A 1125 kg car carrying four 80 kg people travels over a rough "washboard" dirt road with corrugations 4.0 m apart which causes the car to bounce on its spring suspension. The car bounces with maximum amplitude when its speed is 17 km/h. The car now stops, and the four people get out. By how much does the car body rise on its suspension owing to this decrease in weight?
Use the information provided to get the natural (and resonant) frequency of the suspension system with a total mass of M = 1205 kg. From that you can derive the spring constant, k.
f = [1/(2 pi)] sqrt(k/M)
The natural frequency will be the rate at which the car goes over washboard bumps at the resonant (maximum amplitude) condition.
When the people get out, the car body will rise by an amount
(80 kg)(9.8 m/s^2)/k
Thank you!
Can't figure it out. Does it have something to do with finding w?
w=2pi/T = square root of k/m but I don't have K or T?
To find out how much the car body rises on its suspension due to the decrease in weight, we can use the concept of conservation of energy. Here are the steps to solve the problem:
1. Determine the initial kinetic energy of the car when it is bouncing at maximum amplitude. Since the maximum bouncing occurs at its speed of 17 km/h, we need to convert it to m/s. 1 km/h is equal to 0.2778 m/s, so the car's initial speed is 17 x 0.2778 = 4.7222 m/s. The kinetic energy of the car can be calculated using the formula KE = 0.5 * mass * velocity^2.
- Mass of the car = 1125 kg
- Velocity of the car = 4.7222 m/s
- Initial kinetic energy of the car = 0.5 * 1125 kg * (4.7222 m/s)^2
2. Calculate the final kinetic energy of the car when the four people get out.
- Mass of the car without people = 1125 kg - (4 * 80 kg) = 1125 kg - 320 kg = 805 kg (as each person weighs 80 kg)
- Since the car stops, its final velocity is 0 m/s.
- Final kinetic energy of the car = 0.5 * 805 kg * (0 m/s)^2
3. The difference between the initial and final kinetic energies gives us the energy used to lift the car body.
- Energy used to lift the car body = Initial kinetic energy - Final kinetic energy
4. Use the equation for potential energy to determine the height by which the car body rises.
- Potential energy = mass * acceleration due to gravity * height
- The mass of the car is the same without the people, which is 805 kg.
- The acceleration due to gravity is 9.8 m/s^2.
- The height is what we need to find.
Set the energy used to lift the car body equal to the potential energy and solve for height:
Energy used to lift the car body = Potential energy
Initial kinetic energy - Final kinetic energy = mass * acceleration due to gravity * height
Substitute the values and solve for height to find out by how much the car body rises on its suspension due to the decrease in weight.