Question

a system consists of two identical blocks connected by a rod of negligible mass. at the instant shown, the velocity of the center of mass is zero and the system has a nonzero acceleration to the right. which of the following statements must be true?
a the net force on the system is zero.
b the net force on the right block is greater than the net force on the left block.
c there is a net force exerted on the system directed to the left.
d there is a net force exerted on the system directed to the right.

Explanation:

Step1: Recall Newton's second law for the system

Newton's second law for a system is \(F_{net} = M_{total}a_{cm}\), where \(F_{net}\) is the net force on the system, \(M_{total}\) is the total mass of the system, and \(a_{cm}\) is the acceleration of the center of mass.

Step2: Analyze the given information

Given that the system has a nonzero acceleration \(a_{cm}\) to the right. Let the total mass of the two - block system be \(M\) (since the blocks are identical, if each has mass \(m\), \(M = 2m\)).
Since \(a_{cm}
eq0\) and \(M>0\), from \(F_{net}=M a_{cm}\), the net force \(F_{net}\) on the system is not zero. Also, because \(a_{cm}\) is to the right, \(F_{net}\) is in the direction of \(a_{cm}\) (to the right).
For option B: The two blocks have the same acceleration (since they are connected by a rigid rod). Using \(F = ma\) (Newton's second law for a single object), and since \(m_{left}=m_{right}\) and \(a_{left} = a_{right}\) (because of the rigid connection), \(F_{net - left}=m_{left}a_{left}\) and \(F_{net - right}=m_{right}a_{right}\), so \(F_{net - left}=F_{net - right}\)

Answer:

D. There is a net force exerted on the system directed to the right.