Question

two objects of different masses are pulled by the same force through the same distance. the work done on 1 is 500J and after the force, 1 moves twice as fast as 2. what is kinetic energy of 1 and 2. please explain

Answer 1

The force applied to each object is the same and the distance over which the force is applied is also the same for both objects.

So the work done (Fd) on each object is the same and that means that 500 J of work are done on object 2.

W = ? KE = mv^2 [Because the initial velocity of the objects is zero since they both start from rest]

So the kinetic energy of both objects immediately after being pulled is 500 J

Object 1 moves twice as fast as object 2

So for object 1 m(2v)^2 = 500 where m is the mass of object 1 and v is the velocity of object 2

4mv^2 = 500

mv^2 = 125

and for object 2 Mv^2 = 500 where M is the mass of object 2 and v is its velocity


Required ratio is mv^2/Mv^2 = 125/500

m/M = 1/4

So the ratio of the mass of object 1 to the mass of object 2 is 1/4