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 understand how power is related to work done.
Power (P) is defined as the rate at which work is done or energy is transferred, and it is given by the equation:
P = W / t
where P is power, W is work done, and t is the time.
Work done (W) can be calculated using the formula:
W = F * d
where W is work done, F is the force applied, and d is the distance over which the force is applied.
In this case, the power of the source is given as 5 kilowatts, which can be converted to watts:
5 kilowatts = 5000 watts (since 1 kilowatt = 1000 watts).
Since power is the rate at which work is done, we can rearrange the equation to solve for work done:
W = P * t
Substituting the given values:
W = 5000 watts * 6 seconds = 30000 joules
Now, let's calculate the force applied to lift the mass. The force acting on an object can be determined using Newton's second law of motion:
F = m * g
where F is the force, m is the mass, and g is the acceleration due to gravity.
Substituting the given values:
F = 30 kg * 9.8 m/s^2 (approximating acceleration due to gravity as 9.8 m/s^2) = 294 N
Finally, we can solve for the distance (d) using the equation:
W = F * d
Rearranging the equation to solve for d:
d = W / F
Substituting the calculated values:
d = 30000 joules / 294 N ≈ 102 meters
Therefore, the mass will move approximately 102 meters in 6 seconds.