You push downward on a trunk at an angle 25° below the horizontal with a force of $750 \mathrm {~N} .$ 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?
A)81 kg
B)93 kg
C)73 kg
D)112 kg

Question

Quizplus · Accepted Answer

The correct answer is A.The force of friction is given by:$$f_s = \mu_s n$$where $\mu_s$ is the coefficient of static friction and $n$ is the normal force.The normal force is given by:$$n = mg - F_y$$where $m$ is the mass of the trunk, $g$ is the acceleration due to gravity, and $F_y$ is the component of the force applied in the vertical direction.The component of the force applied in the vertical direction is given by:$$F_y = F \sin 25^\circ$$Substituting these equations into the equation for the force of friction, we get:$$f_s = \mu_s (mg - F \sin 25^\circ)$$The maximum force of friction that can be applied without causing the trunk to move is given by:$$f_s \leq \mu_s n$$Substituting the equations for $f_s$ and $n$ into this equation, we get:$$\mu_s (mg - F \sin 25^\circ) \leq \mu_s mg$$Solving for $m$, we get:$$m \leq \frac{F \sin 25^\circ}{g}$$Substituting the given values into this equation, we get:$$m \leq \frac{750 \mathrm{~N} \sin 25^\circ}{9.81 \mathrm{~m/s^2}} = 81 \mathrm{~kg}$$Therefore, the most massive trunk that can be moved is 81 kg.

You Push Downward on a Trunk at an Angle 25° 750 N.750 \mathrm {~N} .750 N.

You Push Downward on a Trunk at an Angle 25° $750 \mathrm {~N} .$