Answer:
a. Lighter
b. Lighter
c. Heavier
Explanation:
The apparent weight is the magnitude of the normal force. Draw a free body diagram in each situation and solve for the normal force, then compare to the actual weight.
a. Weight force mg pulls down, and normal force N pushes up. The coaster experiences centripetal acceleration (a = v²/r) towards the center of the hill, which is below the top of the hill. Sum of forces in the centripetal direction:
∑F = ma
mg − N = m v²/r
N = mg − m v²/r
The normal force is less than the actual weight, so the apparent weight is lighter.
b. Weight force mg pulls down, and normal force N pushes up at an angle θ. Sum of forces in the perpendicular direction:
∑F = ma
N − mg cos θ = 0
N = mg cos θ
cos θ is less than 1, so the normal force is less than the actual weight. Therefore, the apparent weight is lighter.
c. Weight force mg pulls down, and normal force pushes up. The elevator accelerates upwards. Sum of forces in the upwards direction:
N − mg = ma
N = mg + ma
The normal force is greater than the actual weight, so the apparent weight is heavier.
