A man pushes a lawn mower on a level lawn with a force of 203 N. If 26% of this force is directed downward, how much work is done by the man in pushing the mower 7.0 m?
To find the work done by the man in pushing the mower, we need to calculate the force component and multiply it by the distance.
Given:
Force exerted by the man = 203 N
Percentage of force directed downward = 26%
Distance covered = 7.0 m
Step 1: Calculate the force component directed downward.
Force component directed downward = (26/100) * 203 N
= 52.78 N (rounded to two decimal places)
Step 2: Calculate the force component directed horizontally (level lawn).
Force component directed horizontally = Force exerted by the man - Force component directed downward
= 203 N - 52.78 N
= 150.22 N (rounded to two decimal places)
Step 3: Calculate the work done by multiplying the force component directed horizontally by the distance covered.
Work done = Force component directed horizontally * Distance covered
= 150.22 N * 7.0 m
= 1051.54 joules (rounded to two decimal places)
Therefore, the man does 1051.54 joules of work in pushing the mower 7.0 m.
To calculate the work done, we need to know the formula for work, which is:
Work = Force x Distance x Cosine(θ)
In this case, the force is the total force exerted by the man, which is 203 N. However, we need to find the component of the force directed downward, which is 26% of the total force.
So, the force directed downward is calculated as:
Force downward = 26% of 203 N = 0.26 x 203 N = 52.78 N
Now, we can calculate the work done using the formula mentioned above. The distance is given as 7.0 m, and since the lawn is level, the angle θ between the force and the direction of motion is 0 degrees (cosine of 0 degrees is 1).
Therefore, the work done is:
Work = Force x Distance x Cosine(θ)
= (203 N - 52.78 N) x 7.0 m x Cosine(0 degrees)
= (150.22 N) x 7.0 m x 1
= 1051.54 Nm
Therefore, the work done by the man in pushing the mower 7.0 m is 1051.54 Nm.