A lawn roller is rolled across a lawn by a force
of 115 N along the direction of the handle,
which is 18.7 degrees above the horizontal.
If the lawn roller develops 65.9 W of power
for 53 s, what distance is the roller pushed?
Answer in units of m.
To find the distance the lawn roller is pushed, we need to calculate the work done by the force applied to it. The formula for work is:
Work = Force x Distance x cos(theta)
Where:
- Work is measured in joules (J)
- Force is the magnitude of the force applied, measured in newtons (N)
- Distance is the distance over which the force is applied, measured in meters (m)
- theta (θ) is the angle between the force vector and the displacement vector
In this case, we are given the force (115 N) and the power (65.9 W). Power is defined as the rate at which work is done, given by the formula:
Power = Work / Time
Rearranging the formula, we can write:
Work = Power x Time
Let's substitute the given power and time into this equation and solve for the work done:
Work = 65.9 W x 53 s
Work = 3492.7 J
Now, we can rearrange the work formula to find the distance:
Distance = Work / (Force x cos(theta))
Substituting the known values:
Distance = 3492.7 J / (115 N x cos(18.7°))
Now, we can calculate the angle's cosine value and substitute it into the equation:
cos(18.7°) = 0.948
Distance = 3492.7 J / (115 N x 0.948)
Calculating the result:
Distance = 31.29 m
Therefore, the lawn roller is pushed a distance of 31.29 meters.