Newton's Three Laws (moving a box)

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In summary, the problem involves finding the force P needed to drag block B to the left at a constant speed in three different scenarios. In scenario A, where block A rests on B and moves with it, the force of friction is equal to 3 N. In scenario B, where block A is held at rest, the force of static friction on both blocks must be equal, but it is unclear whether P should be on the A or B side. In scenario C, where A and B are connected by a light flexible cord passing around a fixed frictionless pulley, the sum of the forces in the x-direction is equal to P, and the value of T must be determined in order to solve for P.
  • #1
southernbelle
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Homework Statement


Block A weighs 4 N and block B weighs 8N. The coefficient of sliding friction between all surfaces is 0.25. Find the force P necessary to drag block B to the left at a constant speed if
A) if A rests on B and moves with it
B) if A is held at rest
C) if A and B are connected by a light flexible cord passing around a fixed frictionless pulley.


The Attempt at a Solution


I have drawn the free body diagrams.

A) Ff=coefficient x Fn
= .25 (8 + 4)
= 3
Is that right?

B) I know the fsB = (8 + 4) coefficient of static friction
fsA = coefficient of static friction (4)

I also know that these have to be equal in order to move.
So...
fsA = fsB
But where do I put the P? On the A side or the B side?

C) I know that P must be equal to all the forces in the x-direction in order for the block to move.

The sum of the forces in the x-direction = T + fsA + fsB

so...
P = T + fsB + fsA
and
P = T + (.25)(4) + (.25)(12)
P = T + 4

How do I find T?
I know that the sum of all the forces = ma
And the acceleration in this case is 0.

But 0 = T + 4 would give T= -4.
And P =0.

I don't think that can be right.
 
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  • #2
A) correct

b) I think that block A is supposed to be held in place as B is dragged out from under it.
In this case there will be two forces of friction opposing force P

C) are the two weights hanging on either side of the pulley? is one on a surface while the other is hanging? I can't "see" what this one is supposed to look like.
 
  • #3


Your understanding and approach to Newton's laws in this scenario is generally correct. Let's go through each part in more detail:

A) For block B to move at a constant speed, the net force on it must be zero. This means that the force of friction (Ff) must equal the applied force (P). The calculation for Ff that you did is correct, but you need to also consider the weight of block B (8N) and its normal force (Fn) from block A. The normal force is equal to the weight of block A (4N) plus the weight of block B (8N). So the equation would be Ff = P = 0.25(8 + 4 + 8) = 5N.

B) In this case, block B is being held at rest, so the net force on it must be zero. This means that the force of static friction (fsB) must equal the applied force (P). The force of static friction is equal to the coefficient of static friction (0.25) times the normal force (Fn), which in this case is equal to the weight of block A (4N). So the equation would be fsB = P = 0.25(4) = 1N. This means that you would need to apply a force of at least 1N to block B in order to start moving it.

C) In this scenario, the force of tension (T) in the cord must be equal to the force of friction (Ff) in order for the blocks to move at a constant speed. The force of friction is equal to the coefficient of friction (0.25) times the normal force (Fn). The normal force in this case is equal to the weight of block A (4N). So the equation would be T = Ff = 0.25(4) = 1N. This means that you would need to apply a force of at least 1N to the cord in order to move the blocks at a constant speed.

Overall, your understanding of Newton's laws and the use of free body diagrams is good. Just make sure to consider all the forces (such as weight and normal force) and use the appropriate equations for each scenario.
 

What are Newton's Three Laws?

Newton's Three Laws are fundamental principles in physics that explain the behavior of objects in motion. They were developed by Sir Isaac Newton in the 17th century.

What is the first law of motion?

The first law, 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.

How do Newton's laws apply to moving a box?

For moving a box, the first law explains that the box will stay at rest or continue moving at a constant speed unless a force is applied to move it. The second law explains that the amount of force needed to move the box is directly proportional to its mass and acceleration. The third law states that for every action (force) there is an equal and opposite reaction, so pushing the box will also push back on you.

What is the second law of motion?

The second law, also known as the Law of Acceleration, states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. This means that the greater the force applied to the box, the greater its acceleration will be, and the heavier the box, the less it will accelerate.

How can Newton's Third Law be demonstrated when moving a box?

When moving a box, you can demonstrate the third law by pushing on the box and feeling the push back against your hand. This shows that for every force you apply to the box, there is an equal and opposite force being applied back on you. This is also why it can be difficult to move a heavy box - the box is pushing back against you with an equal force.

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