Alden G. answered • 09/12/20
Work with Physics since high school up to university level
A problem like this works best when drawn with a free body diagram. Let's break this down into steps of how you would set that up.
1.) Define a coordinate system in x and y axes, and label which direction of each axis is positive. A common system to use is where the x axis has a positive direction going to the right, and the y axis has a positive direction going upwards. The opposite directions of each axis would be negative.
2.) Draw a general shape like a square to define as the "body" part of the free body diagram in your coordinate system. This behaves as the object being observed under motion in the free body diagram.
3.) Draw each vector of the forces behaving on the object. Do keep in mind that we have friction influencing our object's motion, so it will want to oppose the forces acting on the object in the same direction as frictional force. Let's assume the force acting on the object will move it to the right. In general:
> The 19N force should be drawn pointing right with respect to the object.
>The frictional force should point in a direction opposite to the force producing motion. Since the 19N force produces motion to the right, frictional force will point to the left.
>The weight of the object is produced from gravitational acceleration acting on the body. As a result, the force of weight on the object should be drawn pointing downwards.
>The normal force acts in response to the force of weight of the object in the opposite direction. In this case, the normal force of the object should be drawn pointing upwards.
4.) Now we must understand the relationship between Newton's second law and the motion of the object in two directions.
In general, we recall: ∑F = m*a, where m is the mass of the object, and a is the acceleration which produces motion.
In the x-direction, the problem tells us the object moves at a constant speed. If speed is constant, that means there is nothing which influences how speed changes over time for the object. As a result, the acceleration of the object in the x-direction is 0. Therefore:
∑Fx = m * ax = m * 0 = 0
∑Fx = 0 (Equation 1)
In the y-direction, our object does not move. As a result, there is no acceleration in the y-direction producing motion in that respective direction. Therefore:
∑Fy = m * ay = m * 0 = 0
∑Fy = 0 (Equation 2)
5.) Now that we have established the relationship of Newton's second law in two directions to the motion of the object, we can use each equation to help us find the coefficient of kinetic friction.
For each direction of motion, find the summation of forces in that particular direction, and set them equal to 0.
====>Using equation 1:
∑Fx = 0
19 - Ffriction = 0
Ffriction = 19
Now we can unravel this equation further to isolate the coefficient of kinetic friction in it. Recall that kinetic friction is equal to the product of the normal force of an object under the influence of kinetic friction and the coefficient of kinetic friction between the object and the surface where friction occurs:
FN * µk = 19
µk = 19 / FN (Equation 3)
=====>Using equation 2:
FN - W = 0
FN = W
We already know that the weight of the object, W, has a value of W = 173 N as described in the problem. Thus, from equation 2, we see that the value of our normal force, FN, is also equal to 173 N. Therefore:
FN = 173 (Equation 4)
6.) Finally, we can combine equations 3 and 4 to find the value of µk:
µk = 19 / FN
µk = 19 / 173
When calculated, we see our coefficient of kinetic friction, µk, has a value of approximately 0.1098, or, in solution form:
µk ≈ 0.1098
We do not need units for this value. Remember that a coefficient itself has no units. And just like that, we're done. Hope this helps!
