# Connected particles on an inclined plane

• Taylan
In summary, the mass of m2 needed to hold the system in balance is 57.85kg and the minimum mass of m2 needed to make m1 move upwards is 78.54kg. When considering the acceleration of both particles, the static friction coefficient can be left out of the calculations since the blocks are moving, and the resulting acceleration is 1.81m/s2.
Taylan

## Homework Statement

Mass of m1=90kg
Inclination is 40degrees. (see the attachment)

a) What must be the size of m2 , to hold the system in balance (no movement) ?

b)what must be the size of m2 at least, to make m1 move upwards. The static friction coefficient between m1 and the plane is 0.3.

c) what is the acceleration of the both particles in b) if the static coefficient of friction is overcome and the sliding friction coefficient is 0.15=

F=ma
Ffriction= μR

## The Attempt at a Solution

I am clear with a and b. the tension pulling both particles and the acceleration of the particles is the same in this kind of questions. I write equations for T (tension) for both particles separately (ex.. for m2 --> T-mg=ma) and substitute them to find a and T.
in a, mass of m2 found to be 57.85kg and in b it is 78.54kg.

I am confused about c. So once again suming up the data I have for c and trying to solve it:
m1= 90gk

m2= 78.53kg

μ= 0.15 ( ı just used the sliding friction coefficent and didn't involve the static one anywhere since the particles are moving. This is where I am confused about. Should I really leave the static friction coefficient out of my calculations?)
a=?

-------writing equations for m2-------------
m2.g-T=m2.a
T=m2.g-m2.a ...(1)

------writing equations for m1---------
T-m1gsin(40)-μ.m1.g.cos40=m1.a
T=m1.a+m1.g.sin(40)+μ.m1.g.cos40.....(2)T (1) = T (2)

m2.g-m2.a=m1.a+m1.g.sin(40)+μ.m1.g.cos40

solving for a give a=1.81m/s2

#### Attachments

• inclined plane.jpg
21.8 KB · Views: 219
Taylan said:
( ı just used the sliding friction coefficent and didn't involve the static one anywhere since the particles are moving. This is where I am confused about. Should I really leave the static friction coefficient out of my calculations?)
Yes. When the blocks are moving, the only friction in play is kinetic.

solving for a give a=1.81m/s2
I believe that's correct. Your work looks good.

Taylan

## 1. What are connected particles on an inclined plane?

Connected particles on an inclined plane refer to a system of two or more particles that are linked together and placed on an inclined surface. The particles are connected by strings, rods, or other means, and are subject to the force of gravity as they slide down the incline.

## 2. How does the angle of the incline affect the motion of connected particles?

The angle of the incline has a significant impact on the motion of connected particles. As the incline becomes steeper, the force of gravity acting on the particles increases, causing them to accelerate faster down the incline. At a certain angle known as the critical angle, the particles will begin to slide down the incline without any external force.

## 3. What is the role of friction in the motion of connected particles on an inclined plane?

Friction plays a crucial role in the motion of connected particles on an inclined plane. Without friction, the particles would slide down the incline at a constant velocity. However, as the particles move, they experience frictional forces that oppose their motion, causing them to slow down and eventually come to a stop.

## 4. How does the mass of the particles affect their motion on an inclined plane?

The mass of the particles has a direct impact on their motion on an inclined plane. Heavier particles will experience a greater force of gravity, causing them to accelerate faster down the incline. On the other hand, lighter particles will accelerate slower and may even remain stationary on a less steep incline.

## 5. What are some real-world applications of connected particles on an inclined plane?

Connected particles on an inclined plane have several real-world applications, including roller coasters, conveyor belts, and ramps. In these systems, the particles represent objects or people, and the incline simulates the force of gravity. By understanding the principles of connected particles on an inclined plane, engineers can design efficient and safe systems for various purposes.

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