Question

A 3.0 kg mass is released from rest at point A. The mass slides along the curved surface to point B in 6.0 seconds. Point B is 2.0 m lower than A and the mass is moving at 2.0 m/s at point B. Find the average power exerted by kinetic friction on the mass during this segment. a) 0 W b) -3 W c) -6 W d) -9 W e) -18 W

Answer 1

option d) -9 J

Step-by-step explanation:

Given:

Mass, m = 3.0 kg

time, t = 6.0 seconds

Velocity of mass, v = 2.0 m/s

height, h = 2 m

Now, using the concept of work-Energy theorem

we have

Net work done = change in kinetic energy

or

Work done by gravity + work done by the friction = Final kinetic energy - Initial kinetic energy

mgh +
`W_f` =
`(1)/(2)mv^2-0`

on substituting the values in the above equation, we get

3 × 9.8 × 2 +
`W_f` =
`(1)/(2)* 3*2^2`

or

58.8 +
`W_f` = 6

or

`W_f` = -52.8 J

here negative sign depicts that the work is done against the motion of the mass

also,

Power = (Work done)/time

or

Power = -52.8/6 = -8.8 W ≈ 9 J

Hence, option d) -9 J is correct