A person exerts a force of 12.0 N on the end of a door 65.0 cm wide. What is the magnitude of the torque (in newton-meters) if the force is exerted perpendicularly to the door?

12 N x 0.65 m = 7.8 N-m

thank you.

To find the magnitude of the torque exerted on the door, we need to calculate the moment arm and multiply it by the force applied. The formula for torque is given by:

Torque = Force x Moment arm

In this case, the force applied is 12.0 N and it is exerted perpendicular to the door. The moment arm is the shortest distance from the axis of rotation (in this case, the hinges of the door) to the line of action of the force. Since the force is exerted perpendicular to the door, the moment arm is equal to half the width of the door.

First, we need to convert the width of the door from centimeters to meters:
65.0 cm = 65.0 ÷ 100 = 0.65 m

Next, we can calculate the moment arm by dividing the width of the door by 2:
Moment arm = 0.65 m ÷ 2 = 0.325 m

Now, we can calculate the torque by multiplying the force by the moment arm:
Torque = 12.0 N x 0.325 m = 3.9 Nm

Therefore, the magnitude of the torque exerted on the door is 3.9 Newton-meters (Nm).