In a canyon between two mountains, a spherical

boulder with a radius of 1.4 m is just set
in motion by a force of 230 N. The force is
applied at an angle of 73.9
◦ measured with
respect to the radius of the boulder.
What is the magnitude of the torque on the
boulder?
Answer in units of N · m.

To find the magnitude of the torque on the boulder, we need to use the formula for torque:

Torque = force * lever arm

In this case, the lever arm is the radius of the boulder, and the force is the component of the applied force perpendicular to the radius.

To find the perpendicular component of the force, we need to use trigonometry. The perpendicular force can be expressed as:

perpendicular force = force * sin(angle)

Now we can substitute this value into our torque formula:

Torque = perpendicular force * radius
= (force * sin(angle)) * radius

Let's plug in the values provided in the question:

force = 230 N
angle = 73.9 degrees
radius = 1.4 m

First, we need to convert the angle from degrees to radians:

angle = 73.9 * π/180

Now we can calculate the torque:

Torque = (230 * sin(73.9 * π/180)) * 1.4

Calculating this expression will give us the magnitude of the torque on the boulder in units of N · m.