A 3.0-kg block slides on a frictionless 20$\degree$inclined plane. A force of 16 N acting parallel to the incline and up the incline is applied to the block. What is the acceleration of the block?
A)2.0 m/s2 down the incline
B)5.3 m/s2 up the incline
C)2.0 m/s2 up the incline
D)3.9 m/s2 down the incline
E)3.9 m/s2 up the incline

Question

Quizplus · Accepted Answer

The weight of the block down the incline is given by:
W = mg sinθ
where m = 3.0 kg, g = 9.8 m/s^2, and θ = 20°
W = (3.0 kg)(9.8 m/s^2)(sin20°) ≈ 9.95 N
The force parallel to the incline and up the incline is F = 16 N
The net force acting on the block up the incline is given by:
Fnet = F - W
Fnet = 16 N - 9.95 N = 6.05 N
The acceleration of the block up the incline is given by:
a = Fnet/m
a = (6.05 N)/(3.0 kg) ≈ 2.0 m/s^2
Therefore, the correct choice is C, with the block accelerating up the incline at 2.0 m/s^2.

A 30-Kg Block Slides on a Frictionless 20 °\degree° Inclined Plane

A 30-Kg Block Slides on a Frictionless 20 $\degree$ Inclined Plane