Il A 100 kg basketball player can leap straight up in the...

Il A $100 \mathrm{kg}$ basketball player can leap straight up in the air to a height of $80 \mathrm{cm},$ as shown in FIGURE P7.47 You can understand how by analyzing the situation as follows: a. The player bends his legs until the upper part of his body has dropped by $60 \mathrm{cm},$ then he begins his jump. Draw separate free-body diagrams for the player and for the floor as he is jumping, but before his feet leave the ground. b. Is there a net force on the player as he jumps (before his feet leave the ground)? How can that be? Explain. c. With what speed must the player leave the ground to reach a height of $80 \mathrm{cm} ?$ d. What was his acceleration, assumed to be constant, as be jumped? e. Suppose the player jumps while standing on a bathroom scale that reads in newtons. What does the scale read before he jumps, as he is jumping, and after his feet leave the ground?

Il A $100 \mathrm{kg}$ basketball player can leap straight up in the air to a height of $80 \mathrm{cm},$ as shown in FIGURE P7.47 You can understand how by analyzing the situation as follows:
a. The player bends his legs until the upper part of his body has dropped by $60 \mathrm{cm},$ then he begins his jump. Draw separate free-body diagrams for the player and for the floor as he is jumping, but before his feet leave the ground.
b. Is there a net force on the player as he jumps (before his feet leave the ground)? How can that be? Explain.
c. With what speed must the player leave the ground to reach a height of $80 \mathrm{cm} ?$
d. What was his acceleration, assumed to be constant, as be jumped?
e. Suppose the player jumps while standing on a bathroom scale that reads in newtons. What does the scale read before he jumps, as he is jumping, and after his feet leave the ground?

Key Concepts

Normal Force and Scale Readings

The normal force is the force exerted by a surface to support the weight of an object resting on it. It directly correlates with what a force-measuring device, like a scale, reads. Analyzing the variations in the normal force during different phases of a jump—before, during, and after takeoff—helps understand how the scale would display different readings based on the additional forces generated during the action.

Constant Acceleration Kinematics

Kinematics under constant acceleration offers the formulas needed to relate displacement, initial velocity, time, and acceleration. In the context of a jump, these kinematic equations allow us to determine the initial takeoff speed needed to reach a certain height and the average acceleration experienced during the jump, assuming the acceleration phase is constant.

Action-Reaction Pairs

Action-reaction pairs are central to understanding interactions in physical systems. When the player applies a force against the floor, the floor applies an equal and opposite force back on the player. This concept, as described in Newton's third law, is key to analyzing the forces involved in the jump and helps explain why the player can experience acceleration even when the net external force seems balanced at certain instants.

Newton's Laws of Motion

Newton's laws, particularly the second and third laws, are fundamental in analyzing the forces during a jump. Newton's second law explains that the net force on an object is equal to its mass times its acceleration, which is critical when calculating accelerations and required forces during the jump. Meanwhile, Newton's third law—the principle of action and reaction—clarifies that forces always occur in pairs, such as the force the athlete exerts on the floor and the equal and opposite reaction force acting on the athlete.

Free-Body Diagram

A free-body diagram is a graphical illustration used to visualize all the forces acting on a single object. In physics problems, especially involving motion and forces like a jump, drawing these diagrams helps isolate the body and account for gravitational forces, normal forces, and any applied forces, facilitating the application of Newton's laws in a systematic way.

Work-Energy Principle

The work-energy principle relates the work done on an object to its change in kinetic energy, which is especially useful in jump problems. When a basketball player jumps, the work performed by the muscles (through leg extension) is converted into kinetic energy that eventually transforms into gravitational potential energy at the peak of the jump. This principle allows one to calculate the necessary initial speed by equating the kinetic energy at takeoff to the potential energy at the maximum height.

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