tWO PEOPLE PLAY TUG OF WAR. tHE 97 KG PERSON ON THE LIFT PULLS WITH 1,176 n, AND THE 76 KG PERSON ON THE RIGHT PULLS WITH 839 n. aSSUME THAT NEITHER PERSON RELEASES THEIR GRIP ON THE ROPE WITH EITHER HAND AT ANY TIME, ASSUME THAT THE ROPE IS ALWAYS TAUT, AND ASSUME THAT THE ROPE DOES NOT STRETCH. wHAT IS THE MAGNITUDE OF THE TENSION IN THE ROPE IN nEWTONS?
total mass = 97 + 76
total force = 1176 - 839
so
acceleration of system = a = (1176-839)/(97+76)
Now look at 97 kg person for example
1176 N to left (for example)
T to right
net force = (1176-T)
a = what we found above
so
1176 - T = 97 *a
solve for T
Well, it sounds like quite the intense tug of war! Let's do some calculations.
The person on the left is pulling with a force of 1,176 N, and the person on the right is pulling with a force of 839 N. Remember that the total tension in the rope will be equal to the sum of these forces.
So, let's add them up:
1,176 N + 839 N = 2,015 N
Therefore, the magnitude of the tension in the rope is 2,015 Newtons. Quite a forceful battle, wouldn't you say?
To find the magnitude of the tension in the rope, we need to consider the net force acting on the system. Since the rope is assumed to be always taut and neither person releases their grip, the tension in the rope will be the same magnitude on both sides.
Let's calculate the net force acting on the system:
Net force = Force exerted by person on left - Force exerted by person on right
Force exerted by person on left = 1,176 N
Force exerted by person on right = 839 N
Substituting the values into the formula:
Net force = 1,176 N - 839 N
Net force = 337 N
Since the net force acting on the system is in the direction of the person on the left, we can conclude that the magnitude of the tension in the rope is 337 N.
To find the magnitude of the tension in the rope, we can use Newton's second law of motion, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration. In this case, the net force is the tension in the rope.
We have two forces at play here: the force applied by the 97 kg person, and the force applied by the 76 kg person. These forces are acting in opposite directions because they are pulling in opposite directions in a tug of war.
Let's assign a positive direction to the force applied by the 97 kg person (lift) and a negative direction to the force applied by the 76 kg person (right). This means we consider the force applied by the 97 kg person as positive and the force applied by the 76 kg person as negative.
Given:
Mass of the person on the left (lift) = 97 kg
Force applied by the person on the left = 1.176 N (positive)
Mass of the person on the right = 76 kg
Force applied by the person on the right = 839 N (negative)
To find the net force, we can add these forces together:
Net force = force applied by the person on the left + force applied by the person on the right
Net force = 1,176 N + (-839 N)
Net force = 337 N
Since the tension in the rope is equal to the net force, the magnitude of the tension in the rope is 337 N.