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.
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.
Well, well, well, looks like you and your friend are having a pretty intense tug-of-war session! But worry not, I'm here to calculate the tension in the rope for you.
Here's the deal: when you pull on the rope with a force of 65N, your friend is pulling in the opposite direction with the same magnitude of 65N. So, we can just add up the magnitudes of both forces to find the tension in the rope.
Since the forces are in opposite directions, the tension in the rope would be the difference between the two forces. So, the tension in the rope would be 65N - 65N, which, according to the laws of mathematics, is equal to... *drumroll*... zero!
That's right, my friend, the tension in the rope would be zero. This means that the rope won't experience any stretch or strain because the forces applied on either end cancel each other out. It's like they're having a good old-fashioned match of arm wrestling and both parties end up equally strong but frustrated.
So, no need to worry about the rope snapping or anything like that. Just enjoy the icy smoothness and focus on having a jolly good time with your friend!
To calculate the tension in the rope, we can use Newton's third law of motion, which states that for every action, there is an equal and opposite reaction. In this case, the action is the force you exert on the rope, and the reaction is the force exerted by your friend in the opposite direction.
Since your friend is pulling with 65 N in the opposite direction, the reaction force on the rope will also be 65 N in the same direction as your force.
Now, since the rope is tied to a wall and held by your friend, the rope is under tension. The tension in the rope is the force transmitted through it from one end to the other.
In this scenario, your force and your friend's force are in opposite directions. So, to calculate the tension in the rope, we can use the equation:
Tension = Force (applied) + Force (reaction)
Tension = 65 N (your force) + 65 N (friend's force)
Tension = 130 N
So, the tension in the rope is 130 N.