How Do Newton's Laws Apply in Calculating Contact Force Between Boxes?

In summary, the conversation is about a physics problem involving three boxes with different masses and a horizontal force of 20.0 N. The solution involves using Newton's second law to find the contact force between the 3.45 kg and 5.55 kg boxes, which is found to be 10.95 N. The conversation also mentions the use of a free body diagram and Newton's third law to solve the problem. Ultimately, the easiest way to solve the problem is by examining the ratio of the total force to the total mass.
  • #1
pulau_tiga
13
0
Hi.

I have a physics question. I cannot get the right naswer.

The question:
Three boxes rest side-by-side on a smooth horizontal floor. Their masses are 1.10 kg, 3.45 kg, and 5.55 kg, with the 3.45 kg one in the center. A horizontal force of 20.0 N pushes on the 1.10 kg mass which pushes against the other two masses. What is thte contact force between the 3.45 kg and 5.55 kg boxes?

My solution:
I know that the force applied (20.0 N) is not constant throughout. However, acceleration of the full system is. Therefore I thought I could use Newton's 2nd Law. Fnet = ma.

Fnet of mass 1.10 kg = ma
rearranging gives a = 18.18 m/s^2.

Fnet of mass 3.45 = ma = 62.7 N

I thought this would be my contact force as this is the force that the 3.45 kg block pushes against the 5.55 kg box?/ Isn't this the answer? Can someone point me in the right direction or help me out.?? Thanks.
 
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  • #2
Have you drawn the free body diagram of the boxes individually ?
Have you applied Newton's third law as well ?For example, two forces acts on the 1.10 kg block which are the 20.0 N force and the contact force exerted on it by the middle block.
The 20.0 N force applied is constant of course or the question will get quite complicated.
 
  • #3
i assume friction is negligible.
i would like to use Newton's second law like this
first, the 20N force accelerates the whole system:
20N = (1.10 + 3.45 + 5.55)(kg)*a; => a_total = 1.99m/^s^2
so, the acceleration of the whole system of boxes is 1.99m/s^2.
Next, for the last box of weight 5.55kg to get an acceleration of 1.99m/s^2 you will need the contact force
F = m*a = (5.55)(kg)*(1.99)(m/s^2) = 10.95N.
This should be the force excerted on the last box of 5.55kg. Haven't had my morning coffee yet though, so i might be wrong :)

/edit
although the easiest way to solve this problem would be to examine the quota F/m. since the acceleration is the same for all parts of the system you could solve it like
F_tot/m_tot = F_3/m_3 and thus get the force on the third box (F_3)
 
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FAQ: How Do Newton's Laws Apply in Calculating Contact Force Between Boxes?

What are Newton's Laws of Motion?

Newton's Laws of Motion are three fundamental principles that describe the relationship between forces and motion. They were developed by Sir Isaac Newton in the 17th century and are still used today to understand and predict the behavior of objects in motion.

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 a straight line at a constant speed unless acted upon by an external force. This means that an object will not change its state of motion unless a force acts upon it.

What is the second law of motion?

The second law of motion 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 an object, the greater its acceleration will be. Similarly, the more massive an object is, the less it will accelerate for a given force.

What is the third law of motion?

The third law of motion 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. This is why we feel a push back when we push against a wall.

How do Newton's Laws of Motion apply to real-life situations?

Newton's Laws of Motion can be applied to a wide range of real-life situations, from the movement of objects on Earth to the motion of planets in the solar system. For example, the first law explains why a car will continue moving forward even after the engine has been turned off. The second law can be seen in action when a person jumps off a diving board and the third law is evident in the propulsion of a rocket into space.

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