Solving Newton Law Problem: Find Acceleration & Tension

In summary, the conversation is about a physics problem involving four masses connected by strings on an incline. The goal is to find the acceleration of one mass and the tensions in the strings. A shortcut method is suggested, but the correct method is to apply F=ma to each mass separately. The final equation for acceleration is a = (F + mg sin(theta)) / m.
  • #1
moooocow
12
0
It is almost time for the end of term exam and I am looking over my old exams and am confused by one problem. Masses m1,m2,m3,m4 are cnnected together(by a "string") on an incline [tex]theta[/tex] = 22 degrees. m1 and tension = T1(connects m1 and m2) start nearest the bottem of the ramp, and a force F = 30N is pulling on m4 parallel to the ramp. We had to find the acceleration of m2 and the m3 tensions. The acceleration of course is the same for all of them.

I got a = F cos[tex]theta[/tex] / (m4 + m3 + m2 + m1) This got marked wrong, if anyone knows why I would greatly appreciate it. Thank you
 
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  • #2
Hint: the force F is parallel to the ramp.
 
  • #3
I am just really confused on this one, is it not needed to take the force in the "x" direction because since the acceleration and force are on the same "line", which we could use as the "x" axis? When finding the tension I had, for one example, m4*a = F cos(theta) - T3 cos(theta) and this was wrong too. I am really confused here if anyone could help with this type of problem, thank you very much.
 
  • #4
I guess my "hint" wasn't that helpful. :smile: I'll try again.

To find the overall acceleration, first find all the external forces acting on the masses (taking them as a system), taking their components parallel to the plane. The weight acts down, so you need to find the component of the weights acting down the plane. (Careful with the angles!) The only other force is the applied force F. Now add these forces, then apply
Fnet = mtotal a

To find the tension in the strings, apply F=ma to each mass separately and solve the set of equations.

Edit: Just to be clear, the first comment is a "short cut". By treating the masses as a single system, you can ignore the tensions in the strings--since they are all internal forces. If this is confusing you, forget it. Just apply F=ma to each mass separately: you'll get the same answer.
 
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  • #5
So the force on the individual pieces, and the object as a whole would just be the applied force to the x plane and the gravitational force to the x plane?

a = F + mg sin(Theta) / m

Thank you very much for the help, I have no idea why I was having so much trouble.
 
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  • #6
Originally posted by moooocow
So the force on the individual pieces, and the object as a whole would just be the applied force to the x plane and the gravitational force to the x plane?

a = F + mg sin(Theta) / m
Right! Treating the four masses as a single object, that's how you can find the acceleration. (I assume you meant a = (F + mg sin(Theta)) / m )

When treating each mass separately (which you must do to find the tension each string), don't forget to include the tension in any string touching the piece as well as the weight.
 

1. What is Newton's Second Law of Motion?

Newton's Second Law of Motion states that the acceleration of an object is directly proportional to the net force acting on the object and inversely proportional to its mass. This can be represented by the formula F=ma, where F is the net force, m is the mass, and a is the acceleration.

2. How do you solve for acceleration using Newton's Second Law?

To solve for acceleration, you need to determine the net force acting on the object and its mass. Then, plug these values into the formula F=ma and solve for a. Make sure to use consistent units for force (N) and mass (kg).

3. How do you solve for tension in a Newton's Law problem?

To solve for tension, you need to consider all the forces acting on the object including the force of tension. Use Newton's Second Law to set up an equation with all the forces and their respective directions. Then, solve for tension by isolating it in the equation.

4. Can you use Newton's Second Law to solve problems with multiple objects?

Yes, Newton's Second Law can be applied to solve problems with multiple objects. Each object will have its own equation of F=ma, and the net force acting on each object will be the sum of all the individual forces.

5. What are some common units used to measure acceleration and force in Newton's Second Law problems?

Acceleration is typically measured in meters per second squared (m/s^2) and force is measured in Newtons (N). However, other units such as feet per second squared (ft/s^2) and pounds (lb) may also be used, as long as they are consistent throughout the problem.

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