Question

A 1220 kg automobile travels at 75 m/s. what net work would be required to bring it to a stop ​

Answer 1

W = - 3431250 [N]

Step-by-step explanation:

In order to solve this problem, we must use the theorem of work and energy conservation. This theorem tells us that the initial mechanical energy of a body plus the work done on this body must be equal to the final mechanical energy of the body. We must remember that the mechanical energy of a body is equal to the sum of kinetic energies plus potential energy plus elastic energy.

In this problem, we only have kinetic energy.

`E_(1)+W_(1-2)=E_(2)\\where:\\E_(1)=E_(pot)+E_(kine)+E_(elas)\\E_(pot) = 0\\E_(elas)=0\\E_(kine)=(1)/(2) *m*v^(2)`

And we have:

m = mass = 1220 [kg]

v = velocity = 75 [m/s]

As the carriage stops the final kinetic energy is zero.

Now replacing:

`(1)/(2) *1220*(75)^(2) +W_(1-2)=0\\W_(1-2)= - 3431250[N]`

Note: The negative force means that the force has to be carried out by the carriage. That is, no external force acts on the car to stop it.