Question

A heavy iron gate is stuck closed. Opening the gate requires pushing hard along the y axis and lifting at the same time along the z axis. A force of (850j + 160k) N is applied to the top right corner of the gate such that the position vector from the axis of rotation to the top right corner is given by r = 3.4i m. What is the torque on the gate due to this force?

Answer 1

The torque on the gate due to the applied force is calculated as the cross product of the position vector r = 3.4i m and the force vector F = (850j + 160k) N, resulting in a torque of -2890k N·m, indicating a clockwise rotation.

Step-by-step explanation:

To calculate the torque on the gate, we use the formula t = r × F, where t is the torque, r is the position vector from the axis of rotation, and F is the force applied. In vector form, the torque is found by taking the cross product of the position vector and the force vector. In this problem, the position vector is r = 3.4i m and the force applied is F = (850j + 160k) N. The torque t is therefore the cross product of these two vectors.

The cross product r × F is calculated as:

i component: (0)(160) - (3.4)(850) = -2890

j component: (3.4)(0) - (0)(0) = 0

k component: (0)(850) - (3.4)(0) = 0