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)
1. 0.040 hp
2. 0.024 hp
3. 0.034 hp
4. 0.020 hp
5. 0.030 hp
6. 0.044 hp
horizontal force = 112 cos 37
speed = .2 m/s
power = 112 cos 37 * .2 = 17.9 Watts
17.9/746 = 0.024 Hp
To find the woman's power output, we need to first calculate the work done by the woman in pushing the lawn mower. The formula for work is given by:
Work = Force * Distance * cos(theta)
Where:
Force = 112 N (constant force applied by the woman)
Distance = speed * time
speed = 20 cm/sec
theta = 37º (angle made with the horizontal)
Let's calculate the distance:
Distance = speed * time
We are not given a specific time, so we cannot calculate the distance accurately. Therefore, we need to assume a time to proceed with the calculation. Let's assume that the time is 1 second.
Distance = 20 cm/sec * 1 sec = 20 cm
Now we can calculate the work done:
Work = 112 N * 20 cm * cos(37º)
To find the power, we need to divide the work by the time taken. Assuming the time taken is 1 second, we can proceed with the calculation.
Power = Work / time
Now, let's calculate the power in watts and then convert it to horsepower:
Power (in watts) = Work (in joules) / time (in seconds)
But since we don't have the time given, let's calculate the power in watts first and then convert it to horsepower:
Power (in watts) = 112 N * 20 cm * cos(37º) / 1 s
Now, let's convert the power to horsepower:
Power (in hp) = Power (in watts) / 746
Calculating the expression for power (in watts) and then converting it to horsepower gives us the value.