Kinetic Energy - Spring Stiffness

[Kev1n]

1. A container of mass 100kg runs on overhead rails. the container is mounted on two wheels each having a mass of 15 kg,a diameter of 1.2 m and a radius of gyration of 0.4 m.
A)the total kinetic energy of the vehicle when traveling at 4ms-1
B) the spring stiffness reguired to bring the vehicle to rest in a distance of 300mm.



2. KE=(1/2)MV^2, Spring KE = (1/2) x stiffness x displacement ^2



3. A). KE = (1/2) 115x4^2 = 920nm
B). unsure

any pointers appreciated

 

[rl.bhat]

Total energy = Energy due to transactional motion of container + two wheels, and energy due to rotational motion of wheels.

 

[kerimek]

.

Hello, thank you for sharing this information. I would like to clarify and expand on your response to provide a more comprehensive understanding of the relationship between kinetic energy and spring stiffness.

Kinetic energy is the energy an object possesses due to its motion. In this case, the container on the overhead rails has a total mass of 100kg, which includes the two wheels with a mass of 15kg each. The container is traveling at a speed of 4ms^-1, which means it has a kinetic energy of 920 Joules (using the formula KE = 1/2 x mass x velocity^2).

Now, let's discuss the role of spring stiffness in bringing the vehicle to rest. Spring stiffness is a measure of how much force is required to compress or extend a spring by a certain distance. In this scenario, we need to calculate the spring stiffness required to bring the vehicle to rest in a distance of 300mm (0.3m).

The formula for spring potential energy is PE = 1/2 x spring stiffness x displacement^2. Therefore, to bring the vehicle to rest, the spring potential energy must be equal to the kinetic energy of the vehicle.

Setting these two equations equal to each other, we can solve for the spring stiffness (k):

1/2 x k x 0.3^2 = 920

k = (920 x 2)/0.3^2

k = 20,444.44 N/m

This means that a spring stiffness of 20,444.44 N/m is required to bring the vehicle to rest in a distance of 300mm.

I hope this explanation helps to clarify the relationship between kinetic energy and spring stiffness in this scenario. If you have any further questions, please don't hesitate to ask. Keep up the good work in your studies!