The correct approach to determining the net force on the rope is:
The forces are in opposite directions, so the newtons can be subtracted.
To calculate the net force, you would subtract the total force applied in one direction from the total force applied in the opposite direction.
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Calculate the total force exerted by the five children pulling with 10 newtons: \[ 5 \times 10 = 50 \text{ newtons (in one direction)} \]
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Calculate the total force exerted by the ten children pulling with 15 newtons: \[ 10 \times 15 = 150 \text{ newtons (in the opposite direction)} \]
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To find the net force, subtract the smaller total force from the larger total force: \[ 150 \text{ newtons} - 50 \text{ newtons} = 100 \text{ newtons (in the direction of the 15 newtons)} \]
Thus, the net force is 100 newtons in the direction of the ten children pulling with 15 newtons.