18. A backpack full of books weighing 52.0 N rests on a table in a physics laboratory classroom. A spring with a force constant of 150 N/m is attached to the backpack and pulled horizontally. (a) If the spring is pulled until it stretches 2.00 cm and the pack remains at rest, what is the force of friction exerted on the backpack by the table? (b) Does your answer to part (a) change if the mass of the backpack is doubled? Explain.
18. A backpack full of books weighing 52.0 N rests on a table in a physics laboratory classroom. A spring with a force constant of 150 N/m is attached to the backpack and pulled horizontally. (a) If the spring is pulled until it stretches 2.00 cm and the pack remains at rest, what is the force of friction exerted on the backpack by the table? (b) Does your answer to part (a) change if the mass of the backpack is doubled? Explain.
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![**Problem 18:**
A backpack full of books weighing 52.0 N rests on a table in a physics laboratory classroom. A spring with a force constant of 150 N/m is attached to the backpack and pulled horizontally.
(a) If the spring is pulled until it stretches 2.00 cm and the pack remains at rest, what is the force of friction exerted on the backpack by the table?
(b) Does your answer to part (a) change if the mass of the backpack is doubled? Explain.
**Solution:**
1. **Finding the force of friction (part a):**
- The force exerted by the spring \( (F_{spring}) \) can be calculated using Hooke's Law: \( F_{spring} = k \cdot x \)
- \( k \) = 150 N/m (force constant of the spring)
- \( x \) = 2.00 cm = 0.020 m (stretch of the spring)
\[
F_{spring} = 150 \, \text{N/m} \times 0.020 \, \text{m} = 3.0 \, \text{N}
\]
- Since the backpack is at rest, the force of friction \( (f) \) must balance the spring force:
\[
f = 3.0 \, \text{N}
\]
2. **Effect of doubling the mass of the backpack (part b):**
- If the mass of the backpack is doubled, its weight will also be doubled.
- However, the force of friction in part (a) is only dependent on the force applied by the spring and not the weight of the backpack, given that the backpack remains at rest.
Therefore, the force of friction remains the same (3.0 N) even if the mass of the backpack is doubled.
---
This problem provides insight into the fundamental concept of friction and its independence from mass in certain static scenarios when analyzed under the condition of static equilibrium.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F356a0aa6-63f1-4559-a4cd-b1f23f853332%2Faf967037-b945-441e-9d3a-105e17b71279%2Fcvpu3uj_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem 18:**
A backpack full of books weighing 52.0 N rests on a table in a physics laboratory classroom. A spring with a force constant of 150 N/m is attached to the backpack and pulled horizontally.
(a) If the spring is pulled until it stretches 2.00 cm and the pack remains at rest, what is the force of friction exerted on the backpack by the table?
(b) Does your answer to part (a) change if the mass of the backpack is doubled? Explain.
**Solution:**
1. **Finding the force of friction (part a):**
- The force exerted by the spring \( (F_{spring}) \) can be calculated using Hooke's Law: \( F_{spring} = k \cdot x \)
- \( k \) = 150 N/m (force constant of the spring)
- \( x \) = 2.00 cm = 0.020 m (stretch of the spring)
\[
F_{spring} = 150 \, \text{N/m} \times 0.020 \, \text{m} = 3.0 \, \text{N}
\]
- Since the backpack is at rest, the force of friction \( (f) \) must balance the spring force:
\[
f = 3.0 \, \text{N}
\]
2. **Effect of doubling the mass of the backpack (part b):**
- If the mass of the backpack is doubled, its weight will also be doubled.
- However, the force of friction in part (a) is only dependent on the force applied by the spring and not the weight of the backpack, given that the backpack remains at rest.
Therefore, the force of friction remains the same (3.0 N) even if the mass of the backpack is doubled.
---
This problem provides insight into the fundamental concept of friction and its independence from mass in certain static scenarios when analyzed under the condition of static equilibrium.
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