A mechanic jacks up the front of a car to an angle of 8.8° with the horizontal in order to change the front tires. The car is 2.92 m long and has a mass of 1330 kg. Gravitational force acts at the center of mass, which is located 1.02 m from the front end. The rear wheels are 0.41 from the back end. Calculate the magnitude of the torque exerted by the jack.

Question

A mechanic jacks up the front of a car to an angle of 8.8° with the horizontal in order to change the front tires. The car is 2.92 m long and has a mass of 1330 kg. Gravitational force acts at the center of mass, which is located 1.02 m from the front end. The rear wheels are 0.41 from the back end. Calculate the magnitude of the torque exerted by the jack.

Answer 1

To calculate the magnitude of the torque exerted by the jack, we first need to understand the concept of torque.

Torque is the measure of the force's ability to cause rotational motion around an axis. It is calculated as the product of the force and the distance between the axis of rotation and the line of action of the force. In this case, the force is the gravitational force acting on the car and the axis of rotation is at the point of contact between the jack and the car.

To calculate the torque, we will use the following formula:

Torque = Force x Distance

First, let's calculate the force acting on the car. The force is the gravitational force, which can be calculated using the formula:

Force = mass x acceleration due to gravity

Given that the mass of the car is 1330 kg and the acceleration due to gravity is approximately 9.8 m/s², we can calculate the force:

Force = 1330 kg x 9.8 m/s²

Next, we need to calculate the distance between the point of contact and the line of action of the force. This distance can be determined by finding the vertical component of the distance between the center of mass of the car and the point of contact with the jack.

Let's call this distance "L." We can calculate it using basic trigonometry:

L = sin(angle) x length

Given that the angle is 8.8° and the length of the car is 2.92 m:

L = sin(8.8°) x 2.92 m

Now we have all the values needed to calculate the torque:

Torque = Force x L

Substituting the values we calculated earlier:

Torque = (1330 kg x 9.8 m/s²) x (sin(8.8°) x 2.92 m)

Calculating this expression will give us the magnitude of the torque exerted by the jack on the car.

Please note that the final torque value will depend on the accuracy of the provided measurements and assumptions made.