How Do You Calculate the Acceleration of a Box on a Smooth Floor?

In summary, a box is released on a 30.6° incline and accelerates down the incline at 0.55 m/s2. The coefficient of kinetic friction between the two surfaces is 35.604.
  • #1
black_hole
75
0

Homework Statement



A student pulls a box of books on a smooth horizontal floor with a force of 138 N in a direction of 23.9° above the horizontal. If the mass of the box and the books is 51.6 kg, what is the acceleration of the box?

Homework Equations





The Attempt at a Solution



I got a force diagram. I know that Fg = 505.68N and that should be equal to Fn. I know that Ft is the force causing acceleration. What do I do from there?
 
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  • #2


black_hole said:
I got a force diagram.
Good.
I know that Fg = 505.68N
Right.
and that should be equal to Fn.
Not right. That pulling force, since it's at an angle, will affect the normal force. Luckily, that doesn't matter for this problem since there's no friction.
I know that Ft is the force causing acceleration.
What's the component of the pulling force in the direction of motion?
What do I do from there?
Apply Newton's 2nd law. What's the net force?
 
  • #3


Do you want to help me with this other one too?

A constant force of 2.2 N is required to drag a 49.2 kg box across a rough wooden floor at a constant speed of 2.2 m/s. Find the coefficient of sliding friction between the floor and the box.

I think Fn= Fg this time (b/c it is not at an angle), but what is Ff?
 
  • #4


black_hole said:
I think Fn= Fg this time (b/c it is not at an angle),
Good.
but what is Ff?
Hint: Since the box moves at a constant speed, what's the net force on it? (That should allow you to solve for Ff.)
 
  • #5


I don`t understand !
the box moves at a constant speed
so the net force would be F = 0
but what about friction ? wouldn`t be 0 ?
I`m confused
 
  • #6


MiniSmSm said:
the box moves at a constant speed
so the net force would be F = 0
That's true.
but what about friction ? wouldn`t be 0 ?
No, the friction isn't zero. (Friction is just one of the forces acting on the box.)
 
  • #7


So does that mean that Ff = 2.2 N? That would mean that the coefficient of friction would be 0.005?
 
  • #8


black_hole said:
So does that mean that Ff = 2.2 N?
Right.
That would mean that the coefficient of friction would be 0.005?
I would round off the answer to two significant figures, not one. But yes.
 
  • #9


Now I know I'm being really annoying, but what about this one...

A 7.4 kg box is released on a 30.6° incline and accelerates down the incline at 0.55 m/s2. What is the coefficient of kinetic friction between the two surfaces?

I found Fg = 72.52 N and Fgperpendicular = 62.421 N = Fn, Fgparallel = 36.916 N. But again I don't know how to find Ff?
 
  • #10


black_hole said:
But again I don't know how to find Ff?
Hint: Use Newton's 2nd law to find the net force.
 
  • #11


I don't get it? Fgparallel - Ff = Fnet = 72.52 N. So, Ff = 35.604?
 
  • #12


black_hole said:
Fgparallel - Ff = Fnet
That's correct.
= 72.52 N.
That's incorrect. Fnet ≠ Fg. Use Newton's 2nd law to get Fnet.
 
  • #13


Thank you. You've been a big help!
 

Related to How Do You Calculate the Acceleration of a Box on a Smooth Floor?

1. What is the purpose of "Forces coursework question"?

The purpose of "Forces coursework question" is to test your understanding and knowledge of the concept of forces, including Newton's Laws of Motion and other related topics. This coursework is typically assigned in physics or mechanics courses and is used to assess your ability to apply the principles of forces to real-world scenarios.

2. How is "Forces coursework question" typically structured?

"Forces coursework question" is typically structured as a problem-solving exercise. You will be given a scenario or situation and asked to identify the forces at play, their magnitudes and directions, and how they affect the objects in the scenario. You may also be asked to calculate the resulting acceleration or other related quantities.

3. What are some common topics covered in "Forces coursework question"?

Some common topics covered in "Forces coursework question" include Newton's Laws of Motion, friction, tension, gravity, and centripetal force. You may also be asked to apply these concepts to real-world scenarios, such as objects in motion, pulley systems, or objects on inclined planes.

4. How should I prepare for "Forces coursework question"?

To prepare for "Forces coursework question", it is important to have a solid understanding of the underlying concepts and principles. Reviewing your notes, textbook, and class lectures can be helpful. It is also beneficial to practice solving problems similar to those you may encounter in the coursework. Working with a study group or seeking help from your instructor can also aid in your preparation.

5. How will "Forces coursework question" be graded?

"Forces coursework question" is typically graded on the accuracy and completeness of your solutions. This includes correctly identifying forces, using appropriate equations, and showing your work. Your understanding of the underlying concepts and your ability to apply them to a variety of scenarios will also be evaluated. It is important to carefully read and follow the instructions and show all of your work to receive the best possible grade.

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