A lawn mower handle makes an angle of 60° with the ground. A woman pushes on the handle with a force of 30 pounds. How much work is done in moving the lawn mower a distance of 75 feet on level ground?
The work done in moving the lawn mower a distance of 75 feet on level ground is 1,125 foot-pounds. This can be calculated by multiplying the force (30 pounds) by the distance (75 feet) and then multiplying the result by the cosine of the angle (60°): (30 pounds) * (75 feet) * cos(60°) = 1,125 foot-pounds.
To calculate the work done in moving the lawn mower, we need to multiply the force applied by the distance moved in the direction of the force. In this case, the force applied is 30 pounds, and the distance moved is 75 feet.
However, we first need to find the component of the force that is in the direction of motion. Since the handle makes an angle of 60° with the ground, we need to determine the cosine of this angle to find the horizontal component of the force.
Cosine of 60° = adjacent/hypotenuse
Cosine of 60° = horizontal component of the force / 30 pounds
Simplifying this equation:
Horizontal component of the force = 30 pounds * cosine of 60°
The distance moved in the direction of the force is 75 feet. Therefore, the work done is:
Work = horizontal component of the force * distance moved
Work = (30 pounds * cosine of 60°) * 75 feet
Calculating the cosine of 60°:
Cosine of 60° = 0.5
Substituting this value into the equation:
Work = (30 pounds * 0.5) * 75 feet
Work = 15 pounds * 75 feet
Work = 1125 foot-pounds
Therefore, the work done in moving the lawn mower a distance of 75 feet on level ground is 1125 foot-pounds.
To find the work done in moving the lawn mower, we can use the formula:
Work = Force × Distance × cos(θ)
Where:
- Force is the amount of force applied (given as 30 pounds)
- Distance is the distance moved (given as 75 feet)
- θ (theta) is the angle between the force applied and the direction of movement (given as 60°)
First, we need to convert the force from pounds to Newtons (since the formula requires measurement in Newtons for consistency):
1 pound = 0.45359237 kg (approximately)
1 kg = 9.8 Newtons
So, the force in Newtons is:
Force = 30 × 0.45359237 × 9.8 ≈ 132.35 N
Now, we can substitute the values into the formula:
Work = 132.35 N × 75 ft × cos(60°)
To calculate this work, we need to convert feet to meters since the SI unit for distance is meters.
1 foot ≈ 0.3048 meters
So, the distance in meters is:
75 ft × 0.3048 ≈ 22.86 meters
Now, let's calculate the work:
Work = 132.35 N × 22.86 m × cos(60°)
The cosine of 60° is 0.5:
Work = 132.35 N × 22.86 m × 0.5
Finally, we can calculate the work:
Work = 1512.56 joules
Therefore, the work done in moving the lawn mower a distance of 75 feet on level ground is approximately 1512.56 joules.