Question

A block of mass 2.0 kg, initially at rest is pulled up on a smooth incline of angle 30⁰ with the horizontal. If the block moves with an acceleration of 1.0 m/s², find the power delivered by the pulling force at a time 4.0 s after the motion starts. What is the average power delivered during the 4.0 s after the motion starts?

• A. 47 W, 24 W
• B. 94 N, 48 N
• C. 23 N, 12 N
• D. None of these

Answer 1

Answer: (A)

. 47 W, 24 W

Resolving the forces parallel to the incline , we get

F-mg sin$\theta$=ma

or, F=ma+mg sin$\theta$

Substituting the values, we get

$F=2\times 1+2\times 9.8\times \frac{1}{2}=11.8N$

The velocity at t = 4s is

v = u + at = 0 + 1.4 = 4 m/s.

The power delivered by the force at t = 4 s is

$P=F.v=11.8\times 8=47W$.

The displacement during the first 4 sec is

$x=\frac{1}{2}$a$t^2$ = 8 m.

The work done by F in these 4 sec = $W=F.x=11.8\times 8=94.4J$.

Average power delivered =$P_{avg}=\frac{W}{t}=\frac{94.4}{4}$ = 24 W.