Free-Body Diagrams: Several Objects and Newton's Third Law

In summary, a system consisting of a box with mass 3.5 kg on a frictionless shelf, attached by strings to boxes with masses 1.5 kg and 2.5 kg, respectively, is released from rest. The acceleration of each box and the tension in each string are to be determined. Using the equation for the summation of forces in the x direction and the equation for the summation of forces in the y direction, the acceleration of each box is found to be 1.3 m/s^2. However, the signs in the equation for T1 may have been reversed, causing an incorrect result. Acknowledging that M1 will be in the upward direction and M3 in the downward direction may
  • #1
stridle
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Homework Statement


A box of mass m2=3.5 kg rests on a frictionless horizontal shelf and is attached by strings to bodes of masses m1 = 1.5 kg and m3 = 2.5kg. Both pulleys are frictionless and massless. The system is released from rest. After it is released, find (A) the acceleration of each of the boxes, and (B) the tension in each string.
T1=M1*g-M1*accel
T2=M2*g-M3g-M3*accel
Fn=M2*G
-T1+T2 = M3*accel

Homework Equations


Summation of Force in the x direction = m * acceleration. I set up three of these equations one for each object. I also set up the equation summation of force in the y direction = m * acceleration for m2 on a horizontal shelf.

The Attempt at a Solution


I have attempted to find ways of plugging the different equations into the other equations to produce the acceleration, but have failed to get the answer the textbook gets. Which is 1.3.
 
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  • #2
I figured it out. My T1 equation has reversed signs! Silly me. Thanks!
 
  • #3
Actually I cannot figure out where I went wrong on the T1 equation to mess up the signs. Do I need to acknowledge that M1 will be the weight going up and M3 will be in the downward direction? I think that will give me the correct signs for T1? I am a little confused I must admit.
 

FAQ: Free-Body Diagrams: Several Objects and Newton's Third Law

What is a free-body diagram?

A free-body diagram is a visual representation of all the forces acting on an object. It helps to analyze the motion of an object and understand the forces that are causing the motion.

How do you draw a free-body diagram?

To draw a free-body diagram, you need to first identify all the forces acting on the object. Then, draw a dot or a box to represent the object and draw arrows to represent the direction and magnitude of each force.

What is Newton's Third Law?

Newton's Third Law 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 force in the opposite direction.

How does Newton's Third Law apply to free-body diagrams?

In a free-body diagram, if there are two objects interacting with each other, the forces they exert on each other will be equal and opposite. This is shown by drawing arrows in opposite directions with the same magnitude for each force.

What is the purpose of using free-body diagrams in physics?

Free-body diagrams are used in physics to analyze and understand the forces acting on an object. By drawing a free-body diagram, we can identify the forces involved in a particular situation and use Newton's laws of motion to predict the motion of the object.

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