A​ heavy-duty shock absorber is compressed 4 cm from its equilibrium position by a mass of 500nbspkg. How much work is required to compress the shock absorber 4 cm from its equilibrium​ position? (A mass of 500 kg exerts a force​ (in newtons) of 500​g, where galmost equals9.8 m divided by s squared​.)

To solve this problem, we need to calculate the work required to compress the shock absorber by 4 cm from its equilibrium position, given that a 500 kg mass is compressing it. Let's break it down step-by-step.

### Step 1: Determine the force exerted by the mass
The force exerted by the mass of 500 kg is due to gravity. The formula for gravitational force is:

\[
F = m \cdot g
\]

Where:
- \( m = 500 \, \text{kg} \) (mass of the object),
- \( g = 9.8 \, \text{m/s}^2 \) (acceleration due to gravity).

Substitute the values:

\[
F = 500 \, \text{kg} \times 9.8 \, \text{m/s}^2 = 4900 \, \text{N}
\]

Thus, the force exerted by the mass is 4900 N.

### Step 2: Work done in compressing the spring
Work done to compress a spring (or shock absorber) follows Hooke's Law, which is expressed as:

\[
W = \frac{1}{2} k x^2
\]

Where:
- \( W \) is the work done,
- \( k \) is the spring constant,
- \( x \) is the compression distance from the equilibrium position.

We need to find \( k \), the spring constant. From Hooke's Law, the force exerted by a spring is:

\[
F = kx
\]

Where:
- \( F = 4900 \, \text{N} \) (force exerted by the mass),
- \( x = 0.04 \, \text{m} \) (compression distance in meters, since 4 cm = 0.04 m).

Rearranging this equation to solve for \( k \):

\[
k = \frac{F}{x} = \frac{4900}{0.04} = 122500 \, \text{N/m}
\]

### Step 3: Calculate the work required
Now, we can substitute \( k = 122500 \, \text{N/m} \) and \( x = 0.04 \, \text{m} \) into the work formula:

\[
W = \frac{1}{2} \cdot 122500 \cdot (0.04)^2
\]

Let's calculate this.

\[
W = \frac{1}{2} \cdot 122500 \cdot 0.0016 = 98 \, \text{J}
\]

Thus, the work required to compress the shock absorber by 4 cm from its equilibrium position is **98 joules**.

---

Would you like more details on any part of this explanation or further questions? Here are some related questions:

1. What is Hooke's Law, and how does it apply to springs and shock absorbers?
2. How is the spring constant determined for different materials?
3. What is the difference between potential energy stored in a spring and work done to compress it?
4. How does gravitational force relate to mass and acceleration?
5. Can we generalize this process for non-linear shock absorbers?

**Tip:** Always convert all units to SI (meters, kilograms, and seconds) for consistency when calculating forces and work.

A heavy-duty shock absorber is compressed 4 cm from its equilibrium position by a mass of 500 kg. How much work is required to compress the shock absorber 4 cm from its equilibrium position? (A mass of 500 kg exerts a force (in newtons) of 500g, where g almost equals 9.8 m/s².)

Learn how to calculate the work required to compress a heavy-duty shock absorber by 4 cm from its equilibrium position using Hooke's Law. This problem involves the gravitational force of a 500 kg mass and the compression of the spring. Suitable for students in Grades 9-12.

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