if a 700-kg piano us lifted 4.0 meters in 14 seconds, how much power is developed
To calculate the power developed, we can use the formula:
Power (P) = Work (W) / Time (t)
First, we need to calculate the work done. The work done is given by the formula:
Work (W) = Force (F) x Distance (d)
The force required to lift the piano is equal to its weight. The weight is given by the formula:
Weight (W) = mass (m) x acceleration due to gravity (g)
The acceleration due to gravity is approximately 9.8 m/s^2.
Using the given information:
Mass (m) = 700 kg
Distance (d) = 4.0 m
Time (t) = 14 s
Acceleration due to gravity (g) = 9.8 m/s^2
Step 1: Calculate the weight of the piano:
Weight (W) = m x g
Weight (W) = 700 kg x 9.8 m/s^2
Step 2: Calculate the work done:
Work (W) = F x d
Work (W) = W x d
Step 3: Calculate the power:
Power (P) = W / t
Let's plug in the values and calculate:
Weight (W) = 700 kg x 9.8 m/s^2
Work (W) = W x d
Power (P) = W / t
Weight (W) = 6860 N
Work (W) = 6860 N x 4.0 m
Power (P) = (6860 N x 4.0 m) / 14 s
Power (P) = 1960 Watts
Therefore, the power developed is 1960 Watts.
To determine the power developed in lifting the piano, we need to use the formula for power:
Power = Work / Time
To find the work done, we can use the formula:
Work = Force × Distance
In this case, the force exerted on the piano is equal to its weight, which can be calculated using the formula:
Weight = mass × gravity
The mass of the piano is given as 700 kg, and the acceleration due to gravity on Earth is approximately 9.8 m/s^2.
Let's calculate step by step:
1. Calculate the weight of the piano:
Weight = mass × gravity
Weight = 700 kg × 9.8 m/s^2
2. Calculate the work done:
Work = Force × Distance
Work = Weight × Distance
Work = <result from step 1> × 4.0 meters
3. Calculate the power:
Power = Work / Time
Power = <result from step 2> / 14 seconds
Now, let's do the calculations:
1. Weight = 700 kg × 9.8 m/s^2 = 6860 N
2. Work = 6860 N × 4.0 meters = 27440 N·m
3. Power = 27440 N·m / 14 seconds
Calculating the final result:
Power = 1960 watts
Therefore, the power developed in lifting the 700-kg piano is 1960 watts.