A 36 kg box hangs from a rope. What is the tension in the rope if the following are true?
(a) The box moves up a steady 5.0 m/s?
(b) The box has vy = 5.0 m/s and is slowing down up at 5.0 m/s2?
To find the tension in the rope, we need to consider the forces acting on the box.
(a) The box moves up a steady 5.0 m/s.
When the box is moving at a constant velocity, the net force acting on it is zero. So, the tension in the rope is equal in magnitude to the weight of the box.
The weight of the box can be calculated using the formula: weight = mass * acceleration due to gravity.
Given that the mass of the box is 36 kg, and acceleration due to gravity is approximately 9.8 m/s², we can calculate the weight of the box.
Weight = 36 kg * 9.8 m/s² = 352.8 N
Therefore, the tension in the rope is also 352.8 N.
(b) The box has vy = 5.0 m/s and is slowing down at 5.0 m/s².
When the box is slowing down, there is an additional force acting on it due to the acceleration. In this case, the net force acting on the box is the difference between the tension in the rope and the force due to acceleration.
The force due to acceleration can be calculated using the formula: force = mass * acceleration.
Given that the mass of the box is 36 kg and the acceleration is 5.0 m/s², we can calculate the force due to acceleration.
Force = 36 kg * 5.0 m/s² = 180 N
To find the tension in the rope, we need to subtract the force due to acceleration from the weight of the box.
Tension = Weight - Force due to acceleration
Tension = 352.8 N - 180 N
Tension = 172.8 N
Therefore, the tension in the rope is 172.8 N.