Final answer:
The power required to lift a box weighing 2.4 x 10^2 Newtons to a shelf 1.2 meters high in 4.0 seconds is calculated using the formula for power, resulting in a power of 72 watts.
Step-by-step explanation:
The question requires us to calculate the power required to lift a box to a certain height at a constant speed. To find the power, we can use the formula:
P = rac{W}{t}
where P is power, W is work done, and t is time. The work done, W, when lifting an object is equal to the force applied (which is equal to the weight of the object) times the distance moved in the direction of the force:
W = Fd
In this case, the force, F, is the weight of the box, which is 2.4 x 10^2 Newtons, and the distance, d, is 1.2 meters. Since the box is lifted at a constant speed, the work done equals the gravitational potential energy gained by the box:
W = 2.4 x 10^2 N × 1.2 m = 2.88 x 10^2 J
Power is then:
P = rac{2.88 x 10^2 J}{4.0 s} = 72 W
Therefore, the power required to lift the box is 72 watts.