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

Answer:

a = 1 m/s²  and

Explanation:

The first two parts can be seen in attachment

We use Newton's second law on each axis

Y axis

      Ty - W = 0        

      Ty = w

X axis

     Tx = m a

With trigonometry we find the components of tension

    Sin θ = Ty / T

    Ty = T sin θ

    Cos θ = Tx / T

    Tx = T cos θ

We calculate the acceleration with kinematics

   Vf = Vo + a t

   a = (Vf -Vo) / t

   a = (20 -10) / 10

   a = 1 m/s²

We substitute in Newton's equations

     

  T Sin θ = mg

  T cos θ = ma

We divide the two equations

  Tan θ = g / a

  θ = tan⁻¹ (g / a)

  θ = tan⁻¹ (9.8 / 1)

  θ = 84º

We see that in the expression of the angle the mass does not appear therefore you should not change the angle