Understanding Tension in Cable when Lifting a Load
(a) What is the tension in the cable if the load initially accelerates upwards at 1.50 m/s²? (b) What is the tension during the remainder of the lift when the load moves at constant velocity?
(a) To determine the tension in the cable when the load initially accelerates upwards at 1.50 m/s², we need to consider the forces acting on the load. The tension in the cable will be equal to the sum of the weight of the load and the force required to accelerate it. Given: Weight of the load = 849 N Acceleration of the load = 1.50 m/s² The force required to accelerate the load can be calculated using Newton's second law of motion, which states that force is equal to mass multiplied by acceleration (F = m * a). We can calculate the mass of the load using the formula: mass = weight / acceleration due to gravity. Acceleration due to gravity (g) is approximately 9.8 m/s². mass = weight / g mass = 849 N / 9.8 m/s² ≈ 86.6 kg Now, we can calculate the force required to accelerate the load: force = mass * acceleration force = 86.6 kg * 1.50 m/s² ≈ 129.9 N Therefore, the tension in the cable when the load initially accelerates upwards is approximately 129.9 N. (b) During the remainder of the lift when the load moves at a constant velocity, the acceleration is zero. This means that the net force acting on the load is zero since there is no acceleration. The tension in the cable during this phase will be equal to the weight of the load. Therefore, the tension in the cable during the remainder of the lift when the load moves at a constant velocity is 849 N.