Solve Free Body Diagram: 2 Boxes, m1=35kg, m2=45kg

In summary, the homework problem involves two boxes of masses 35kg and 45kg hanging vertically from opposite ends of a rope over a horizontal metal rod. The task is to determine the acceleration of the boxes, the tension in the rope, and the displacement of each box after 0.5s. Applying Newton's 2nd law and assuming negligible friction, two equations can be solved together to find the unknown variables. It is important to establish a consistent sign convention and consider the relation between the accelerations of the two masses.
  • #1
cindy!
4
0

Homework Statement



Two boxes of masses m=35kg and m2=45kg, are hung vertically from opposite ends of a rope passing over a rigid horizontal metal rod. They system starts moving from rest. Assuming that friction between the rod and the rope is negligible, determine the magnitude of
(a) the acceleration of the boxes
(b) the tension in the rope
(c) the magnitude of each box's displacement after 0.5s

Homework Equations



Fnet=ma
Fnet= FT - Fg
ma=FT-Fg

(well i think this is right, depending on how the free body diagram is drawn..)


The Attempt at a Solution



Well...I have no idea what the question is saying, I am unsure how to draw the actual diagram and also how to draw the FBD. This is how i inteperted it:

2dtzqs5.jpg


4bso6zq.jpg
 
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  • #2
maybe I am reading it wrong, but the way i read it was that there are 2 boxes tied to each other with a rope and that rope is hung on an iron bar.
 
  • #3
What's F_R in your diagram?? I agree with fizz on the interpretation of the problem.
 
  • #4
I assume you are to treat this just as you would if the rod were a frictionless (and massless) pulley. Draw a free body diagram for each mass separately.

Apply Newton's 2nd law to each mass (just like in your equations) to get two equations, which you'll solve together. Hint: Adopt a consistent sign convention, for example: up is positive and down is negative. Let "a" be the magnitude of the acceleration; how do the accelerations of the masses relate to each other?
 

1. How do you draw a free body diagram?

To draw a free body diagram, you first need to identify all of the forces acting on the system. These can include external forces, such as gravity or friction, as well as internal forces, such as tension or compression. Then, draw a dot to represent the object and arrows to represent each force, with the direction and magnitude of the force labeled.

2. What are the steps to solve a free body diagram?

The steps to solve a free body diagram are:

  1. Identify all the forces acting on the system.
  2. Draw a dot to represent the object and arrows to represent each force.
  3. Label the direction and magnitude of each force.
  4. Apply Newton's Second Law (F=ma) to find the acceleration of the system.
  5. Use the acceleration to calculate the net force on the system.
  6. Check for equilibrium by making sure the sum of all forces equals zero.

3. How do you calculate the net force in a free body diagram?

To calculate the net force in a free body diagram, you need to add up all of the forces acting on the system. If the forces are acting in the same direction, you simply add them together. If the forces are acting in opposite directions, you subtract the smaller force from the larger one. The net force can also be calculated by using the equation F=ma, where F is the net force and a is the acceleration of the system.

4. What is the importance of solving a free body diagram?

Solving a free body diagram is important because it allows us to understand the forces acting on a system and how they affect the motion of that system. It helps us to predict the behavior of objects in different situations and can be used to design and analyze structures and machines. Free body diagrams are also an important tool in understanding and applying Newton's laws of motion.

5. Can a free body diagram be used to solve any type of problem?

Yes, a free body diagram can be used to solve many different types of problems, as long as the system can be represented by a dot and arrows to represent forces. Free body diagrams can be applied to objects at rest, moving with constant velocity, or accelerating. They can also be used to analyze systems with multiple objects or to determine the forces acting on a single object in a complex system.

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