Problem on Suspension of Cars

[sparsh]

Hi

The question is

In practice the suspension system of cars consists of a spring under compression combined with a shock absorber.which damps the vertical oscillations of the car . Drwa sketch graphs one in each case to illustrate how the vertical height of the car above the road will vary with time as the car just passes over a hump if the shock absorber is a) functioning properly b) improper functioning...

when a driver of mass 80kg steps into a car of mass 920 kg the vertical height of the car decreases by 2cm . If the car is driven over a series of equally spaced humps the amplitude of vibration becomes much larger for a ertain velocity.
- Explain why this occurs and calculate the particular velocity .

Please help me out with the above problems. I could not get anything related to it .

 

[Nate810]

The suspension system of a car consists of a spring and a shock absorber, which is designed to damp the vertical oscillations of the car when it passes over a hump. When the shock absorber is functioning properly, the vertical height of the car above the road will vary in a sinusoidal manner with time, as the car passes over the hump, with the amplitude of the oscillation gradually decreasing until it reaches a steady state. However, when the shock absorber is not functioning correctly, the amplitude of the oscillation will increase dramatically, resulting in a much higher vertical height of the car above the road.When a driver of mass 80kg steps into a car of mass 920 kg, the vertical height of the car decreases by 2cm. This is due to the additional weight of the driver, which causes the spring to compress slightly. When the car is travelling at a certain velocity over a series of equally spaced humps, the amplitude of vibration will increase due to the increased inertia of the car. This is because the car has more momentum at this velocity and therefore is able to overcome the damping forces of the shock absorber more easily. To calculate the particular velocity at which this occurs, we can use the equation v=√2gh, where g is the acceleration due to gravity and h is the height of the hump.

 

[kyle8921]

Hello,

The suspension system of cars is an important aspect of vehicle design that helps to provide a smooth and comfortable ride for passengers. As you mentioned, it consists of a spring under compression and a shock absorber, which work together to dampen the vertical oscillations of the car. However, if the shock absorber is not functioning properly, it can lead to an increase in the amplitude of vibration when the car passes over a hump.

To illustrate this, I have attached two graphs - one for a functioning shock absorber and one for an improper functioning shock absorber. In both cases, the vertical height of the car above the road is shown as a function of time as the car passes over a hump. As you can see, with a functioning shock absorber, the vertical height of the car decreases gradually and returns to the original height quickly. This is because the shock absorber is able to absorb the energy from the hump and prevent excessive oscillations.

However, with an improper functioning shock absorber, the vertical height of the car decreases rapidly and then bounces back up, creating a larger amplitude of vibration. This is because the shock absorber is unable to properly absorb the energy from the hump, resulting in a more jarring and uncomfortable ride for the passengers.

The reason for this increase in amplitude is due to the relationship between the mass of the car and the driver, as well as the velocity at which the car is traveling over the humps. When the driver steps into the car, the added mass causes the car to compress the spring more, resulting in a decrease in the vertical height. This decrease becomes even more significant when the car is driven over a series of equally spaced humps, as the added mass continues to compress the spring and increase the amplitude of vibration.

To calculate the particular velocity at which this occurs, we can use the equation F = ma, where F is the force exerted on the car, m is the mass of the car and driver, and a is the acceleration. When the car is driven over a hump, the force exerted on the car is equal to the weight of the car and driver, which we can calculate using the equation F = mg, where g is the acceleration due to gravity (9.8 m/s^2). By rearranging the equation F = ma, we can solve for the acceleration, which then gives us the particular velocity at which the amplitude of vibration becomes larger. This calculation