Finding acceleration and tension on an incline

In summary, the conversation discusses a question involving two boxes connected by a rope on an inclined plane. The question asks for the acceleration and tension, with given values for the masses, coefficient of friction, and angle of the incline. The conversation includes equations found online and an attempt at solving the problem, but a mistake is pointed out and the person is advised to derive the equations themselves for better understanding.
  • #1
soysauce
2
0

Homework Statement


Hi everyone, I hope you're enjoying your weekends!
I've been trying this question for a while not having any luck, I'm hoping someone can tell me where I'm going wrong

The question is:
Two boxes are connected by a rope that passes through a pulley on the corner of a incline. Box A is 2.5 kg and box B is 5.5 kg. The coefficient of kinetic friction on the incline is 0.54. Box A is on the incline and box B hangs over. The angle of the incline is 25.4º. Find the acceleration and the tension.

The answers given are 3.8 m/s2 [down] and 33 N [up]


Homework Equations



I got these equations from here:https://www.physicsforums.com/showthread.php?t=27346 and I understand why I would use them

Ft = m1 *a + m1gcosθ + μm1gcosθ and
Ft = m2(g-a)



The Attempt at a Solution



m1 = 2.5 kg, m2 = 5.5 kg, μ = 0.54, θ = 25.4°

I know I can equate the two tension equations to get:

m2(g-a) = m1 *a + m1gcosθ + μm1gcosθ

But when I plug in the known values and solve:

5.5(9.8-a) = 2.5*a + 2.5*9.8*cos(25.4) + 0.54*2.5*9.8cos(25.4)

I get a value of a = 2.4

Could someone tell me where I'm going wrong here?
Thanks so much in advance!
 
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  • #2
soysauce said:
Ft = m1 *a + m1gcosθ + μm1gcosθ and
Ft = m2(g-a)
In that first equation, one of those cosines should be a sine.

But please don't use someone else's derived equations. Derive them yourself, using Newton's 2nd law. Then you'll understand where they come from.
 
  • #3
Doc Al said:
In that first equation, one of those cosines should be a sine.

But please don't use someone else's derived equations. Derive them yourself, using Newton's 2nd law. Then you'll understand where they come from.

Whoops, that's true!
Thanks so much, I'll definitely be sure to in the future.
 

1. What is the formula for finding acceleration on an incline?

The formula for finding acceleration on an incline is a = sin(theta) * g, where theta is the angle of the incline and g is the acceleration due to gravity.

2. How do you calculate the tension on an incline?

The tension on an incline can be calculated using the formula T = m * (a + g * sin(theta)), where m is the mass of the object on the incline, a is the acceleration, and theta is the angle of the incline.

3. What is the relationship between acceleration and the angle of the incline?

The relationship between acceleration and the angle of the incline is directly proportional. This means that as the angle of the incline increases, the acceleration also increases.

4. How does the mass of the object affect the acceleration and tension on an incline?

The mass of the object has a direct effect on both the acceleration and tension on an incline. As the mass increases, the acceleration decreases, and the tension increases.

5. Can the acceleration on an incline ever be greater than the acceleration due to gravity?

No, the acceleration on an incline can never be greater than the acceleration due to gravity. The maximum acceleration on an incline will always be equal to the acceleration due to gravity, which is 9.8 m/s^2.

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