How Does Inclination and Friction Affect Box Acceleration?

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In summary, a student is attempting to move a box of books into her dormitory room by pulling on a rope attached to the box with a force of 80 N at an angle of 25 degrees above the horizontal. The box has a mass of 25 kg and a coefficient of kinetic friction of 0.300 with the floor. After calculating the acceleration of the box on a flat surface, the student now attempts to move the box up a 10 degree incline while maintaining the same force and angle. However, the calculations show that the box will not move under these conditions.
  • #1
cy19861126
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A student decides to move a box of books into her dormitory room by pulling on a rope attached to the box. She pulls with a force of 80 N at an angle of 25 degree above the horizontal. The box has a mass of 25 kg, and the coefficient of kinetic friction between box and floor is 0.300. a) Find the acceleration of the box b) The student now starts moving the box up a 10 degree incline, keeping her 80 N force directed at 25 degree above the line of the incline. If the coefficient of friction is unchanged, what is the new acceleration of the box?

Thanks for the patience for reading the problem, my work so far is:
a) For the y component,
Fy = ma, since a is 0...
Ty+Ny-Wy = 0
80sin25+Ny-25*9.8 = 0
Ny = 211N

fx(friction) = uNy = 0.300*211N = 63.4

For the x component,
Fx = ma
Tx-fx = ma
80cos25-fx = 25a
72.5-63.4 = 25a
a = 0.364m/s2. This is my answer, but I'm not sure whether it's right or not, but the problem begins in part b.

b) For the y component
Fy = ma
Ny + Ty + Wy = 0
Ny + 80sin25-245cos10 = 0
Ny = 207.5

f = uN = 0.300 * 207.5 = 62.2N

For the x component.
F = ma
Tx-Wx-fx = ma
80cos25 - 245sin10-62.2 = 25a
a = -1.29m/s2

I do not believe the acceleration to be negative in the incline. If so, the student cannot pull the box up and the problem cannot have taken place. I checked my work for like 10 times. Can someone check what I did wrong? Thanks
 
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  • #2
a) looks good, but I didn't check your calculations.

b) is almost there. You just forgot to include the tilt of the incline when you computed the force of the student on the box.

Dorothy
 
  • #3
I didn't check your actual numbers (as I had broken the problem down slightly differently.) However, I agree (other than rounding) with your frictional force in part B. I too found that the parallel downhill component of the weight, along with the frictional force add up to more than the parallel uphill force from the string. i.e. it's not going up hill. (and therefore, friction would not actually be 62 Newtons)
 
  • #4
Dorothy Weglend said:
a) looks good, but I didn't check your calculations.

b) is almost there. You just forgot to include the tilt of the incline when you computed the force of the student on the box.

Dorothy

You sure about that? I may be mistaken, but I drew a free body diagram, and other than checking his final acceleration, I agreed with each of his values. :) Maybe I need help too!

Besides, just estimating - the parallel component of the acceleration of gravity to the surface of the incline would be 9.81 m/s^2 sin 10 degrees ~1.7m/s^2. Significantly more than his answer in part A. From that, it seems apparent that it's not going to go uphill.
 
  • #5
"keeping her 80 N force directed at 25 degree above the line of the incline."

The 25 degrees is above the incline, not above the horizontal... or am I having a complete brain fart here?
 
  • #6
Hi Sorry...

I needed more coffee. Yes, I agree, the box won't be moving uphill under these conditions. My mistake, and sorry about that.

Dorothy
 
  • #7
Alright, thanks guys. I thought I made a mistake up there but I couldn't figure out why. So the box will never be moved under these conditions
 

Related to How Does Inclination and Friction Affect Box Acceleration?

1. What is a force-related problem?

A force-related problem is any issue or situation that involves the application or interaction of forces. This can include problems related to motion, equilibrium, energy, or any other concept related to forces.

2. How do you solve a force-related problem?

To solve a force-related problem, you first need to identify the forces at play and their respective magnitudes and directions. Then, you can use laws and principles such as Newton's laws of motion or the principle of conservation of energy to analyze the problem and determine a solution.

3. What are some common examples of force-related problems?

Some common examples of force-related problems include calculating the tension in a string that is supporting an object, determining the acceleration of an object on an inclined plane, or finding the work done by a force on an object.

4. What are the units used to measure forces?

The unit of force is the Newton (N), named after Sir Isaac Newton. In the metric system, force can also be measured in kilogram-force (kgf) or gram-force (gf). In the imperial system, force is often measured in pounds (lbs) or pounds-force (lbf).

5. How can understanding force-related problems be useful in everyday life?

Understanding force-related problems can be useful in everyday life in many ways. For example, by understanding the forces involved in driving a car, you can make informed decisions on how to brake, accelerate, and turn safely. Additionally, understanding forces can help you to analyze and improve your performance in sports or other physical activities.

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