Piano movers hoist a 200 kg piano 10 m high in 30 s using a rope and simple pulley. What is their power output?
(Points : 1)
70 W
700 W
7,000 W
6 × 10^5 W
700 W
Thank you!
Why did the piano go to the gym? It wanted to increase its power output! Speaking of power, let's calculate it. Power is defined as the amount of work done per unit of time. In this case, the work done is lifting the piano 10 m high, which is given by the formula work = force × distance. The force is equal to the weight of the piano, which is given by the formula weight = mass × acceleration due to gravity. Plugging in the values, we get weight = 200 kg × 9.8 m/s² = 1960 N. Therefore, the work done is work = 1960 N × 10 m = 19600 J. Now, let's calculate the power by dividing the work done by the time taken: power = work / time = 19600 J / 30 s = 653.33 W. Rounding to the nearest whole number, the power output of the piano movers is approximately 700 W. So the answer is 700 W.
To calculate the power output, we can use the formula:
Power = Work / Time
First, we need to calculate the work done by the piano movers. The work done is equal to the force applied multiplied by the distance moved. In this case, the force applied is equal to the weight of the piano, which can be calculated using the formula:
Weight = mass * gravity
where mass is given as 200 kg and gravity is approximately 9.8 m/s^2.
Weight = 200 kg * 9.8 m/s^2 = 1960 N
The distance moved is given as 10 m.
Now we can calculate the work done:
Work = Force * Distance = 1960 N * 10 m = 19,600 N·m (Joules)
Finally, we can calculate the power output using the formula:
Power = Work / Time = 19,600 J / 30 s = 653.33 W, which can be approximated to 650 W.
Therefore, the correct answer is:
700 W
To calculate the power output of the piano movers, we need to use the formula:
Power = Work / Time
First, let's calculate the work done. The work done is equal to the force applied multiplied by the distance over which the force is applied. In this case, the force applied is the weight of the piano, which can be calculated using the formula:
Weight = mass * gravity
where the mass is 200 kg and gravity is approximately 9.8 m/s^2. Therefore:
Weight = 200 kg * 9.8 m/s^2 = 1960 N
Next, we calculate the work done by multiplying the weight by the distance:
Work = Weight * Distance = 1960 N * 10 m = 19600 Nm or J (joules)
Now that we have the work done, we can calculate the power using the given time of 30 seconds:
Power = Work / Time = 19600 J / 30 s
Now, divide 19600 J by 30 s to get the power in watts:
Power = 653.33 W
Considering the given options, the closest answer is 700 W, as it is the next highest value.