A man pushes a lawn mower on a level lawn with a force of 200N it 40% of this force is directed downward how much woek is done by the man in pushing the mower 6.0m
Q. It the man in the above question expended 60 W of power in pushing the mower 6.0m, how much time is spent in pushing the mower this distance?
A. 10 seconds
To find the time spent in pushing the lawn mower, we can use the formula:
Work = Power × Time
First, let's find the work done by the man in pushing the mower. The work is calculated using the formula:
Work = Force × Distance × cos(θ)
where
Force = 200 N (the force exerted by the man)
Distance = 6.0 m (the distance pushed by the man)
However, we know that only 40% of the force is directed downward, which means we need to calculate the effective force:
Effective force = 40% * 200 N = 0.4 * 200 N = 80 N
Now, we can calculate the work done by the man:
Work = 80 N * 6.0 m = 480 J
Now, let's substitute the values in the power formula:
Power = Work / Time
We know that the power exerted by the man is 60 W, and the work done is 480 J. Substituting these values into the power formula, we get:
60 W = 480 J / Time
To find the time spent in pushing the mower, we rearrange the equation:
Time = 480 J / 60 W = 8 seconds
Therefore, the man spent 8 seconds in pushing the lawn mower a distance of 6.0 meters.
To find the work done by the man in pushing the mower, we can use the formula:
Work = Force * Distance * cos(theta)
where theta is the angle between the force vector and the displacement vector.
Given that the force applied by the man is 200N and 40% of this force is directed downward, we can calculate the vertical component of the force:
Vertical Force = 40% of 200N = 0.4 * 200N = 80N
Since the motion is happening on a level lawn, the vertical component of force does not contribute to the work done. Therefore, we only consider the horizontal component of force:
Horizontal Force = Total Force - Vertical Force = 200N - 80N = 120N
Now we can calculate the work done:
Work = Horizontal Force * Distance = 120N * 6.0m = 720 Joules
The work done by the man in pushing the mower is 720 Joules.
To find the time spent in pushing the mower, we can use the formula:
Power = Work / Time
Given that the power expended by the man is 60W and the work done is 720 Joules, we can rearrange the formula to solve for time:
Time = Work / Power = 720J / 60W = 12 seconds
Therefore, the man spends 12 seconds in pushing the mower this distance.