Forces and movement：練習問題

In judo, a player often lowers their center of gravity and widens their base of support to resist an opponent's throw. Which of the following best explains why this increases stability?

A diver performs a multiple-rotation somersault. If the diver moves from a tuck position to a straight position (layout) in mid-air, how do the moment of inertia and angular velocity change, assuming angular momentum is conserved?

During a 100m sprint start, an athlete pushes against the starting blocks with a resultant force of \( 800 \text{ N} \) at an angle of \( 30^\circ \) to the horizontal. Which of the following statements regarding the force components is correct?

In projectile motion, a shot putter releases the shot at a height of \( 2.1 \text{ meters} \) above the ground. To achieve the maximum horizontal distance, why is the optimal release angle usually less than \( 45^\circ \)?

Most joints in the human body function as third-class levers. Which of the following is a mechanical characteristic of this lever system during physical activity?

A sprinter is preparing for the start of a race in the blocks. Using the concept of Newton's Second Law of Motion, explain why a greater force applied against the blocks results in a higher acceleration.

A biomechanist calculates the moment of force (torque) at the hip during a leg extension. If the weight of the leg is \( 120 \text{ N} \) acting at a distance of \( 0.4 \text{ m} \) from the hip, and the quadriceps exert a force at varying angles, explain why the mechanical advantage changes throughout the range of motion.

How does Newton's Third Law of Motion explain the propulsion of a swimmer performing the breaststroke?

A cyclist is competing on a velodrome track with a banked curve of angle \( \theta \). The radius of the curve is \( r \).

(a) Identify the two primary forces whose components provide the necessary centripetal force for the cyclist to maintain a circular path on a banked track. (2 points)
(b) Using the formula for centripetal force \( F_c = \frac{mv^2}{r} \), calculate the factor by which the required inward force increases if the cyclist's speed \( v \) increases by \( 50\% \) while the radius \( r \) remains constant. (2 points)
(c) Explain why a steeper banking angle allows a cyclist to travel at higher speeds without sliding outwards, even if the coefficient of friction between the tires and the track is very low. (2 points)