What is the acceleration of a crate with two applied forces and friction?

In summary, the conversation discusses a problem involving a 25 kg crate initially at rest. Two forces, F1 and F2, are applied to the crate and it starts to move. The coefficient of kinetic friction between the crate and the floor is .35. The goal is to determine the magnitude and direction of the crate's acceleration relative to the x-axis. After working out the problem, there is a discrepancy between the answer in the book and the answer calculated by the person involved in the conversation. It is suggested that the book may be wrong due to the assumption that the normal force is equal to the weight of the box. However, it is clarified that the perspective used is a "bird's-eye" perspective.
  • #1
gharada
3
0
1. A 25 kg crate is initially at rest. Two forces, F1 and F2, are applied to the crate and it begins to move. The coefficient of kinetic friction between the crate and the floor is .35. Determine the magnitude and direction of (relative to the x-axis) the acceleration of the crate.

F1= 88N 55 degrees north of east.
F2= 54N east.

2. Equations:

Fk= (.35)Fn
a^2 + b^2= c^2

3. I worked out the problem and got an answer of 2.21 m/s^2 33 degrees north of east. However the answer in the book says 1.65 m/s^2 34 degrees north of east. I solved for the kinetic friction and got 85.75 N. I then broke the 88N and 85.75 friction down into horizontal and vertical components. I combined them, did the pythagorean thm, and found 55.75 for my force. I divided by 25kg to find the acceleration I got.

I did the problem again, but mistakingly switched the x and y components of the kinetic friction (49.18 and 70.242 respectively) and got the exact answer in the book? Could the book be wrong? Help please! Thanks.
 
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  • #2
Hello and welcome to PF!

Your problem is that you treat the normal force as if it were equal to the weight of the box. Draw a free body diagram and you will see that if this were the case, the box would be accelerating upwards!
 
  • #3
Sorry, I forgot to mention that the box is looked at from a "bird's-eye" perspective. Does that change anything?
 

FAQ: What is the acceleration of a crate with two applied forces and friction?

What is a vector force with friction?

A vector force with friction is a type of force that occurs when two objects come into contact and one object's motion is hindered by the other object's rough surface. The force has both magnitude and direction, and can be represented graphically as an arrow.

How is the magnitude of a vector force with friction determined?

The magnitude of a vector force with friction is determined by the coefficient of friction between the two surfaces in contact and the normal force acting between them. It can be calculated using the formula Ff = μFn, where Ff is the force of friction, μ is the coefficient of friction, and Fn is the normal force.

What is the difference between static and kinetic friction?

Static friction occurs when two objects are not moving relative to each other, while kinetic friction occurs when two objects are sliding against each other. The coefficient of static friction is typically higher than the coefficient of kinetic friction, meaning that it takes more force to overcome static friction and start an object moving than it does to keep an object in motion.

How is the direction of a vector force with friction determined?

The direction of a vector force with friction is determined by the direction of the normal force acting between the two surfaces in contact. The force of friction always acts in the opposite direction of the motion or potential motion of an object.

What are some real-life examples of vector forces with friction?

Some real-life examples of vector forces with friction include pushing a heavy object across the floor, rubbing your hands together to generate heat, and stopping a car by applying the brakes. These situations all involve two surfaces in contact with each other and a force that opposes motion or potential motion between them.

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