- #1
PFuser1232
- 479
- 20
Suppose two people, A and B, are pulling on a rope of mass ##M_r## in space. The force exerted by B is ##F_B## and the force exerted by A is ##F_A## (in magnitude). Suppose B pulls harder than A, we now have the equation of motion:
$$F_B - F_A = Ma_{rope}$$
We also have a constraint; since A, B and the rope are all connected, their accelerations must all be the same. That is ##a_A = a_B = a_{rope}##. According to Newton's third law, the force exerted by the rope on B is equal in magnitude and opposite in direction to the force exerted by B on the rope. That is, it is not in the same direction as the acceleration of B, which is confusing because this force (tension) seems to be the only force acting directly on B, thus one would expect the acceleration of B to be in the same direction as the tension acting on B, in accordance with Newton's second law, except it isn't. I am really confused.
$$F_B - F_A = Ma_{rope}$$
We also have a constraint; since A, B and the rope are all connected, their accelerations must all be the same. That is ##a_A = a_B = a_{rope}##. According to Newton's third law, the force exerted by the rope on B is equal in magnitude and opposite in direction to the force exerted by B on the rope. That is, it is not in the same direction as the acceleration of B, which is confusing because this force (tension) seems to be the only force acting directly on B, thus one would expect the acceleration of B to be in the same direction as the tension acting on B, in accordance with Newton's second law, except it isn't. I am really confused.