Q27E - University Physics with Modern Physics

Question

A ball is hanging from a long string that is tied to the ceiling of a train car traveling eastward on horizontal tracks. An observer inside the train car sees the ball hang motionless. Draw a clearly labeled free-body diagram for the ball if (a) the train has a uniform velocity and (b) the train is speeding up uniformly.  Is the net force on the ball zero in either case? Explain.

Step-by-Step Solution

Answer

   (a)  The free-body diagram for the ball if the train has a uniform velocity is,
                          

                                           

In this case, the net force on the ball is equal to zero.

      (b) The free-body diagram for the ball if the train is speeding up uniformly is,

                        

                                                         

In this case the net force on the ball is not equal to zero. The ball will experience a net force.                                                        

Step 1: Significance of free-body diagram:

When a number of forces are applied to a body, then a diagram that represents only the forces acting on the body is known as the free-body diagram. It helps to analyze the forces acting on the body and calculation unknown forces.

Step 2: (a) Drawing the free body diagram for the ball if the train has a uniform velocity:

The free-body diagram for the ball if the train has a uniform velocity is given below.

            

                                                                            

Here, $\mathrm{T}$ is the tension force in the string and $\mathrm{W}$ is the weight of the ball.

Since the train has a uniform velocity, the train is moving without acceleration, and the observer sees the ball hang motionless. From the above free-body diagram, the net force that acts on the ball is equal to zero.

Step 3: (b) Draw the free body diagram for the ball if the train is speeding up uniformly

The free-body diagram for the ball if the train is speeding up uniformly is given below.

                                       

Here, $\mathrm{T}$ is the tension force in the string, $\mathrm{W}$ is the weight of the ball and $\mathrm{a}$ is the uniform acceleration of the train.

Since the train is speeding up uniformly, the train is moving with acceleration, and the observer will see the ball hang with motion due to a specific net force that acts on the ball. From the above free-body diagram, the net force that acts on the ball is not equal to zero, and the ball will experience a specific net force.