A woman pushes a lawn mower with a con-
stant force of 112 Newtons at an angle of
37� with respect to the horizontal. The lawn
mower moves at a speed of 20 cm/sec.
What is her power output? (1 hp = 746
Watts)
v = .2 m/s
F = 112 cos 37
power = F v = .2 * 112 cos 37 Watts
to get HP divide by 746
To find the power output, we need to calculate the work done by the woman pushing the lawn mower. The formula for work is given by:
Work = Force * Distance * cos(theta)
Where:
- Force is the applied force (in Newtons)
- Distance is the distance covered (in meters)
- theta is the angle between the applied force and the direction of motion
To find the distance covered, we need to convert the speed from centimeters per second to meters per second since the formula for work requires distance in meters.
Distance = Speed / 100
Now, let's plug in the values we have:
Force = 112 N
Distance = 20 cm / 100 = 0.2 m
theta = 37 degrees
Work = 112 N * 0.2 m * cos(37 degrees)
To calculate the power output, we need to divide the work done by the time taken. However, the time is not given in this problem. So we'll assume it to be 1 second for simplicity.
Power = Work / Time
Now let's calculate the power output:
Power = (112 N * 0.2 m * cos(37 degrees)) / 1 s
Using a calculator, we find:
Power ≈ 42.5 Watts
To convert this to horsepower, we use the conversion factor of 1 hp = 746 Watts:
Power = 42.5 Watts / 746
And finally:
Power ≈ 0.057 hp