In FIGURE EX12.19, for what value of X_axle will the two forces provide 1.8 Nm of torque about the axle?

검증된 단계별 안내

Step 1: Recall the formula for torque: τ = F × r × sin(θ), where F is the force, r is the distance from the axis of rotation to the point of application of the force, and θ is the angle between the force vector and the lever arm.

Step 2: Analyze the diagram. The forces F1 and F2 are applied at different points on the rectangle. F1 is applied horizontally to the left, and F2 is applied horizontally to the right. The axle is located at point A(x_A, y_A). The distances from the axle to the points of application of F1 and F2 need to be determined.

Step 3: For F1, the perpendicular distance to the axle is the vertical distance y_A. For F2, the perpendicular distance to the axle is the horizontal distance x_A. These distances will be used to calculate the torque contributions from each force.

Step 4: Write the torque equation for the system. The total torque about the axle is given as τ_total = τ_F1 + τ_F2. Substitute the values: τ_total = F1 × y_A + F2 × x_A. The total torque is specified as 1.8 Nm.

Step 5: Solve for x_A. Rearrange the equation to isolate x_A: x_A = (τ_total - F1 × y_A) / F2. Substitute the given values for τ_total, F1, y_A, and F2 to find x_A.

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

영상 길이:

16m

주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Torque

Torque is a measure of the rotational force applied to an object, calculated as the product of the force and the distance from the pivot point (lever arm). It is expressed in Newton-meters (Nm). The direction of the torque is determined by the direction of the force and the position of the lever arm relative to the pivot.

Lever Arm

The lever arm is the perpendicular distance from the line of action of the force to the axis of rotation. In torque calculations, the lever arm is crucial because it directly influences the amount of torque produced by a given force. A longer lever arm results in greater torque for the same force.

Equilibrium of Forces

In physics, the equilibrium of forces occurs when the sum of all forces acting on an object is zero, resulting in no net force and no acceleration. For torque, this means that the clockwise and counterclockwise torques must balance each other out, allowing for the calculation of unknown forces or distances in a system.