Two people with a combined mass of 130 kg hop into an old car with worn-out shock absorbers. This causes the springs to compress by 9.50 cm. When the car hits a bump in the road, it oscillates up and down with a period of 1.66 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 consider the equilibrium position of the car when it is not hitting any bumps.
The equilibrium position occurs when the car is stationary and the springs are fully extended. In this position, the weight of the car and the weight of the people are balanced by the upward force from the compressed springs.
Let's denote the total load supported by the springs as F_load. Since we know the mass of the two people combined is 130 kg, we can calculate the weight of the people as follows:
Weight of the people = combined mass of the people × acceleration due to gravity
Weight of the people = 130 kg × 9.8 m/s^2 = 1274 N
In the equilibrium position, the force exerted by the springs upward is equal in magnitude but opposite in direction to the weight of the people. Therefore, we can say:
F_load = Weight of the people
F_load = 1274 N
So, the total load supported by the springs is 1274 N.
To find the mass of the car, we can use the period of oscillation of the car. The period is given as 1.66 s.
The period of oscillation, denoted as T, is related to the mass of the car and the spring constant, k, by the equation:
T = 2π × √(m/k)
Where T is the period, m is the mass, and k is the spring constant.
Since we are given the period and want to find the mass of the car, we can rewrite the equation as:
m = (T/2π)^2 × k
We need to determine the spring constant, k, to find the mass of the car. Unfortunately, the given information does not provide the spring constant.
Therefore, without knowing the spring constant, we cannot determine the mass of the car.