if a particle has work of 8J and doubles its speed. how much work it has done? Can we still determine work in this problem without mass
doubling speed makes energy increase by 2^2.
so 8*4=32J
Work must be done ON the particle to increase its speed. Doubling the spped increases the kinetic energy to 32 J. Thus 24 J of work was done ON the particle. The particle "did" -24 J of work.
When you start by saying the particle "has work of 8J" I assumed you meant that it already had a kinetic energy of 8 J. Work is not something that you "have". It is something that you DO.
To determine the work done by the particle, we need to know the mass of the particle. Work is defined as the product of the force applied on an object and the displacement of the object in the direction of the force. The equation for calculating work is:
Work = Force × Displacement × cos(theta),
where theta is the angle between the force vector and the displacement vector.
In this case, we are given that the work done by the particle is 8J and the particle doubles its speed. However, without knowing the mass of the particle, we cannot determine the work done because we do not have enough information to calculate the force applied.
Work is directly proportional to the force applied, so if the speed of the particle doubles but the mass remains constant, the force required to achieve this change in speed would also increase. Therefore, the work done by the particle would also increase, but the exact value cannot be determined without knowing the mass.