You hold one end of a rope and pull horizontally with a force of 65N. Calculate the tension in the rope if the other end is tied to a wall and held by a friend who pulls with 65 N in the opposite direction. It's tied to a object on a smooth ice.
3 answers
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89N
a) If it's tied to a wall, then we can imagine an FBD for you, where the forces are the tension in the rope (or Ft) and the applied force (65N or Fa). Since you're not moving, the net force is 0 and these forces must balance out. Hence, the tension in the rope would be 65N as well.
b) You and your friend are both pulling in opposite directions with a force of 65N. According to Newton's third law, every action has an opposite and equal reaction. Thus, if you're pulling on the rope with 65N, the rope should pull back with 65N. The same would happen with your friend. Therefore, instead of a tension force of 0 or 130N in the rope as is generally assumed, it would still be 65N.
c) If the object is tied to an object on ice, we can assume negligible friction. We can look at this from 2 perspectives. One, think of the object like the wall from part a), so we get the same FBD for you (as you're not moving), and the tension in the rope would be 65N. Another way would be to imagine that you are a car and you have a rope tying you to an x kg object. So, your engine is giving a force of 65N [f] and you have a force of tension (or Ft) on the back. if you're not accelerating or are at rest, your net force would be 0. Thus, 0 = Fa + Ft --> 65N + Ft = 0 --> Ft = -65N [f] or Ft = 65N [backwards]. As a result, in all of these cases, the force of tension in the rope is 65N.
b) You and your friend are both pulling in opposite directions with a force of 65N. According to Newton's third law, every action has an opposite and equal reaction. Thus, if you're pulling on the rope with 65N, the rope should pull back with 65N. The same would happen with your friend. Therefore, instead of a tension force of 0 or 130N in the rope as is generally assumed, it would still be 65N.
c) If the object is tied to an object on ice, we can assume negligible friction. We can look at this from 2 perspectives. One, think of the object like the wall from part a), so we get the same FBD for you (as you're not moving), and the tension in the rope would be 65N. Another way would be to imagine that you are a car and you have a rope tying you to an x kg object. So, your engine is giving a force of 65N [f] and you have a force of tension (or Ft) on the back. if you're not accelerating or are at rest, your net force would be 0. Thus, 0 = Fa + Ft --> 65N + Ft = 0 --> Ft = -65N [f] or Ft = 65N [backwards]. As a result, in all of these cases, the force of tension in the rope is 65N.