1 pulley, 2 masses, 2 inclines

[TheronSimon]

Homework Statement

Calculate the tension in the cable connecting the two masses. Assume all surfaces are frictionless.
in lieu of the picture here are the given specs:

on the left side a 5 kg mass with a 60' incline
on the right side a 6 kg mass with a 70'incline

Homework Equations

a=Fgsinθ
Fnet = ma

The Attempt at a Solution

my attempt was to calculate both sides for acceleration since its frictionless both would be non dependant on the weight of the mass
then i used
Fnet=ma
so Ft-Fg = ma
and after the math Ft = 41.45 and for the right side Ft= 114.66 but its the wrong answer so how do i complete this question?

 

[PhanthomJay]

my attempt was to calculate both sides for acceleration since its frictionless both would be non dependant on the weight of the mass

that is not true when you have diffferent inclines with the masses connected by a cable

then i used
Fnet=ma

you have to look at each mass separately using a free body diagram to identify the forces acting along the incline and apply Newton 2 to each mass separately

so Ft-Fg = ma

the tension force on each block is Ft directed along the incline and pulling away from the mass you are examining. But the gravity force along the incline is a component of Fg.

and after the math Ft = 41.45 and for the right side Ft= 114.66 but its the wrong answer so how do i complete this question?

Note when you redo this problem that the tension in a cable wrapped around an ideal pulley is the same on both sides of the pulley.

 

[TheronSimon]

Im still lost :S

 

[emailanmol]

As mentioned by PhanthomJay,

the only analytical approach is to draw a Free Body Diagram(FBD) of both bodies and the string and identifying the constraints.

Guessing that the values shouldn't depend on mass, is risky and should be avoided at all costs.

When you draw the FBD of blocks, forces acting on them are their weight components parallel and perpendicular to incline.The normal reaction exerted by inclines and the tension force exerted by chord.

Now you draw the FBD of string which will help you corelate the tension forces exerted by strings on both bodies.(What is it? How does the mass of string affect this relation?)

Finally you identify the constraints.The only possible movement can be parallel to the inclined surfaces (body 1 will move parallel to incline 1, body 2 will move parallel to incline 2)and at all times no motion takes place perpendicular to the incline(body 1 has no motion perpendicular to incline 1 and body 2 has no motion perpendicular to incline 2).

Plug in the values.
Apply Netwons 2nd and Third Law relating action reaction forces.
What do you see?

 

[asteriatic]

I would like to point out that your attempted solution is on the right track, but there are a few errors that may have led to the wrong answer. Here are some suggestions for solving this problem correctly:

1. Draw a free body diagram for each mass, showing all the forces acting on them. This will help you visualize the problem and identify the relevant forces.

2. Since the surfaces are frictionless, the only forces acting on the masses are their weight (Fg) and the tension in the cable (Ft). Use the equations you listed to set up a system of equations that relates the two masses and their respective accelerations.

3. Remember that the acceleration of the two masses must be the same, since they are connected by a cable and cannot move independently of each other. This means that you can set the two equations for acceleration equal to each other and solve for the tension (Ft).

4. Be careful with the signs of the forces. For example, on the left side, the weight of the mass is acting down the incline, so it should be Fg sin(60°), not Fg sin(70°) as you have written. Similarly, on the right side, the weight of the mass is acting down the incline, so it should be Fg sin(70°), not Fg sin(60°).

By following these steps, you should be able to solve for the tension in the cable connecting the two masses. Remember to double check your calculations and make sure your units are consistent. Good luck!