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Alex73 [517]
2 years ago
13

Suppose a 60-kg boy and a 41-kg girl use a massless rope in a tug-of-war on an icy, resistance-free surface. If the acceleration

of the girl toward the boy is 3.0 m/s2, find the magnitude of the acceleration of the boy toward the girl.
A.
2.05 m/s2
B.
2 m/s2
C.
2.1 m/s2
Physics
1 answer:
Digiron [165]2 years ago
3 0

Answer:

Approximately 2.05\; {\rm m\cdot s^{-2}}.

Explanation:

The net force on the girl would be:

\begin{aligned}m(\text{girl}) \, a(\text{girl}) &= 41\; {\rm kg} \times 3.0\; {\rm m\cdot s^{-2}} \\ &= 123.0\; {\rm N} \end{aligned}.

Under the assumptions, the net force on this girl would be equal to the tension force in the rope. All other forces on the girl would be balanced.

In other words, the tension force that the rope exerted on the girl would be 123.0\; {\rm N}. The girl would exert a reaction force on the rope at the same magnitude (123.0\; {\rm N}\!) in the opposite direction. This force would translate to a 123.0\; {\rm N}\!\! force on the boy towards the girl.

Under similar assumptions, the net force on the boy would also be 123.0\; {\rm N}. Since the mass of the boy is m(\text{boy}) = 60\; {\rm kg}, the acceleration of the boy would be:

\begin{aligned}a(\text{boy}) &= \frac{(\text{net force})}{m(\text{boy})} \\ &= \frac{123.0\; {\rm N}}{60\; {\rm kg}} \\ &= 2.05\; {\rm m\cdot s^{-2}}\end{aligned}.

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