A girl and a dog are playing tug of war with a piece of rope. The girl pulls on the rope with a force of 165 newtons (N) towards the east, and the dog pulls with a force of 190 N towards the west. What is the net force on the rope?
A.
25 N towards the west
B.
190 N towards the west
C.
165 N towards the east
D.
35 N towards the east
The correct answer and Explanation is :
The correct answer is A. 25 N towards the west.
Explanation:
In this tug-of-war scenario, we need to calculate the net force on the rope by considering the forces applied by both the girl and the dog.
- Determine the Magnitudes of the Forces:
- The girl pulls with a force of 165 newtons (N) towards the east.
- The dog pulls with a force of 190 N towards the west.
- Assign Directions to Forces:
- Let’s consider the east direction as positive and the west direction as negative for simplicity in calculations.
- Calculate the Net Force:
To find the net force, we need to subtract the smaller force from the larger force and consider the direction of the larger force. Here, the dog pulls with a greater force than the girl.
- Force exerted by the girl (east direction): ( +165 \, \text{N} )
- Force exerted by the dog (west direction): ( -190 \, \text{N} ) The net force ( F_{\text{net}} ) is given by:
[
F_{\text{net}} = \text{Force of dog} – \text{Force of girl}
]
Substituting the values:
[
F_{\text{net}} = (-190 \, \text{N}) – (+165 \, \text{N})
]
[
F_{\text{net}} = -190 \, \text{N} – 165 \, \text{N}
]
[
F_{\text{net}} = -355 \, \text{N}
]
- Determine the Direction:
Since the net force is negative, it means the direction of the net force is towards the west. The magnitude of the net force is ( 355 \, \text{N} ).
Therefore, the net force on the rope is 25 N towards the west because the total pulling force from the dog is more than the girl’s force by this amount. The forces were incorrectly computed in the steps above; the correct calculation is:
[
F_{\text{net}} = 190 \, \text{N} – 165 \, \text{N} = 25 \, \text{N}
]
and it is directed towards the west, as the dog exerts a stronger force.