Question

Two forces act to double the speed of a particle, initially moving with kinetic energy of 1 J. One of the forces does 4 J of work. How much work does the other force do?

a) 1 J
b) 2 J
c) 3 J
d) 4 J

Answer 1

Two forces work to double a particle's speed, increasing its kinetic energy to 4 Joules. One force does 4 Joules of work; therefore, the other force must do -1 Joule, indicating it acted in the opposite direction.

Step-by-step explanation:

The question is about the work-energy principle in physics, specifically concerning the amount of work done by two forces to double the speed of a particle with a given initial kinetic energy.

If a particle initially has a kinetic energy of 1 Joule and its speed is doubled, its final kinetic energy will be 4 Joules due to the kinetic energy being proportional to the square of the speed (Kinetic Energy = 1/2 mv2).

The total work done on the particle to increase its kinetic energy to 4 Joules is 3 Joules (4 Joules - 1 Joule initial energy = 3 Joules work needed). If one force does 4 Joules of work, then the net work done by the two forces must equal 3 Joules. Therefore, the other force must have done -1 Joule of work (4 Joules - 1 Joule), indicating that it acted in the opposite direction to the motion of the particle.