-wheel drive. Prof. Schulz, the driver, spins the front wheels, and the coefficient of kinetic friction \( \mu_k = 0.02 \). [Hint: Think about what direction friction should be drawn. The car is in reverse...] The combined effect of friction and a snow pile behind the rear tires exerts a horizontal resisting force \( S \). Getting the car to move requires overcoming a resisting force \( S = 420 \, \text{N} \).
Questions:
a. What force \( P \) must Dean Fabien exert?
b. What value of \( \alpha \) will minimize the magnitude of \( P \) that Dean Fabien would have to exert to overcome the resisting force \( S = 420 \, \text{N} \)? [Hint: Think calculus!]
c. What force must he exert (at this new angle)?
**Visual Explanation:**
1. **Image of a Car:**
- A person is seen pushing a snow-covered car. The car is positioned in front of a snow pile which offers resistance.
2. **Diagram of Forces:**
- A side view of the car is shown with dimensions:
- Distance from the rear to the center of mass: 1.62 m
- Distance from the front to the center of mass: 2.55 m
- Total length from rear to front: 3.40 m
- Height from the ground to the point where force \( P \) is applied: 0.90 m
- Force \( P \) is shown acting at an angle \( \alpha \) from the horizontal.
- The resisting force \( S \) is displayed acting horizontally at the rear.
This exercise involves applying concepts of physics, specifically forces and friction, to solve problems regarding the movement of the car stuck in snow with the application of external force and optimizing that force using basic calculus principles.](https://content.bartleby.com/qna-images/question/f920003c-b80d-4d46-9199-437e1336b936/71d38d76-2255-41bd-a514-c26d48b08042/9nxutc_processed.png)
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