You push downward on a trunk at an angle 25° below the horizontal with a force of If the trunk is on a flat surface and the coefficient of static friction between the surface and the trunk is 0.61, what is the most massive trunk you will be able to move?

Complete question is;

You push downward on a trunk at an angle 25° below the horizontal with a force of 750N. if the trunk is on a flat surface and the coefficient of static friction between the surface and the trunk is 0.61, what is the most massive trunk you will be able to move?

The most massive trunk is about 81.3 kg

Explanation:

I've attached a free body diagram that depicts this question.

Where;

N = normal force on the trunk

m = mass of the trunk

W = weight of the trunk = mg

F = static frictional force

Using equilibrium of force in vertical direction, we obtain;

N = W + 750 Sin25

N = mg + 750 Sin25    - - - - (eq 1)

Now, we are given that Coefficient of static friction: μ = 0.61

static frictional force is given by the formula;

F = μN

Since N = mg + 750 Sin25, we now have;

F = (0.61) (mg + 750 Sin25)   - - - (eq 2)

Along the horizontal direction, for the trunk to move, force equation must be;

F = 750 Cos25

Thus, we now have;

750 Cos25 = 0.61(mg + 750 Sin25)

g = 9.81.

So,we now have ;

750 Cos25 = 0.61(m(9.81) + 750Sin25)

750 × 0.9063 = 0.61(9.81m + (750 × 0.4226))

Divide both sides by 0.61;

(750 × 0.9063)/0.61 = 9.81m + 316.95

1114.3 = 9.81m + 316.95

1114.3 - 316.95 = 9.81m

797.35 = 9.81m

m = 797.35/9.81

m = 81.3 kg

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hope this