To calculate the tension in the cable supporting the load under different scenarios, we need to consider the forces acting on the load and apply Newton's second law of motion, which states that the net force acting on an object is equal to its mass multiplied by its acceleration (F = ma). In this case, the net force is the tension in the cable.
(a) When the load is accelerated upward at 2 m/s²: In this scenario, we have an upward acceleration, so the tension in the cable needs to overcome the force of gravity acting on the load.
The force of gravity (weight) acting on the load can be calculated as follows: F_gravity = m * g where m = mass of the load (1000 kg) and g = acceleration due to gravity (approximately 9.8 m/s²).
F_gravity = 1000 kg * 9.8 m/s² = 9800 N
Since the load is being accelerated upward, the net force required will be the sum of the force of gravity and the force required to produce the upward acceleration.
F_net = F_gravity + m * a F_net = 9800 N + 1000 kg * 2 m/s² = 11800 N
Therefore, the tension in the cable when the load is accelerated upward at 2 m/s² is 11800 N.
(b) When the load is lifted at a constant speed: When the load is lifted at a constant speed, it means there is no net force acting on it. The tension in the cable must balance the force of gravity.
The force of gravity acting on the load is still given by: F_gravity = m * g = 1000 kg * 9.8 m/s² = 9800 N
Since the load is lifted at a constant speed, the tension in the cable will be equal to the force of gravity.
Therefore, the tension in the cable when the load is lifted at a constant speed is 9800 N.
(c) When the load moves upward with speed decreasing by 2 m/s each second: In this scenario, the load is decelerating. The tension in the cable must balance the force of gravity and provide the necessary net force to decelerate the load.
The force of gravity acting on the load is still 9800 N.
To determine the net force required for deceleration, we use the equation: F_net = F_gravity - m * a F_net = 9800 N - 1000 kg * (-2 m/s²) = 11800 N
Therefore, the tension in the cable when the load moves upward with a speed decreasing by 2 m/s each second is 11800 N.
In summary: (a) Tension in the cable when the load is accelerated upward at 2 m/s²: 11800 N (b) Tension in the cable when the load is lifted at a constant speed: 9800 N (c) Tension in the cable when the load moves upward with speed decreasing by 2 m/s each second: 11800 N