Final answer:
To determine how long it takes for a crane with a power output of 2.5 kW to lift a 250 kg block to a height of 5 m at a constant speed, the work done and the power are used to calculate the time. The work done is 12250 J, and dividing this by the power gives a time of approximately 4.9 seconds. Therefore, the closest option is 10 seconds (option a).
Step-by-step explanation:
To calculate how long it will take for the crane to lift a 250 kg block to a height of 5 m at a constant speed, we must first determine the work done by the crane and then use the power output. The work done (W) is equal to the force applied by the crane (F) times the distance (d), where F is equal to the weight of the metal block (mass times the acceleration due to gravity, g = 9.8 m/s2). The weight of the block is 250 kg × 9.8 m/s2 = 2450 N. So, W = 2450 N × 5 m = 12250 J.
The power (P) is the rate at which work is done, which is given as 2.5 kW (2,500 W). The time (t) taken to do the work can be found using the formula P = W/t, rearranging it as t = W/P. Therefore, t = 12250 J / 2500 W = 4.9 seconds. Since 4.9 seconds is not presented in the options given, the closest higher option should be chosen, which is option a) 10 seconds.