Two masses on inclined plane with frictionless pulley

In summary, two blocks of different masses are attached by a string over a frictionless pulley and allowed to move on a fixed wedge. The coefficient of static friction for the aluminum block on steel is 0.61 and for the copper block on steel is 0.53. The coefficient of kinetic friction for the aluminum block on steel is 0.47 and for the copper block on steel is 0.36. The normal force on the copper block is 33.6 N and on the aluminum block is 9.8 N. The acceleration of both blocks will be the same parallel to the surfaces of the wedge. To solve for tension and acceleration, the equations for both blocks must be written and added, with the tension
  • #1
APPhysic
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0

Homework Statement



A 1.00-kg aluminum block and a 4.00-kg copper block are connected by a light string over a frictionless pulley. The two blocks
are allowed to move on a fixed steel block wedge (of angle 31.0°). The aluminum block is on the left side, on a flat plane. On the right is the copper block, sitting at a 31 degree angle. Picture is attached for clarification.
Coefficient of static friction for aluminum on steel: .61 Copper on steel: .53
Coefficient of kinetic friction for aluminum on steel: .47 Copper on steel: .36

Homework Equations


F=ma
ƩFx=Fgx-tension-frictional force=(m2)(acceleration)
Normal force=(massofcopperblock)(gravity)(cosθ)




The Attempt at a Solution


I was able to get the components of the force of gravity on the copper block: ≈33.6 N perpendicular to the plane, and ≈20.19 N parallel to the plane. Also, the normal force is 33.6 N. On the aluminum block, the normal and gravitational forces are both 9.8 N. From here, I am unsure how to incorporate the angle, the frictional forces, and how these will factor into solving for tension and acceleration of the bl

I seriously appreciate any help. It really means a lot for you to take the time to help a stranger out, I thank you immensely.
 

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  • #2
Hi APPhysic, welcome to PF:smile:

I see the equation for the cooper block, but miss the one for the aluminium block. What is its acceleration with respect to the acceleration of the cooper block? What forces act on it?

ehild
 
  • #3
ehild,

Thanks for the welcome! I believe the aluminum block has tension, normal & gravitational force, and the force of friction acting on it. And won't the copper and aluminum block have the same acceleration or no?
 
  • #4
Yes, the accelerations would be the same in this system.
 
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  • #5
APPhysic said:
ehild,

Thanks for the welcome! I believe the aluminum block has tension, normal & gravitational force, and the force of friction acting on it. And won't the copper and aluminum block have the same acceleration or no?

Yes, the acceleration of both blocks is the same parallel to the surfaces of the wedge. The normal force comes in by determining the force of friction. So what is the equation ƩF=ma for the aluminium block? .

ehild
 
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  • #6
Well, for the x component, ƩFx=T-fk=m1a1

And for y, ƩFy=n-m1g

So then, can I say that T-μkm1g=m1a1 ?

m1 in this case being the aluminum block
 
  • #7
APPhysic said:
Well, for the x component, ƩFx=T-fk=m1a1

And for y, ƩFy=n-m1g

So then, can I say that T-μkm1g=m1a1 ?

m1 in this case being the aluminum block

Calculate the friction forces, write up the equations for both blocks. Add them, the tension will cancel, and you can get the acceleration.


ehild
 

Related to Two masses on inclined plane with frictionless pulley

1. What is the purpose of using an inclined plane in this experiment?

The inclined plane allows for the two masses to move at a constant velocity without the influence of gravity. This allows for the effects of friction and the pulley to be isolated and studied.

2. What is the role of the frictionless pulley in this experiment?

The frictionless pulley is used to redirect the force of gravity, allowing for the two masses to move in opposite directions with equal tension on the string. This eliminates any external forces acting on the system and allows for the effects of friction to be observed.

3. How does the angle of the inclined plane affect the motion of the masses?

The steeper the angle of the inclined plane, the greater the acceleration of the masses. This is due to the increased component of gravity acting along the plane's surface. As the angle decreases, the acceleration decreases and eventually reaches zero at a horizontal angle.

4. Why is it important to have a frictionless pulley in this experiment?

If the pulley had friction, it would introduce an external force on the system and affect the acceleration of the masses. This would make it difficult to accurately analyze the effects of the inclined plane and friction on the motion of the masses.

5. How does the presence of friction on the inclined plane affect the results of the experiment?

If there is friction present on the inclined plane, it will oppose the motion of the masses and cause them to decelerate. This will result in a lower acceleration and a longer time for the masses to reach the bottom of the inclined plane. The coefficient of friction can be calculated from these results and used to understand its impact on the system.

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