# Motion on an incline plane (detailed)

• thomsora
In summary, the conversation discusses a problem involving two masses on an inclined plane connected by a cord and a pulley. The first part of the problem asks for the acceleration in the system and the tension in the rope, which are solved using the equations for sum of forces in the x and y directions. However, there seems to be some confusion about the direction of certain forces and the calculated acceleration may be incorrect. The second part of the problem asks for the final velocity after the masses have moved 1.00m, and the poster is unsure of how to incorporate friction into the velocity equation. They are seeking guidance on how to solve this part of the problem.
thomsora
Hey, folks! I've been working on this one problem for the past little bit. It has been giving me a lot of trouble and I think i just need a pointer or two on how to go about solving it.

http://i.imgur.com/nTGVz.jpg"

## Homework Statement

It's not the best image, but it gives the basic idea. I have two masses on an inclined plane connected with a cord over a pulley (kinetic friction included). It wants me to first solve for the acceleration in the system and then find the tension. The second part asks for me to find the final velocity after the masses have moved 1.00m (starting at rest)

mass #1 - 27.2 kg
mass #2 - 12.5 kg
theta - 5.23 deg
kinetic friction - 0.17

## Homework Equations

$\sum$Fx = max
$\sum$Fy= may

ax = ayramp (mass #1):
$\sum$Fx = -Ff - T + w1sin(theta) = max
$\sum$Fy= Fn - w1cos(theta) = max

hanging weight (mass #2):
$\sum$ T - w2=max

## The Attempt at a Solution

T=m2a+w2
T=12.5a + 122.625

Fn= m1a+ w1
Fn= 27.2a+ 265.721

Sub values in:

-Ff - T + w1sin(theta) = max

Ff = (co-efficient x Fn)

-(27.2a+265.721)0.17 -(12.5a + 122.625) + (27.2 x 9.81x sin of 5.23) = 27.2a

combine values:

44.324a= -143.48

a= -3.24 m/s sq

T= 12.5a + 122.625
T=12.5(-3.24) + 122.625
T= 82.1 N

I solved the first part of this equation by resolving my Fx and Fy into their components and then solving for T and Fn (normal). I then substituted my T and Fn back into my Fx and solved for my acceleration. The answer I got was -3.24 m/s sq.

Now with the second part of this problem i seem to be a little stuck. I am thinking i cannot use the traditional Vfsq= Visq + 2as (correct me if i am wrong). Since there is friction involved (kinetic =0.17) (static = ?) i somehow need to incorporate that as well as my components into my velocity equation but i am unsure on how to do this. If anyone has any tips on how to calculate the velocity it would be much appreciated. I am not looking for *the* answer, i just need some pointers

Thank you!

Last edited by a moderator:
Hi thomsora, welcome to PF.

Your value for the acceleration looks a bit high. Also, I'm not quite following your methodology; it looks to me like some of your force directions are mixed up. For example, on mass one (on the slope), shouldn't the frictional force OPPOSE the downslope force due to gravity of m1 AND the tension applied by the rope? Did you draw a Free Body Diagram for each mass?

## 1. What is motion on an incline plane?

Motion on an incline plane refers to the movement of an object along a sloped surface, such as a ramp or hill. The motion is influenced by both the force of gravity and the angle of the incline.

## 2. How is motion on an incline plane different from motion on a flat surface?

The main difference is that on an incline plane, the force of gravity acts on the object at an angle, causing it to accelerate both downwards and along the incline. On a flat surface, the force of gravity acts straight downwards and does not contribute to the object's horizontal acceleration.

## 3. What factors affect the motion of an object on an incline plane?

The motion of an object on an incline plane is affected by the angle of the incline, the force of gravity, the mass of the object, and the presence of any other external forces acting on the object.

## 4. How is the acceleration of an object on an incline plane calculated?

The acceleration of an object on an incline plane is calculated using the formula a = g*sin(θ), where g is the acceleration due to gravity (usually 9.8 m/s^2) and θ is the angle of the incline.

## 5. What is the significance of motion on an incline plane in physics?

Motion on an incline plane is an important concept in physics as it demonstrates the effects of forces acting on objects at different angles. It also helps to understand the relationship between force, mass, and acceleration, and how these factors affect an object's motion.

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