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## Homework Statement

A boy is pushing a lawnmower (25kg) with 200N of force on a handle that is angled 35 below the horizontal. The mower is accelerating at 0.9m/s^2. If the boy would like to maintain a constant velocity, what force does he need to apply to the mower handle.

Assume g = 9.8 [d]

## Homework Equations

F

_{net}= ma

F

_{net}= F

_{app}+ F

_{fr}

F

_{fr}= F

_{N}* μ

## The Attempt at a Solution

To find the components of the 200N force [35 degrees above horizon], I simply draw out the triangle and use sin and cos to find it. I found:

F

_{x}= 200cos35 = 163.83N [forward]

F

_{y}= 200sin35 = 114.71N [down]

Since it's accelerating, there is a net force. Using the two following equations,

F

_{net}= ma

F

_{net}= F

_{app}+ F

_{fr}

(25)(0.9) = F

_{fr}+ F

_{x}

(25)(0.9) = F

_{n}* μ + 163.83

(25)(0.9) = (F

_{g}+ F

_{y}) * μ + 163.83

and I end up with F

_{fr}= 141.33N [backwards], and the coefficient of friction ends up to be 0.393.

To find the force required to keep the lawnmower in constant velocity: (Letting x2 and y2 be the new components of the second applied force)

F

_{fr2}= F

_{x2}

F

_{N2}+ F

_{y2}* μ = (245 + F

_{y2}) * 0.393 = F

_{x2}

I tried my best to show and explain what I have so far, but I don't know how to continue. I only have 1 equation and 2 unknowns. (The answer to the question is apparently 168N)

Thanks in advance.

EDIT:

I noticed a second relation that can be used: F

_{x2}* tan35 = F

_{y2}

But when I solve the 2 unknowns using the 2 equations, I end up with;

F

_{x2}= 132.840N [forward]

F

_{y2}= 92.992N [down]

And if I use the Pythagorean theorem, I end up with F

_{app2}= 162N [35degrees below horizon], which is a little different than the answer of 168N.

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