Question

A starter cord for a generator is 1 m long. It is wound onto a drum with a diameter of 10 cm. A person starts the generator by pulling with a force of 100 N. A) What torque does he apply to the engine? b) How much work does he do?​

Answer 1

A) To calculate the torque applied to the engine, we need to know the force applied, the radius of the drum, and the angle at which the cord is pulled. Assuming that the angle is 180 degrees (i.e. the cord is pulled straight out from the drum), the torque can be calculated as follows:

Torque = force x radius

The radius of the drum is half of its diameter, or 0.05 m. Therefore:

Torque = 100 N x 0.05 m = 5 Nm

B) To calculate the work done by the person, we need to know the distance the cord is pulled. Since the cord is 1 m long, and it is wound around the drum once, the distance it is pulled is equal to the circumference of the drum. The circumference can be calculated as follows:

Circumference = pi x diameter

Circumference = 3.14 x 0.1 m = 0.314 m

Therefore, the work done by the person is:

Work = force x distance

Work = 100 N x 0.314 m = 31.4 J

The person does 31.4 Joules of work to start the generator.

Answer 2

A) To find the torque that the person applies to the engine, we need to first find the force applied at the edge of the drum. We can do this using the formula:

Force = Torque / Radius

where the radius is half the diameter of the drum.

Radius = 10 cm / 2 = 0.05 m

Force = 100 N

Therefore:

Torque = Force x Radius = 100 N x 0.05 m = 5 Nm

So the person applies a torque of 5 Nm to the engine.

B) To find the work done by the person, we need to use the formula:

Work = Force x Distance

where the distance is the length of the starter cord that is pulled out.

Length of cord = 1 m

Since the cord is wound around the drum, the distance that the person pulls is equal to the distance that the drum rotates. The circumference of the drum is:

Circumference = π x diameter = π x 10 cm = 0.314 m

So the distance that the person pulls is 0.314 m.

Therefore:

Work = Force x Distance = 100 N x 0.314 m = 31.4 J

So the person does 31.4 Joules of work