Answer :
Final answer:
The correct answer is a. 4900 W The power supplied by the second crane, which took 2 minutes to lift a 2000 kg car by 30 m, is calculated using the formula P = W/t. The work done is the change in gravitational potential energy (W = mgh), and the power supplied by the second crane comes out to be 4900 W.
Explanation:
To calculate the power supplied by the second crane, we can use the formula for power, P = W/t, where W is the work done, and t is the time taken. Because lifting the car involves changing its gravitational potential energy, the work done by the crane in both cases is equal to the weight of the car (mass times the acceleration due to gravity) multiplied by the height it is raised. So, W = mgh, where m is the mass of the car, g is the acceleration due to gravity (approximately 9.8 m/s2), and h is the height.
In our case, m = 2000 kg, g = 9.8 m/s2, h = 30 m, and for the second crane t = 2 minutes (or 120 seconds). Firstly, calculate W:W = mgh = 2000 kg × 9.8 m/s2 × 30 m = 588,000 JNow we calculate the power P for the second crane:P = W/t = 588,000 J / 120 s = 4900 WTherefore, the power supplied by the second crane is 4900 W, which corresponds to option a.The force exerted by the crane can be calculated using the formula:
Force = Mass x AccelerationSince the car is lifted at a constant speed, the acceleration is zero. Therefore, the force exerted is equal to the weight of the car which is given by:Force = Mass x GravityPlugging in the values:Force = 2000 kg x 9.8 m/s^2 = 19,600 NThe work done by the crane is:Work = Force x Distance = 19,600 N x 30 m = 588,000 JNow, let's calculate the power:Power = Work/Time = 588,000 J/2 minutes = 294,000 J/min = 294,000/60 W = 4,900 WTherefore, the power supplied by the second crane is 4900 W (option a).
