The normal force on an extreme skier descending a very steep slope can be zero if
(a) his speed is great enough.
(b) he leaves the slope (no longer touches the snow).
(c) the slope is greater than 75°.
(d) the slope is vertical (90°).
The correct answer and explanation is :
The correct answer is (b) he leaves the slope (no longer touches the snow).
Explanation:
The normal force is the force exerted by a surface to support the weight of an object resting on it. It acts perpendicular to the surface. In the case of an extreme skier descending a slope, the skier’s weight can be broken down into two components: one parallel to the slope (which causes the skier to accelerate down the slope) and one perpendicular to the slope (which is counteracted by the normal force).
At high speeds, or under certain conditions, the skier may experience a situation where the normal force becomes zero. This happens when the skier is effectively “airborne” — no longer in contact with the slope. When the skier reaches a certain speed or angle, the normal force can disappear entirely as the skier leaves the surface of the slope, experiencing a free-fall situation.
For the skier to leave the slope:
- The skier must be moving at a high enough speed that the component of the gravitational force acting perpendicular to the surface (which creates the normal force) is overcome by the skier’s centripetal force due to the curved path of the descent.
- This typically occurs when the skier reaches the top of a jump or an extreme slope. In this case, there is no longer any contact between the skier and the snow, and the normal force is zero.
For answer choices:
- (a) His speed being great enough might reduce the normal force but does not guarantee it reaches zero.
- (c) Slope greater than 75°: A very steep slope does not ensure zero normal force, though it increases the component of weight parallel to the slope.
- (d) Slope being vertical (90°): At a vertical slope, the skier would likely not be able to maintain contact with the snow due to the forces at play, leading to the skier falling off before this condition is met.
Thus, the only way the normal force can truly be zero is if the skier leaves the slope and is no longer in contact with the snow.
Here is an illustration of the extreme skier descending the steep slope and becoming airborne, where the normal force becomes zero. This demonstrates the situation where the skier is no longer in contact with the snow, confirming that answer (b) is correct.