Two people with a combined mass of 135 kg hop into an old car with worn-out shock absorbers. This causes the springs to compress by 9.80 cm. When the car hits a bump in the road, it oscillates up and down with a period of 1.76 s.

Find the total load supported by the springs.

Find the mass of the car.

To find the total load supported by the springs, we can use Hooke's Law, which states that the force exerted by a spring is proportional to the displacement of the spring.

Step 1: Convert the displacement from centimeters to meters.
Given that the springs compress by 9.80 cm, we need to convert this to meters by dividing by 100:
displacement (m) = 9.80 cm / 100 = 0.098 m

Step 2: Calculate the force exerted by one spring.
Hooke's Law formula is: F = k * x
Where F is the force exerted by the spring, k is the spring constant, and x is the displacement.

Since there are two springs supporting the load, we need to find the force exerted by one spring. So we divide the displacement by 2:
displacement (m) = 0.098 m / 2 = 0.049 m

Step 3: Find the spring constant.
The spring constant represents the stiffness of the springs. It can be calculated using the formula:
k = (2 * π)² * (m / T²)
Where k is the spring constant, π is a mathematical constant (approximately 3.14159), m is the combined mass, and T is the period of oscillation.

Given that the combined mass is 135 kg and the period is 1.76 s, we can substitute these values into the formula:
k = (2 * (3.14159)²) * (135 kg / (1.76 s)²)

Step 4: Calculate the force exerted by one spring.
Now we can calculate the force exerted by one spring using Hooke's Law formula:
F = k * x
Where F is the force exerted by the spring, k is the spring constant, and x is the displacement.

Substituting the spring constant and the displacement into the formula:
F = (k) * (x) = (k) * (0.049 m)

Step 5: Find the total load supported by the springs.
Since there are two springs supporting the load, we multiply the force exerted by one spring by 2 to get the total load supported by the springs.

Total load supported by the springs = 2 * F

To find the mass of the car, we can use the formula for the total load supported by the springs.

Total load supported by the springs = mass of the car * acceleration due to gravity
acceleration due to gravity ≈ 9.8 m/s²

Step 6: Calculate the mass of the car.
Using the formula for the total load supported by the springs, we can rearrange it to solve for the mass of the car:

mass of the car = Total load supported by the springs / acceleration due to gravity

Substituting the values into the formula:
mass of the car = (Total load supported by the springs) / (9.8 m/s²)