Question

A magic medallion is suspended from a string inside a compartment of Hogwarts Express which is running straight westwards on horizontal tracks. a) Draw a free-free body diagram for the medallion if the train is moving at constant speed. b) Draw a free-body diagram for the medallion if the train is accelerating at a constant rate. Indicate acceleration and the direction of the net force. c) Calculate the angle the string makes with the vertical if the train accelerates at a constant rate from rest to 20 m/s in 10 seconds. d) If the mass of the medallion is doubled, how will the angle change?

Answer 1

The free body diagram for the medallion inside the Hogwarts Express compartment will show a tension force from the string when the train is moving at a constant speed. When the train is accelerating at a constant rate, the medallion will experience an additional net force in the direction of acceleration. To calculate the angle the string makes with the vertical, the formula tan(theta) = (acceleration / g) can be used. If the mass of the medallion is doubled, the angle of the string will remain the same.

Step-by-step explanation:

a) When the Hogwarts Express is moving at a constant speed, the magic medallion inside the compartment is also moving at a constant speed. This means that there is no acceleration acting on the medallion. Therefore, the free body diagram for the medallion will show only one force acting on it, which is the tension force from the string.

b) When the train is accelerating at a constant rate, the medallion experiences an acceleration in the same direction as the train. In this case, the free body diagram will show the tension force from the string and an additional net force in the direction of acceleration.

c) To calculate the angle the string makes with the vertical, we can use the formula tan(theta) = (acceleration / g), where theta is the angle and g is the acceleration due to gravity. Plugging in the values, we get tan(theta) = (acceleration / 9.8 m/s^2). Solving for theta, we find the angle the string makes with the vertical.

d) If the mass of the medallion is doubled, the angle of the string will not change. The angle depends only on the acceleration, not the mass.