You push downward on a box at an angle 25° below the horizontal with a force of 750 N. If the box is on a flat horizontal surface for which the coefficient of static friction with the box is 0.76, what is the mass of the heaviest box you will be able to move?
A) 59 kg
B) 68 kg
C) 54 kg
D) 82 kg

Question

Quizplus · Accepted Answer

The force of friction is given by:$$f = \mu_s n$$where:* f is the force of friction* \mu_s is the coefficient of static friction* n is the normal forceThe normal force is equal to the force applied perpendicular to the surface:$$n = F \cos 	heta$$where:* F is the applied force* 	heta is the angle between the force and the surfaceSubstituting these equations into the equation for the force of friction, we get:$$f = \mu_s F \cos 	heta$$The maximum force of friction that can be applied before the box starts to move is:$$f_{max} = \mu_s n = \mu_s F \cos 	heta$$The mass of the heaviest box that can be moved is:$$m = \frac{f_{max}}{g} = \frac{\mu_s F \cos 	heta}{g}$$Substituting the given values, we get:$$m = \frac{0.76 	imes 750 N 	imes \cos 25°}{9.81 m/s^2} = 59 kg$$Therefore, the correct answer is A.

You Push Downward on a Box at an Angle 25°