Motion with Incline: Masses, Acceleration, Tension & Friction | Incline Homework

In summary, two masses, m1=4.0kg and m2=9.0kg, are connected by a light string over a frictionless pulley. When released from rest, m2 slides 1.00m down an incline at a 40 degree angle in 4.00s. Using the equations Fnet=ma and d=1/2at^2, the acceleration of m2 is found to be 0.125m/s^2. To find the acceleration of m1, separate the forces on each mass by drawing a free body diagram and writing equations for each direction. From this, the acceleration of m1 can be solved for. The tension in the string can be found by
  • #1
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Homework Statement



Masses m1 = 4.0kg and m2 = 9.0kg are connected by a light string that passes over a frictionless pulley. As shown in Figure, m1 is held at rest on the floor and m2 rests on a fixed incline of 40 degree. The masses are released from rest, and m2 slides 1.00m down the incline in 4.00s.

Determine a) the acceleration of each mass b) the tension in the string and c) the coefficient of kinetic friction between m2 and the incline.


DSC00508.jpg



Homework Equations


Fnet = ma
distance formula
d = 1/2at^2 when vi = 0


The Attempt at a Solution



Well, I know the acceleration for m2 is 0.125m/s^2 using the distance formula when vi=0.
but then i got stuck at the rest, i tried to find acceleration of m1 but didn't work out at all.

well if i tried
m2gcos - m1g = m2a1+m1a2
(since incline plane i can find fg by m2gCos)
but the problem is, i totally ignore the friction Ff i think...
this is why i come up with answer like 6.8m/s^2 for mass1.

the rest will be wrong if i can't set up a system of equation for #1
i tried, like

m2gCos + Ft = m2a
m1g + (-Ft) = m1a

Ft means force of tension
 
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  • #2
You need to consider the forces on each mass separately. Remember, force is a vector.

Start by considering just the mass on the incline. Draw a free body diagram. What forces are present? Write out an equation for each direction (take the x direction to be along the incline and the y direction to be perpendicular to the incline).

Now do the same for the other mass. This one is much easier, since there are only forces in one direction.

From this you will get a set of equations that you can use to solve for what you need to find.
 
  • #3

Ft = m2a-m2gCos

sub back to other equation
m1g + (-m2a+m2gCos) = m1a

but i can't get the right answer.

Dear Student,

Thank you for your detailed attempt at solving this problem. It seems like you have a good understanding of the basic equations and concepts related to motion with inclines. However, there are a few mistakes and misunderstandings that are preventing you from getting the correct answer.

Firstly, it is important to note that in this problem, the masses are connected by a string that passes over a frictionless pulley. This means that the tension in the string will be the same for both masses, and can be calculated using the equation Ft = m2a - m2gcosθ, where θ is the angle of the incline. Therefore, your attempt at setting up equations for the tension for each mass separately is not necessary.

Secondly, in your attempt to find the acceleration of m1, you used the equation Fnet = ma, which is correct. However, the forces acting on m1 are not just its weight (mg), but also the tension in the string (Ft). Therefore, the correct equation would be Fnet = m1a = Ft - m1g. Solving for a, we get a = (Ft - m1g)/m1. Now, since we know that the tension in the string is the same for both masses, we can substitute the value of Ft from the previous equation (Ft = m2a - m2gcosθ) and solve for a.

Thirdly, you mentioned that you got an answer of 6.8m/s^2 for the acceleration of m1. This is incorrect, as the acceleration of m1 should be equal to the acceleration of m2 since they are connected by a string. Therefore, the acceleration of both masses should be 0.125m/s^2.

Finally, to find the coefficient of kinetic friction between m2 and the incline, we can use the equation Ff = μkN, where Ff is the force of friction, μk is the coefficient of kinetic friction, and N is the normal force. In this case, the normal force will be equal to the weight of m2, which is m2g. Therefore, the equation becomes Ff = μkm2g. We can
 

Related to Motion with Incline: Masses, Acceleration, Tension & Friction | Incline Homework

1. What is the relationship between the mass and acceleration of an object on an incline?

According to Newton's second law of motion, the acceleration of an object is directly proportional to the net force applied to it and inversely proportional to its mass. This means that as the mass of an object on an incline increases, its acceleration will decrease.

2. How does the angle of the incline affect the acceleration of an object?

The angle of the incline affects the acceleration of an object by changing the component of the gravitational force that acts on it. As the angle of the incline increases, the component of the gravitational force that is parallel to the incline decreases, resulting in a decrease in acceleration.

3. What is the role of tension in motion on an incline?

Tension is the force that is transmitted through a string, cable, or rope when it is pulled tight by forces acting from opposite ends. In the case of motion on an incline, tension is responsible for providing the necessary force to counteract the component of the gravitational force that is parallel to the incline and keep the object from sliding down.

4. How does friction affect the motion of an object on an incline?

Friction is a force that opposes the motion of objects that are in contact with each other. On an incline, friction acts in the opposite direction of the object's motion, and its magnitude depends on the coefficient of friction between the object and the incline. Friction can either aid or hinder the motion of an object on an incline, depending on the direction of the force.

5. What are some real-life applications of motion with incline?

Motion with incline is a common phenomenon in our daily lives. Some real-life applications include objects rolling down a ramp, cars driving up or down a hill, and people skiing down a slope. Understanding the principles of motion with incline can also help in designing efficient machines such as conveyor belts, escalators, and roller coasters.

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