A 40 kg student stands on a 20 kg platform supported by a light cable that passes over an ideal pulley. The student holds the other end of the cable as shown. Assume that both segments of the cable remain vertical.
What is the tension in the cable when the platform is at rest? (newtons)
What force does the platform exert on the person when at rest?(newtons)
The person pulls on the cable so that the person and platform accelerate together at 2 m/s2 upward.
What is the tension in the cable when the platform accelerates?
(Newtons)
What force does the platform exert on the person while accelerating?
(newtons)
To solve this problem, we need to analyze the forces acting on the student and the platform.
1. When the platform is at rest:
- The weight of the student is acting downward, which can be calculated as follows: Weight = mass * gravity, where mass of the student = 40 kg and gravity = 9.8 m/s^2.
- The tension in the cable is upward and is equal to the weight of the student.
So, in this case, the tension in the cable is 40 kg * 9.8 m/s^2 = 392 N.
The force exerted by the platform on the person, using Newton's third law, is also 392 N in the downward direction.
2. When the platform and the person accelerate together:
- In this case, an additional force is acting on the platform and the person, causing them to accelerate. Using Newton's second law (F = m*a), where m is the combined mass of the person and the platform (40 kg + 20 kg) and a is the acceleration (2 m/s^2), we can calculate the net force:
Net force = (40 kg + 20 kg) * 2 m/s^2 = 120 N.
- The net force is equal to the tension in the cable plus the weight of the student. Thus, we can set up an equation: Tension + Weight = Net Force.
Substituting the known values, we have:
Tension + 40 kg * 9.8 m/s^2 = 120 N.
Solving for the tension, we find: Tension = 120 N - 392 N = -272 N.
Note: The negative sign indicates that the tension is acting in the opposite direction to the assumed upward direction. Therefore, we take the magnitude of the tension as 272 N.
The force exerted by the platform on the person is equal to the tension in the cable, considering Newton's third law, so it is also 272 N in the downward direction.
In summary:
1. Tension in the cable when the platform is at rest: 392 N.
Force exerted by the platform on the person when at rest: 392 N.
2. Tension in the cable when the platform accelerates: 272 N.
Force exerted by the platform on the person while accelerating: 272 N.