When a spring is relaxed, it has a length Lo= 18.0 cm. a. (FRC.4) If 1.8 N force is required to stretch the spri Z= 21.0 cm, what is the spring constant k of the

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**2. Spring Mechanics**

When a spring is relaxed, it has a length \(L_0 = 18.0 \, \text{cm}\).

**a.** (FRC.4) If a force of 1.8 N is required to stretch the spring to a length \(|\vec{L}| = 21.0 \, \text{cm}\), what is the spring constant \(k\) of the spring?

**b.** (FRC.4) A 0.25 kg mass is attached to a spring, and the other end is attached to a post on a frictionless table so that the block can slide horizontally on the surface. The spring is compressed by \(|\vec{s}| = 5.0 \, \text{cm}\) and released from rest at \(t=0 \, \text{s}\). 

What is the spring force, \(\vec{F}_p\), when the spring is compressed 5.0 cm, as shown in the diagram?

*Diagram Description:*
The diagram depicts a spring attached to a mass on a frictionless table, compressed to 5.0 cm. The spring is indicated with a coil, and the compressive force is shown as an arrow pushing to the left, labeled \(\vec{L}\). The initial relaxed length \(L_0\) of the spring is also marked.

**c.** (COM.1) If the mass is released from rest from \(\vec{L} = (13.0, 0, 0) \, \text{cm}\) at \(t=0 \, \text{s}\), what is the momentum of the mass after 0.01 s? Assume the force is nearly constant on a 0.01 s timestep.

**d.** (COM.1) What is the position \(\vec{L}\) of the mass at \(t=0.01 \, \text{s}\)?
Transcribed Image Text:**2. Spring Mechanics** When a spring is relaxed, it has a length \(L_0 = 18.0 \, \text{cm}\). **a.** (FRC.4) If a force of 1.8 N is required to stretch the spring to a length \(|\vec{L}| = 21.0 \, \text{cm}\), what is the spring constant \(k\) of the spring? **b.** (FRC.4) A 0.25 kg mass is attached to a spring, and the other end is attached to a post on a frictionless table so that the block can slide horizontally on the surface. The spring is compressed by \(|\vec{s}| = 5.0 \, \text{cm}\) and released from rest at \(t=0 \, \text{s}\). What is the spring force, \(\vec{F}_p\), when the spring is compressed 5.0 cm, as shown in the diagram? *Diagram Description:* The diagram depicts a spring attached to a mass on a frictionless table, compressed to 5.0 cm. The spring is indicated with a coil, and the compressive force is shown as an arrow pushing to the left, labeled \(\vec{L}\). The initial relaxed length \(L_0\) of the spring is also marked. **c.** (COM.1) If the mass is released from rest from \(\vec{L} = (13.0, 0, 0) \, \text{cm}\) at \(t=0 \, \text{s}\), what is the momentum of the mass after 0.01 s? Assume the force is nearly constant on a 0.01 s timestep. **d.** (COM.1) What is the position \(\vec{L}\) of the mass at \(t=0.01 \, \text{s}\)?
Expert Solution
Step 1

Given:-

a)

it has a length Lo= 18.0 cm = 0.18 m 

The force on the spring F = 1.8 N 

The force is required to stretch the spring to a length L = 21.0 cm= 0.21 m 

So the distance of the spring  d = 0.21-0.18 = 0.03 m 

Now The spring force is given as 

F = Kx K = Fx=1.80.03= 60 N/mK = 60 N/m 

So the spring constant is 60 N/m 

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