Forces on a Dancer's Body. Dancers experience large forces...

Forces on a Dancer's Body. Dancers experience large forces associated with the jumps they make. For example, when a dancer lands after a vertical jump, the force exerted on the head by the neck must exceed the head's weight by enough to cause the head to slow down and come to rest. The head is about $9.4 \%$ of a typical person's mass. Video analysis of a $65 \mathrm{~kg}$ dancer landing after a vertical jump shows that her head decelerates from $4.0 \mathrm{~m} / \mathrm{s}$ to rest in a time of $0.20 \mathrm{~s}$. Compared with the force her neck exerts on her head during the landing, the force her head exerts on her neck is (a) the same; (b) greater; (c) smaller; (d) greater during the first half of the landing and smaller during the second half of the landing.

Forces on a Dancer's Body. Dancers experience large forces associated with the jumps they make. For example, when a dancer lands after a vertical jump, the force exerted on the head by the neck must exceed the head's weight by enough to cause the head to slow down and come to rest. The head is about $9.4 \%$ of a typical person's mass. Video analysis of a $65 \mathrm{~kg}$ dancer landing after a vertical jump shows that her head decelerates from $4.0 \mathrm{~m} / \mathrm{s}$ to rest in a time of $0.20 \mathrm{~s}$.
Compared with the force her neck exerts on her head during the landing, the force her head exerts on her neck is (a) the same;
(b) greater; (c) smaller; (d) greater during the first half of the landing and smaller during the second half of the landing.

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Key Concepts

Newton's Third Law

This law states that for every action there is an equal and opposite reaction. In the context of forces during a landing, the force that one body (e.g., the neck) exerts on another body (e.g., the head) is met with an equal magnitude force in the opposite direction from the head back on the neck. This concept is fundamental for understanding interactions between objects and ensures that the forces involved in the landing are symmetric in magnitude.

Momentum Change and Impulse

When an object decelerates, its momentum changes, and this change in momentum over a given time interval can be expressed as an impulse. This principle is used to calculate the average force exerted on an object during events such as a landing. By knowing the initial velocity, mass, and deceleration time, one can determine the impulse and thus the force experienced, highlighting the underlying physics of motion during rapid deceleration scenarios.

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