The shock absorbers in a car act
as a big spring with .
When a 92.5 kg person gets in,
how far does the spring stretch?
(Hint: How much force does the person exert
on the car?)
(Unit = m)

Ask by Warner Stanley. in the United States

Mar 28,2025

Question

The shock absorbers in a car act
as a big spring with .
When a 92.5 kg person gets in,
how far does the spring stretch?
(Hint: How much force does the person exert
on the car?)
(Unit = m)

Ask by Warner Stanley. in the United States

Mar 28,2025

UpStudy AI · Accepted Answer

To find out how far the spring stretches when a 92.5 kg person gets in, we need to calculate the force exerted by the person on the car and then use Hooke's Law to find the distance the spring stretches.

Given:
- Spring constant $$ k = 21900 \, \text{N/m} $$
- Mass of the person $$ m = 92.5 \, \text{kg} $$

1. Calculate the force exerted by the person on the car:
$$ F = m \times g $$
where $$ g $$ is the acceleration due to gravity, approximately $$ 9.81 \, \text{m/s}^2 $$.

2. Use Hooke's Law to find the distance the spring stretches:
$$ F = k \times x $$
where $$ x $$ is the distance the spring stretches.

Let's calculate the force exerted by the person on the car and then find the distance the spring stretches.
Calculate the value by following steps:
- step0: Calculate:
  $$92.5\times 9.81$$
- step1: Multiply the numbers:
  $$907.425$$
The force exerted by the person on the car is approximately $$ 907.425 \, \text{N} $$.

Now, let's use Hooke's Law to find the distance the spring stretches:
$$ F = k \times x $$
$$ 907.425 = 21900 \times x $$

Let's solve for $$ x $$.
Solve the equation by following steps:
- step0: Solve for $$x$$:
  $$907.425=21900x$$
- step1: Swap the sides:
  $$21900x=907.425$$
- step2: Divide both sides:
  $$\frac{21900x}{21900}=\frac{907.425}{21900}$$
- step3: Divide the numbers:
  $$x=\frac{12099}{292000}$$
The distance the spring stretches is $$ x = \frac{12099}{292000} $$ meters.

Therefore, when a 92.5 kg person gets in, the spring stretches by approximately $$ \frac{12099}{292000} $$ meters.
When a 92.5 kg person gets in, the spring stretches by approximately $$ \frac{12099}{292000} $$ meters.

The shock absorbers in a car act
as a big spring with .
When a 92.5 kg person gets in,
how far does the spring stretch?
(Hint: How much force does the person exert
on the car?)
(Unit = m)

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The shock absorbers in a car act as a big spring with . When a 92.5 kg person gets in, how far does the spring stretch? (Hint: How much force does the person exert on the car?) (Unit = m)

Solución de inteligencia artificial de Upstudy

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preguntas relacionadas

Latest Physics Questions

The shock absorbers in a car act
as a big spring with .
When a 92.5 kg person gets in,
how far does the spring stretch?
(Hint: How much force does the person exert
on the car?)
(Unit = m)