Frictional Force (and μ) & Acceleration (w/friction)

[ceceliaz]

1. The problem: 2 blocks are arranged at the ends of a
massless string (mass one is on a table and mass two is hanging straight down off the other side of the pulley that is connected to the edge of the table). The system starts from rest. When the 4.18 kg (the hanging mass) mass has fallen through 0.389 m, its down-ward speed is 1.29 m/s.
The acceleration of gravity is 9.8 m/s2 .
mass one (on table)=5.68 kg
mass two (hanging)=4.18 kg
μ=?
a=? (to the right towards the hanging mass)
What is the frictional force between the 5.68 kg mass and the table?
Answer in units of N.

2. I put together the SumFx and SumFy to make the equation to solve for frictional force:
μ(subk)= (m2)g-a(m1+m2) / (m1g)

3. However, I need acceleration. I tried using both (vf=vi+at) and (vf^2-vi^2/(2deltaX)), but it was wrong (probably because those formulas don't take into account friction.

QUESTION 1: How do you find friction or acceleration without each other?
QUESTION 2: Is "frictional force" the (μ) times (mass on the table) times (acceleration)?

 

[Doc Al]

3. However, I need acceleration. I tried using both (vf=vi+at) and (vf^2-vi^2/(2deltaX)), but it was wrong (probably because those formulas don't take into account friction.

Finding the acceleration is a kinematic exercise; friction is automatically included since the speeds are given. Redo your calculation--those kinematic equations should work just fine.

QUESTION 1: How do you find friction or acceleration without each other?

You don't. But you have all the information needed to solve for acceleration, and then for the friction.

QUESTION 2: Is "frictional force" the (μ) times (mass on the table) times (acceleration)?

No. But why are you solving for μ? Calling the friction force "F" and solve for it directly. (Friction equals μmg, but that's not needed unless you are asked to solve for μ.)

 

[m2003]

Frictional force is a force that opposes the motion of an object and is caused by the interaction between two surfaces. In this case, the frictional force between the 5.68 kg mass and the table can be calculated using the equation μN, where μ is the coefficient of friction and N is the normal force between the two surfaces. The normal force can be found by multiplying the mass of the object by the acceleration due to gravity, which in this case is 9.8 m/s^2.

To find the coefficient of friction, we can use the equation μ = (m2g - a(m1+m2))/(m1g), as you have correctly identified. However, in order to solve for the frictional force, we need to know the acceleration of the system, which is not provided in the given information.

To find the acceleration, we can use the equation F = ma, where F is the net force acting on the system. In this case, the net force is equal to the difference between the weight of the hanging mass and the tension in the string. Once we have found the acceleration, we can use it to solve for the frictional force using the equation μN.

To answer your first question, friction and acceleration are related to each other as they both depend on the net force acting on an object. In order to find one, we need to know the other. In this case, we need to find the acceleration in order to solve for the frictional force.

To answer your second question, frictional force is not equal to μ times the mass on the table times acceleration. The correct equation is μN, where N is the normal force between the two surfaces. The normal force depends on the weight of the object and the acceleration due to gravity, not the mass on the table.