Question

Steven carefully places a 1.65-kg wooden block on a frictionless ramp, so that the block begins to slide down the ramp from rest. The ramp makes an angle of 58.3� up from the horizontal. Which forces below do non-zero work on the block as it slides down the ramp?

a. normal
b. gravity
c. spring
d. friction

Answer 1

a. Gravity and c. Spring

Step-by-step explanation:

Formula for work energy
`W = \vec{F} \bullet \vec{S} = FScos(\alpha)`

whereas F is the force acting on the block, S is the distance traveled, and
`\alpha` is the angle between 2 vectors F and S.

If F is perpendicular to S, then

`\alpha = 90^o`

`cos(\alpha) = cos(90^o) = 0`

`W = FS*0 = 0`

a. Normal force is the reaction force acting from the ramp back on the wooden block. This force is perpendicular to the direction of sliding. Therefore this force would do no work.

b. Gravity is the force acting downward, this would have an angle of
`90^o - 58.3^o = 31.7^o` degrees so the work is non-zero.

c. Spring force would have the same direction as sliding so the work is non-zero.

d. Friction force would have the same direction as sliding. However, as this is a frictionless ramp, the friction coefficient would be 0. Friction force would also be zero and so as its work.