A 17.8-kg object is at rest on a horizontal surface. The coefficient of static friction is 0.65 and the coefficient of kinetic friction is 0.45. A horizontal force acts on the object...

Question

A 17.8-kg object is at rest on a horizontal surface. The coefficient of static friction is 0.65 and the coefficient of kinetic friction is 0.45. A horizontal force acts on the object.

a) Calculate the minimum force required to move the object.

b) Once it has started moving, what force is required to accelerate the object at 0.70 m/s2?

Answer 1

Draw the free body diagram.

F_G = mg = 17.8•9.81 = 174.618 N

∑Fy = 0 = F_N - F_G so F_N = F_G = 174.618 N

To consider initial movement, we look at FF as μs•F_N and we say that F > μs•F_N to begin movement. So the point at which movement begins is just slightly larger than 0.65•174.618 = 113.5 N or rounded F = 110 N

For acceleration, we would use F_NET = ma where F_NET = F - F_F so

F - F_F = ma

F = ma + F_F

F = ma + μ_k•F_N

F = (17.8)(0.70) + (0.45)(174.618)

F = 91 N

Answer 2

Hi Zoe.

The following images are pictures of the situation, along with all of the math. A verbal description is as follows: There are 4 forces acting on the object -- mg pointing down, Normal Force pinting up, F, the force acting on the object to move it, and fric, the frictional force, opposing the motion.

https://i.imgur.com/s24FzTq.jpg

https://i.imgur.com/TRaFcag.jpg?1

Part (a): Because the object is not yet moving, we have to use μ_static. When we do, this always gives us the minimum force needed to set an object in motion.

We treat the forces in the x-direction and y-direction separately -- you see that on the left and right of the image, respectively. The Sum of the Forces = mass x acceleration in that particular direction:

∑F = ma_x

∑F = ma_y

For part (a), since the object is not moving, acceleration in the x AND y directions is ZERO.

The rest is just algebra, which should be clear from the images.

Part (b): Everything is the same, except, since the object is now moving, we use μ_kinetic. Also, since we are now accelerating in the x- direction, now a_x is NOT ZERO.

Again, the rest should be clear from the math. If not, please let me know.

Best wishes

Raffi