Solving Newton Force Problem: Two Blocks on Inclined Surface

In summary: You don't need to do that. You already have an equation that does not contain tension. Solve for a in that equation and then plug that into the first equation. You will then have an equation with only one unknown: theta. Then you can solve for theta.
  • #1

Homework Statement


Two blocks attached by a string are at rest on an inclined surface. The Lower Block has a mass of m1=0.2Kg and a coefficient of static friction u=0.4. The upper block has a mass m2=0.1Kg and a coefficient of static friction u=0.6. The angle theta is slowly increased.

Mass 2 is above Mass 1 in the picture!
Also theta is above the horizontal!


Homework Equations


Here are the questions it is asking for.
a)At what angle theta do the blocks begin to slide?
b)What is the tension in the string just before sliding begins?


I have a few questions myself about the setup.
Does the mass of the blocks have any revelence to the acceleration down the ramp? Or will there be tension in the string solely for the fact that the coefficent of friction for the upper block is higher making it move slower. I doubt a physics book would want do a problem where the rope is slack and the blocks collide. At least not in Newtons chapter about forces.

The Attempt at a Solution



I made the sum of forces for both i and j vectors for both blocks. I solved for the general equation of force normal and friction force for both blocks. Note that they are both the same equations.

Now I have theta, acceleration, and tension as unknown variables. What do I do next?


By the way thanks in advance for any help. And how do you guys actually use greek and mathmatical symbols in your text?
 
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  • #2
bassplayer142 said:

Homework Statement


Two blocks attached by a string are at rest on an inclined surface. The Lower Block has a mass of m1=0.2Kg and a coefficient of static friction u=0.4. The upper block has a mass m2=0.1Kg and a coefficient of static friction u=0.6. The angle theta is slowly increased.

Mass 2 is above Mass 1 in the picture!
Also theta is above the horizontal!


Homework Equations


Here are the questions it is asking for.
a)At what angle theta do the blocks begin to slide?
b)What is the tension in the string just before sliding begins?


I have a few questions myself about the setup.
Does the mass of the blocks have any revelence to the acceleration down the ramp? Or will there be tension in the string solely for the fact that the coefficent of friction for the upper block is higher making it move slower. I doubt a physics book would want do a problem where the rope is slack and the blocks collide. At least not in Newtons chapter about forces.

The Attempt at a Solution



I made the sum of forces for both i and j vectors for both blocks. I solved for the general equation of force normal and friction force for both blocks. Note that they are both the same equations.

Now I have theta, acceleration, and tension as unknown variables. What do I do next?


By the way thanks in advance for any help. And how do you guys actually use greek and mathmatical symbols in your text?
Which block wants to move first if there were no string? It might help to visua;lize what happens when the string is aded to the system. Forget about the acceleration variable...at the instant just before sliding, they are still at rest.
 
  • #3
I worked that out but I don't see how to get any farther. With 3 unknowns I'm not sure where to start. Maybe if my teacher would teach. :)
 
  • #4
bassplayer142 said:
I worked that out but I don't see how to get any farther. With 3 unknowns I'm not sure where to start. Maybe if my teacher would teach. :)
Why don't you show us the equations you are using. Did you take a free body diagram of each block. Don't worry about formula appearance for now ...instead of [tex] mgsin\theta [/tex] you can write mgsin theta...etc
 
  • #5
F=ma and f=un

For mass 1:

i: T + (F-friction) - M1*g*sin Theta = M1*a
j: (F-Normal) - M1*g*cos Theta = 0

for Mass 2:

i: (F-Friction) - T - M2*g*sin theta = M2*a

j: (F-Normal) - m2*g*cos Theta = 0

Note that the 2 in m2 would be a subscipt

Then I substituted F-normal into the friction equation for both masses. That is all I have so far.

thanks
 
  • #6
Your equations look good to me. The next step is to write an equation for the normal force for each case, i.e. (F-Normal) = ... and then substitute this into your (i) expressions for friction. Do you follow?
 
  • #7
Then I substituted F-normal into the friction equation for both masses. That is all I have so far.

I don;t know if you missed that but I did solve for the general equations of Force normal and Force of friction for both mass one and two.
 
  • #8
bassplayer142 said:
Then I substituted F-normal into the friction equation for both masses. That is all I have so far.

I don;t know if you missed that but I did solve for the general equations of Force normal and Force of friction for both mass one and two.
Sorry, didn't see that line. Okay, what can you tell me about the tension?
 
  • #9
I solved for T for mass 1 and then plugged it into the second mass equations T. So T canceled out and I'm left with Theta and Acceleration. I'm pretty sure you can't just set acceleration to zero because there is an infinite amount of possibilities then. Still stuck. Sorry for all the questions and thanks even more.

i got a= (4.578)cosTheta + (3.27)sinTheta
 
  • #10
bassplayer142 said:
I solved for T for mass 1 and then plugged it into the second mass equations T. So T canceled out and I'm left with Theta and Acceleration. I'm pretty sure you can't just set acceleration to zero because there is an infinite amount of possibilities then. Still stuck. Sorry for all the questions and thanks even more.

i got a= (4.578)cosTheta + (3.27)sinTheta
The reason why you might be stuck is that you are insisting that there must be an acceleration! The blocks are at rest at the start...and they are still at rest at the instant they are about to slide. No velocity change implies no acceleration. Try solving those equations again. There is only one solution.
 

1. What is the Newton Force Problem?

The Newton Force Problem refers to a physics problem that involves calculating the force required to move an object on an inclined surface. It is named after Sir Isaac Newton, who first described the relationship between force, mass, and acceleration.

2. How is force calculated in the Newton Force Problem?

Force is calculated using Newton's Second Law of Motion, which states that force equals mass multiplied by acceleration (F=ma). In the case of the Newton Force Problem, the force is the weight of the object being moved up the incline.

3. What factors affect the force required in the Newton Force Problem?

The force required in the Newton Force Problem is affected by the mass of the object being moved, the angle of the incline, and the gravitational force acting on the object. The greater the mass and the steeper the incline, the more force is needed to move the object.

4. How does friction play a role in the Newton Force Problem?

Friction is a force that opposes the motion of an object. In the Newton Force Problem, friction between the object and the incline surface can make it more difficult to move the object. Friction can be calculated and factored into the overall force required to move the object.

5. How is the Newton Force Problem used in real-world applications?

The Newton Force Problem is used in various engineering and construction projects to determine the force needed to move heavy objects on inclined surfaces. It is also used in sports and games that involve objects moving on slopes, such as skiing or billiards. Additionally, understanding the Newton Force Problem is important in the design of machines and vehicles that require force to move up ramps or hills.

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