a 5-kilowatt source powers a motor that is lifting a 30 kg mass straight up. how far will the mass move in 6 seconds
To calculate the distance the mass will move, we need to use the formula:
Work = Force x Distance
Since the mass is being lifted straight up, the force can be calculated using Newton's second law:
Force = Mass x Acceleration
Acceleration due to gravity is approximately 9.8 m/s². Therefore:
Force = 30 kg x 9.8 m/s²
Now, we can find the work done by the motor in 6 seconds using the formula:
Work = Power x Time
The power is given as 5 kilowatts, which needs to be converted to watts:
Power = 5 kilowatts x 1000 = 5000 watts
Finally, we can find the distance using the equation:
Work = Force x Distance
Substituting the values:
5000 watts x 6 seconds = Force x Distance
Now, rearrange the equation to solve for distance:
Distance = (5000 watts x 6 seconds) / (Force)
Plugging in the value for force:
Distance = (5000 watts x 6 seconds) / (30 kg x 9.8 m/s²)
Calculating:
Distance = 30,000 joules / (294 Newtons)
Distance ≈ 102 meters
Therefore, the mass will move approximately 102 meters in 6 seconds when powered by a 5-kilowatt source.