How do Newton's Laws work in these situations?

In summary, we have discussed three scenarios involving forces and friction. In the first scenario, a 5kg box with a friction coefficient of .25 was pulled by a horizontal force of 20N, resulting in a friction force of 12.25N, which is less than the applied force and therefore the box did not move. In the second scenario, a 5kg sled with a friction coefficient of .1 was pulled at an angle of 5 degrees, resulting in an acceleration of 3.004 m/s^2, which was rounded differently than the correct answer of 2.99 m/s^2. In the third scenario, a 2kg object with a constant net force experienced a change in velocity from
  • #1
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1) A 5kg box is pulled by a force F horizontally (no angle). There is friction between the box and horizontal surface. Mu_k = .25 and Mu_s = .5. If F=20N find the magnitude of the friction force and the acceleration of the block.

I used the formula |f_k| = mu_k * |Normal force|

f_k = .25 * 9.8 * 5
f_k = 12.25 N

The correct answer is that the friction is 20 N, meaning that the block didn't move. Where did I go wrong?

2) A 5kg sled is pulled an an angle 5 degree above the horizontal. Friction between the sled and the snow is described by mu_k = .1 and mu_s = .15. What is acceleration of the sled?

The correct answer is 2.99 m/s^2

This is what I did.

I took the 20 N and multiply by cos (5 degree) to get 19.92.

|f_k| = mu_k * N
f_k = .1*5*9.8
f_k = 4.9

(19.92 - 4.9) / 5 = a
a = 3.004

Did I just round my answer differently or did I do something wrong?

3) A 2kg object is under the influences of several forces. Assume that the net force is constant. At t=0, the object's velocity is 3i + 2j and at t=4s its velocity is 11i - 14j . Find the magnitude and direction of net force acting on the object. Please explain this to me. I have no idea how to start.

Thanks in advance for your help.
 
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  • #2
Can you please tell me what Mu_k, Mu_s and |f_k| all mean? I'm doing similar stuff to this at the moment but I don't recognise those things you are using.
 
  • #3
Mu_k is the coefficient of kinetic friction
Mu_s is coefficient of static friction

|f_k| is kinetic friction
|f_s| is static friction
 
  • #4
Oh okay gotcha. Yeah I actually probably can't help because I haven't yet delved into static and kinetic friction really. I have worked with simply friction before without determining differences between the two
 
  • #5
Before the box moves, it is static friction that is important. You calculated the acceleration using kinetic friction. Go back and do it using static friction.
 
  • #6
Thanks for your help. Since the static friction is greater than the force pushing the object, the object will not move. Since 20N is applied on the object, the friction is also 20N according to Newton's Third Law. Am I correct?
 

1. What are Newton's Laws of Motion?

Newton's Laws of Motion are three physical laws that describe the behavior of objects in motion. They were developed by Sir Isaac Newton in the 17th century and are considered the foundation of classical mechanics.

2. What is the First Law of Motion?

The First Law of Motion, also known as the Law of Inertia, states that an object at rest will remain at rest and an object in motion will continue in motion at a constant velocity unless acted upon by an external force.

3. What is the Second Law of Motion?

The Second Law of Motion states that the force applied to an object is equal to its mass multiplied by its acceleration (F=ma). This means that the greater the mass of an object, the more force is needed to accelerate it, and the greater the acceleration, the more force is needed to maintain it.

4. What is the Third Law of Motion?

The Third Law of Motion, also known as the Law of Action and Reaction, states that for every action, there is an equal and opposite reaction. This means that when one object exerts a force on another object, the second object will exert an equal and opposite force back on the first object.

5. How can I apply Newton's Laws to solve problems?

To solve problems involving Newton's Laws, you will need to identify the forces acting on an object, determine the net force, and use Newton's Second Law to calculate the acceleration. You may also need to use Newton's Third Law to determine the reaction force. It is important to draw free-body diagrams and use appropriate units in your calculations.

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