If you have two objects, one four times heavier then the other, both at rest on a frictionless surface, and a person pushes against them for a distance of 5 meters. Assuming the force applied on both objects are equal, the kinetic enrgy of the light object is?
I say one-quarter of the heavier car
They will have the same KE (if pushed separately), since the same amount of work will have been done on each.
If one has 1/4 of the mass, the V^2 of the lighter object will be 4 times higher. That means its speed will be twice the other.
To determine the kinetic energy of the light object in this scenario, we can use the principle of conservation of energy. This principle states that the total mechanical energy within a system remains constant unless acted upon by external forces.
In this case, the person is pushing with the same force on both objects, which means they will have the same acceleration. Since the objects are starting from rest and moving on a frictionless surface, the work done by the person's force will be equal to the change in kinetic energy of the objects.
The work done on an object is given by the formula: work = force * distance * cos(theta). In this case, theta is the angle between the direction of the force and the direction of displacement, so it is 0 degrees since the person is pushing in the same direction as the displacement.
Since the force applied is the same for both objects and the distance is the same, the work done on both objects will be equal. Therefore, the change in kinetic energy will also be the same for both objects.
Now, since the heavier object is four times the weight of the lighter object, we can say that the heavier object has four times the mass. Therefore, the change in kinetic energy for the heavier object will be equal to four times the change in kinetic energy for the lighter object.
Since the total change in kinetic energy for both objects is equal, we can say that the change in kinetic energy for the lighter object is one-fourth the change in kinetic energy for the heavier object.
Hence, the kinetic energy of the light object is one-fourth of the kinetic energy of the heavier object.