You pull the mass down 2 cm and hold it there. You exert a force of 10 N down- wards on the mass to hold it stationary in this position. (b) What force is the spring exerting on the mass? (c) What is the spring constant of the spring? You let the mass go. (d) What is the net force on the mass immediately after you let it go? (e) What is the maximum magnitude of the acceleration of the mass?

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**Problem 7.2:**

A 3 kg mass hangs from a spring such that it is at rest.

(a) What force is the spring exerting on the mass?

---

In this problem, a mass is suspended from a spring, and the mass is at rest. The question is asking for the force exerted by the spring on this mass. This force is typically the tension in the spring and is equal in magnitude to the weight of the mass hanging from it, according to Newton’s third law of motion. The calculation involves using the formula:

\[
\text{Force (F)} = \text{mass (m)} \times \text{acceleration due to gravity (g)}
\]

Given:
- Mass (m): 3 kg
- Gravitational acceleration (g): approximately 9.8 m/s²

Thus, the force exerted by the spring can be calculated as: 

\[
F = 3 \, \text{kg} \times 9.8 \, \text{m/s}^2
\]

Which equals 29.4 N (newtons).

This force is the restoring force that the spring exerts to keep the mass at rest.
Transcribed Image Text:**Problem 7.2:** A 3 kg mass hangs from a spring such that it is at rest. (a) What force is the spring exerting on the mass? --- In this problem, a mass is suspended from a spring, and the mass is at rest. The question is asking for the force exerted by the spring on this mass. This force is typically the tension in the spring and is equal in magnitude to the weight of the mass hanging from it, according to Newton’s third law of motion. The calculation involves using the formula: \[ \text{Force (F)} = \text{mass (m)} \times \text{acceleration due to gravity (g)} \] Given: - Mass (m): 3 kg - Gravitational acceleration (g): approximately 9.8 m/s² Thus, the force exerted by the spring can be calculated as: \[ F = 3 \, \text{kg} \times 9.8 \, \text{m/s}^2 \] Which equals 29.4 N (newtons). This force is the restoring force that the spring exerts to keep the mass at rest.
**Educational Text on Spring-Mass System**

You pull the mass down 2 cm and hold it there. You exert a force of 10 N downwards on the mass to hold it stationary in this position.

**Questions:**

(b) What force is the spring exerting on the mass?

(c) What is the spring constant of the spring?

After releasing the mass:

(d) What is the net force on the mass immediately after you let it go?

(e) What is the maximum magnitude of the acceleration of the mass?

(f) What is the maximum elastic potential energy stored by the mass?

(g) What is the maximum kinetic energy of the mass?

(h) What is the maximum speed of the mass?

(i) What is the time period of the motion?
Transcribed Image Text:**Educational Text on Spring-Mass System** You pull the mass down 2 cm and hold it there. You exert a force of 10 N downwards on the mass to hold it stationary in this position. **Questions:** (b) What force is the spring exerting on the mass? (c) What is the spring constant of the spring? After releasing the mass: (d) What is the net force on the mass immediately after you let it go? (e) What is the maximum magnitude of the acceleration of the mass? (f) What is the maximum elastic potential energy stored by the mass? (g) What is the maximum kinetic energy of the mass? (h) What is the maximum speed of the mass? (i) What is the time period of the motion?
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