Q6CQ - College Physics (Urone)

Question

As you pass a freight truck with a trailer on a highway, you notice that its trailer is bouncing up and down slowly. Is it more likely that the trailer is heavily loaded or nearly empty? Explain your answer.

 

Step-by-Step Solution

Answer

The trailer is more likely to be heavily loaded rather than nearly empty and so it is bouncing up and down slowly.

Step 1: Relation between frequency and mass in a periodic motion

The frequency of a periodic motion is given as follows,

\({\rm{f = }}\frac{{\rm{1}}}{{{\rm{2}}\pi }}\sqrt {\left( {\frac{{\rm{k}}}{{\rm{m}}}} \right)} \)

 

Here, \({\rm{k}}\) is the spring constant and \({\rm{m}}\) is the mass of the system.

 

Step 2: Explanation of the given situation of the freight truck with a trailer

It is observed from the expression of the frequency, that the frequency is inversely proportional to the mass of the system. So, if the system is heavy, it will vibrate with less frequency which means it will oscillate slowly.

As mentioned in the question, the trailer of the truck is bouncing up and down slowly, which means it is vibrating with less frequency. Since less frequency indicates heavy mass, so the trailer is more likely to be heavily loaded rather than nearly empty.