A 315 kg object is lifted 12 meters by a motor in 15 seconds. How much power does the motor deliver?
To find the power delivered by the motor, we need to use the formula for power:
Power = Work / Time
To calculate the work done, we need to know the force applied and the distance over which it is applied. In this case, it is given that the object weighs 315 kg, so the force applied can be found using Newton's second law:
Force = Mass * Acceleration due to gravity
Acceleration due to gravity is approximately 9.8 m/s^2. Therefore:
Force = 315 kg * 9.8 m/s^2 = 3087 N
The work done is given by the formula:
Work = Force * Distance
Substituting the known values:
Work = 3087 N * 12 m = 37044 N·m (or Joules)
Finally, substituting the values of work and time into the power formula:
Power = 37044 N·m / 15 s = 2469.6 Watts (or Joules/second)
So, the motor delivers approximately 2469.6 Watts of power.