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?
Answer:
The most massive trunk is about 81.3 kg
Step-by-step 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