(a)What is the power output of the crane. (ignoring losses)?(b)If it takes the cran2 2 minutes to raise the payload to its final height, how far above the ground is this?(c)If the cable were to break as the payload reaches its final height, how fast would it be traveling as it hit the ground?
a) As the crane is lifting at constant speed, there is no acceleration on the payload, therefore the net forces on the payload are equal to 0. Therefore the crane overcomes just the force of gravity = 500*9.81 = 4905 N Power = force * velocity = 4905 * 0.7 = 3433.5 W b) distance = speed * time = 0.7 * (2 * 60) = 84 m c) assuming that the cable breaks while it is still going up at 0.7 m/s, therefore initial velocity upwards = 0.7 m/s. using v? = u? + 2as: v? = 0.7? + 2(-9.8)(-84) = 1646.89 v = √(1646.89) = 40.9 m/s the payload will be travelling at 40.9 m/s when it hit the ground.
