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 $0.20 \mathrm{~s}$. While the dancer is in the air and holding a fixed pose, what is the magnitude of the force her neck exerts on her head? (a) $0 \mathrm{~N} ;$ (b) $60 \mathrm{~N}$ (c) $120 \mathrm{~N} ;$ (d) $180 \mathrm{~N}$.

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 $0.20 \mathrm{~s}$.
While the dancer is in the air and holding a fixed pose, what is the magnitude of the force her neck exerts on her head?
(a) $0 \mathrm{~N} ;$ (b) $60 \mathrm{~N}$
(c) $120 \mathrm{~N} ;$ (d) $180 \mathrm{~N}$.

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Key Concepts

Mass Distribution

Mass distribution refers to how the total mass of a system is apportioned among its different parts. Knowing the fraction of the mass attributed to the head, for example, is essential for determining how much gravitational force it experiences and, consequently, how much support is required to counteract that force.

Gravitational Force

Gravitational force is the force that pulls objects toward the Earth, calculated by multiplying the mass by the acceleration due to gravity. This concept is critical when assessing the force that must be countered by another force, such as the tension in the neck supporting the head.

Static Equilibrium

Static equilibrium occurs when an object is at rest or moving with constant velocity, meaning all acting forces cancel each other out. In analyzing forces on a body part that is held fixed, understanding that the upward force must exactly oppose the gravitational force is key.

Newton's Second Law

Newton's second law establishes that the net force acting on an object equals the product of its mass and acceleration (F = ma). This concept underpins the calculation of forces during both dynamic events (like deceleration) and static situations (such as when forces are balanced).

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