A cable pulls a crate of mass 19.0 kg across the floor in 6.8s. If the total distance traveled is 5.40 m, find the power used by the cable.
(19)*(9.8)*(5.4)/(6.8) )
147.9 W
Raul pushes a stalled car with a force of 204 N. If the required force decreases at a constant rate from 204 N to 44.0 N for a distance of 16.3 m in 16.0 s, calculate the average power required to move the car.
(1/2)*(204 + 44)*(16.3)/(16.0) )
126 W
ARE THE CORRECT?
yes
To calculate power, we can use the formula:
Power = Work / Time
For the first scenario, the work done can be calculated using the formula:
Work = Force * Distance
Therefore, the power used by the cable is:
Power = (Force * Distance) / Time
Plugging in the given values:
Mass (m) = 19.0 kg
Acceleration due to gravity (g) = 9.8 m/s^2
Distance (d) = 5.40 m
Time (t) = 6.8 s
Force = m * g = 19.0 kg * 9.8 m/s^2 = 186.2 N
Power = (186.2 N * 5.40 m) / 6.8 s = 147.9 W
So, your calculation for the power used by the cable is correct.
For the second scenario, the force decreases at a constant rate from 204 N to 44.0 N. We can calculate the average force as the average of the initial and final forces.
Average Force = (Initial Force + Final Force) / 2
Plugging in the given values:
Initial Force = 204 N
Final Force = 44.0 N
Average Force = (204 N + 44.0 N) / 2 = 124 N
Now, let's calculate the work done using the formula:
Work = Force * Distance
Plugging in the given values:
Distance (d) = 16.3 m
Work = 124 N * 16.3 m = 2015.2 Nm or 2015.2 J
Finally, we can calculate the average power:
Power = Work / Time
Plugging in the given value:
Time (t) = 16.0 s
Power = 2015.2 J / 16.0 s = 126 W
Therefore, your calculation for the average power required to move the car is correct.