The drawing shows a lower leg being exercised. It has a 49-N weight attached to the foot and is

step 1 Hi everyone, this is the problem based on concept of torque acting on the rigid body. It is defi

The drawing shows a lower leg being exercised. It has a 49-N...

The drawing shows a lower leg being exercised. It has a $49-\mathrm{N}$ weight attached to the foot and is extended at an angle $\theta$ with respect to the vertical. Consider a rotational axis at the knee. (a) When $\theta=90.0^{\circ}$, find the magnitude of the torque that the weight creates. (b) At what angle $\theta$ does the magnitude of the torque equal $15 \mathrm{N} \cdot \mathrm{m} ?$

The drawing shows a lower leg being exercised. It has a $49-\mathrm{N}$ weight attached to the foot and is extended at an angle $\theta$ with respect to the vertical. Consider a rotational axis at the knee.
(a) When $\theta=90.0^{\circ}$, find the magnitude of the torque that the weight creates. (b) At what angle $\theta$ does the magnitude of the torque equal $15 \mathrm{N} \cdot \mathrm{m} ?$

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Key Concepts

Trigonometric Relationships in Torque Calculation

Trigonometric functions are often used to resolve the lever arm when forces are applied at an angle relative to the axis of rotation. Specifically, the sine of the angle between the force direction and the lever arm is used to find the component of the force that contributes to the torque. This relationship helps in determining how the torque varies with the angle of application, which is pivotal for solving problems involving angular positioning.

Lever Arm

The lever arm is the perpendicular distance from the pivot or axis of rotation to the line of action of the force. It plays a crucial role in the calculation of torque because the effective torque is directly proportional to this distance. In many scenarios, determining the lever arm involves decomposing forces into their components using geometry and trigonometry.

Torque

Torque is a measure of the rotational force applied about an axis. It is calculated as the product of the force applied and the perpendicular distance (lever arm) from the line of action of the force to the pivot. In problems involving a rotating body, determining the torque is essential for understanding how forces cause angular acceleration or maintain rotational equilibrium.

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