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 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 equal to the force pushing down on the trunk minus the force of friction:$$n = F_g - f_s = mg - \mu_s n$$Solving for $n$, we get:$$n = \frac{mg}{1 + \mu_s}$$The maximum force of friction is equal to the coefficient of static friction times the normal force:$$f_s = \mu_s n = \frac{\mu_s mg}{1 + \mu_s}$$The maximum force that can be applied to the trunk without it moving is equal to the force of friction:$$F = f_s = \frac{\mu_s mg}{1 + \mu_s}$$Substituting in the given values, we get:$$F = \frac{0.61 \times 9.81 \times m}{1 + 0.61} = 3.73m$$The most massive trunk that can be moved is therefore:$$m = \frac{F}{3.73} = \frac{750}{3.73} = 201 \mathrm{~kg}$$

You Push Downward on a Trunk at an Angle 25° 750 N750 \mathrm {~N}750 N

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