A gardener pushes a mower at a distance of 900 m while mowing the yard. The handle of the mower makes an angle of 40.0 with the ground. The gardener exerts a force of 35.0 n along the handle of the mower. How much work does the gardener do in mowing the lawn?
To find the work done by the gardener in mowing the lawn, we can use the equation:
Work = Force * Distance * Cos(theta)
Where:
- Work is the amount of work done
- Force is the force applied by the gardener
- Distance is the distance traveled
- Cos(theta) is the cosine of the angle between the force applied and the direction of motion
In this case, Force = 35.0 N and Distance = 900 m. We also have the angle between the force and the ground, which is 40.0 degrees.
First, we need to convert the angle from degrees to radians, since the cosine function takes radians as input. To convert degrees to radians, we use the formula:
radians = degrees * (pi/180)
So, theta (in radians) = 40.0 * (pi/180)
Next, we can substitute the values into the equation:
Work = 35.0 N * 900 m * cos(40.0 * (pi/180))
Now, we can calculate the work using a calculator or a programming language that supports trigonometric functions. The final answer will depend on the exact value of cos(40.0 * (pi/180)).