Suppose two children push horizontally, but in exactly opposite directions, on wagon with another child inside of it. The first child exerts a force of 75.0 N, the second child exerts a force of 90.0 N in the opposite direction, and 15.0 N of friction acts on the wagon. The mass of the third child plus wagon is 23.0 kg.Consider the system of interest if the acceleration of the child in the wagon is to be calculated. Draw a free-body diagram, including all forces acting on the system. Calculate the acceleration of the system.Group of answer choicesa = 6.5 m/s2a = 1.3 m/s2a = 0.65 m/s2a = 0 m/s2
Question
Suppose two children push horizontally, but in exactly opposite directions, on wagon with another child inside of it. The first child exerts a force of 75.0 N, the second child exerts a force of 90.0 N in the opposite direction, and 15.0 N of friction acts on the wagon. The mass of the third child plus wagon is 23.0 kg.Consider the system of interest if the acceleration of the child in the wagon is to be calculated. Draw a free-body diagram, including all forces acting on the system. Calculate the acceleration of the system.Group of answer choicesa = 6.5 m/s2a = 1.3 m/s2a = 0.65 m/s2a = 0 m/s2
Solution
First, let's identify all the forces acting on the system (wagon and child inside).
- Force exerted by the first child = 75.0 N
- Force exerted by the second child = 90.0 N (in the opposite direction)
- Frictional force = 15.0 N
Since the forces exerted by the two children are in opposite directions, we can find the net force by subtracting the smaller force from the larger one.
Net force = 90.0 N - 75.0 N = 15.0 N
However, we also have a frictional force acting in the opposite direction to the net force. So, the total force acting on the system is:
Total force = Net force - Frictional force = 15.0 N - 15.0 N = 0 N
Now, we can use Newton's second law of motion (F = ma) to find the acceleration (a) of the system. Since the total force is 0, the acceleration of the system is also 0.
So, the acceleration of the system is 0 m/s².
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