Forces, motion and movement：練習題

Which of the following is the correct mathematical definition for impulse in a biomechanical context?

A cyclist and their bike have a combined mass of \( 85 \, kg \). If they are traveling along a flat road at a constant velocity of \( 12 \, m \cdot s^{-1} \) and the total resistive forces (air resistance and friction) equal \( 35 \, N \), what is the magnitude of the forward motive force generated by the cyclist?

An athlete lifts a \( 50 \, kg \) barbell a vertical distance of \( 2.0 \, m \) in \( 0.5 \, seconds \). Calculate the average power generated by the athlete. (Assume \( g = 9.81 \, m \cdot s^{-2} \))

According to Newton’s Third Law of Motion, when a basketball player jumps vertically, the force they exert downwards on the floor is matched by an "equal and opposite" reaction force. What is the primary mechanical effect of this reaction force?

A golfer hits a ball with a specific initial velocity and angle. Ignoring air resistance, which of the following identifies the acceleration of the ball at the very peak of its parabolic flight path?

Define torque (moment of force) and identify the two primary components that determine its magnitude in a sporting context.

Explain the difference between the static coefficient of friction and the dynamic coefficient of friction, and how this affects an athlete's ability to initiate movement from a stationary position.

Using the Magnus effect and principles of fluid dynamics, explain why a soccer ball with clockwise horizontal spin (when viewed from above) will curve to the right during its flight path.

A swimmer competes in a race where they must swim two full lengths of a 50-meter pool, returning exactly to the starting block where they began.

(a) Calculate the total distance traveled by the swimmer.
(b) Determine the displacement of the swimmer upon finishing the race and explain why this value differs from the distance, referring to the properties of vector and scalar quantities.

An elite cyclist and their bicycle have a combined mass of \( 80 \, kg \). From a stationary start, the cyclist accelerates uniformly at a rate of \( 1.5 \, m \cdot s^{-2} \).

(a) Using Newton's Second Law of Motion, calculate the magnitude of the resultant force acting on the cyclist.
(b) After reaching a certain speed, the cyclist continues to apply the same force calculated in part (a), but now encounters an air resistance force of \( 20 \, N \). Calculate the new acceleration of the cyclist.
(c) Distinguish between velocity and speed in the context of a cyclist traveling around a circular velodrome track at a constant pace.