Blocks, incline, tension and acceleration

In summary, the larger block of mass slides down an incline due to the combined action of gravity and the coefficient of kinetic friction.
  • #1
noob314
18
0

Homework Statement


A large block of mass M = 6kg is on an incline which is at an angle of 30 degrees above the horizontal. The coefficient of kinetic friction between the block and the incline is 0.3. The block is attached to a string which runs over a pulley and is connected to a smaller block of mass m = 2.4 kg.

If the block is sliding up the incline, find a) the acceleration (magnitude and direction) of the smaller block m and b) the tension in the string.


The Attempt at a Solution


I need someone to confirm if what I'm doing is correct.

a)
[tex]\Sigma \vec{F}_{M} = Ma = T - f_{k} - Mgsin\theta[/tex]
[tex] T = M(gsin\theta + a + \mu_{k}gcos\theta) [/tex]
[tex]\Sigma\vec{F}_{m} = ma = mg - T[/tex]
[tex]= mg - M(gsin\theta + a + \mu_{k}gcos\theta)[/tex]
[tex] = ma + Ma = mg - Mgsin\theta - \mu_{k}Mgcos\theta[/tex]
[tex] = a(m+M) = mg - Mgsin\theta - \mu_{k}Mgcos\theta[/tex]
[tex] = a = \frac{mg - Mgsin\theta - \mu_{k}Mgcos\theta}{m+M}[/tex]
[tex] = a = -2.52\frac{m}{s^{2}}[/tex]
I'm guessing this is the acceleration in the y-direction, and the acceleration in the x-direction would be 0, so the magnitude is 2.52
[tex] = 2.52\frac{m}{s^{2}}[/tex] down

b)
[tex]\Sigma\vec{F}_{m} = mg - T = ma[/tex]
[tex] T = mg - ma[/tex]
[tex] = (2.4kg)(9.80 \frac{m}{s^{2}}) - (2.4kg)(2.52\frac{m}{s^{2}})[/tex]
[tex] = 17.47N[/tex]

Which looks about right, since in order for m to be moving down, mg needs to be greater than T, which in this case it is.
 

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  • #2
I haven't checked your equations, but you should first check the wording of the problem. The block can't be sliding up the plane, the hanging mass is too small to haul it up. It can't be sliding down the plane, either. Did you copy the problem down correctly?
 
  • #3
Yes, the problem is copied down correctly.
 
  • #4
noob314 said:
Yes, the problem is copied down correctly.
Then someone made a boo-boo. The problem makes no sense as written.
 
  • #5
Is it really impossible? I assumed some unknown force allowed it to overcome whatever static friction there may have been which would have allowed mass m to overcome the kinetic friction.
 
  • #6
noob314 said:
Is it really impossible? I assumed some unknown force allowed it to overcome whatever static friction there may have been which would have allowed mass m to overcome the kinetic friction.
What unknown force?
 
  • #7
I assume it would be a force that's barely able to overcome the static friction and then disappear after that.
 
  • #8
The more you try to make sense of this problem, the more it will confuse you. Just rip it up and try another problem.
 
  • #9
Yeah, you're right. I rechecked my calculations and the numbers didn't add up. I was just curious because it was on one of my old exams.
 

Related to Blocks, incline, tension and acceleration

1. How does the angle of an incline affect the acceleration of a block?

The angle of an incline does not affect the acceleration of a block. The acceleration of the block is determined by the force of gravity and the mass of the block, not the angle of the incline.

2. What is tension in relation to a block on an incline?

Tension is the force exerted by a string or rope that is attached to the block and pulling it up the incline. It is equal to the weight of the block in a static system where the block is not moving.

3. How can you calculate the acceleration of a block on an incline?

The acceleration of a block on an incline can be calculated using the formula a = (mgsinθ)/(m + M), where m is the mass of the block, M is the mass of the incline, g is the acceleration due to gravity (9.8 m/s2), and θ is the angle of the incline.

4. Can the tension in the string ever be greater than the weight of the block?

No, the tension in the string cannot be greater than the weight of the block in a static system. However, in a dynamic system where the block is accelerating, the tension may be greater than the weight of the block.

5. How does increasing the mass of the block affect the tension and acceleration on an incline?

Increasing the mass of the block will increase the tension in the string and decrease the acceleration of the block on an incline. This is because a heavier block requires more force (tension) to move and has a greater inertia, making it harder to accelerate.

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