Finding the coefficient of friction on a ramp

In summary, a child is playing outside on a rainy day and is pushing a trunk with a weight at a constant speed. The weight causes the child to exert a force on the trunk which is in turn equal to the weight's pushing power.
  • #1
Mastevvs
1
0

Homework Statement



You do 2.2 kJ of work pushing a trunk at a constant speed 3.1 m along a ramp inclined upward at 22 degrees. What is the frictional coefficient between the trunk and the ramp?

Homework Equations



W = F*d
Ff = μmg * cos(θ)
Fg = mg * sin(θ)

The Attempt at a Solution



To find the force exerted on the trunk up the ramp, I divide 2200 J by 3.1 m to get 710 N.

Since the trunk is moving at a constant speed, the forces pulling the trunk down the ramp must equal the forces pushing it up the ramp.

So,

710 = Fg + Ff

710 = mg*sin(22) + μmg*cos(22)

710 = mg( sin(22) + μcos(22) )

...Aaaaand this is where I get stuck. I feel like there is some obvious way to either solve for or get rid of the mass that I'm just not seeing. My book gives 0.6 as the answer.

Any help would be greatly appreciated.
 
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  • #2
Hey you told it moves up with constant speed 3.1m/s
then why are you dividing work with speed to get the force
 
  • #3
Viru.universe said:
Hey you told it moves up with constant speed 3.1m/s
then why are you dividing work with speed to get the force
possibly:
1. that would not give force - work/speed has dimensions of force per unit time.
2. the time the work was done in was not given
3. the "3.1" figure is "3.1m" - not "3.1m/s". Spot the difference.

Mastevvs said:
I feel like there is some obvious way to either solve for or get rid of the mass that I'm just not seeing.
Welcome to PF;
Indeed: there is information provided in the problem that has not been used in the attempt at a solution. eg. it says that the movement was at constant speed - what does this tell you about the forces?

The way to handle this sort of problem is, usually, though conservation of energy.
Start by describing the energy changes that happen and recall how this is related to the work.
But in this case you have done enough groundwork already to get away without it.
 
Last edited:
  • #4
Mastevvs said:
710 = mg( sin(22) + μcos(22) )

...Aaaaand this is where I get stuck. I feel like there is some obvious way to either solve for or get rid of the mass that I'm just not seeing. My book gives 0.6 as the answer.

Any help would be greatly appreciated.

Your work is correct and the problem can not be solved without the mass given.

ehild
 
  • #5


I would approach this problem by first identifying the known and unknown variables. We know the work done (2.2 kJ), the distance (3.1 m), the angle of the ramp (22 degrees), and the gravitational constant (g = 9.8 m/s^2). The unknown variable is the coefficient of friction (μ).

Next, I would use the equation W = F*d to calculate the force exerted on the trunk up the ramp, which is 710 N as you correctly calculated.

Then, I would use the equation Ff = μmg * cos(θ) to calculate the frictional force, where m is the mass of the trunk. Since we are given the work done and the distance, we can use the equation W = F*d to solve for the mass of the trunk, which is 0.224 kg.

Substituting this value for m in the equation Ff = μmg * cos(θ), we get:

Ff = μ * 0.224 kg * 9.8 m/s^2 * cos(22)

Solving for μ, we get μ = 0.6, which is the same answer given in your book.

In conclusion, the coefficient of friction between the trunk and the ramp is 0.6.
 

What is the coefficient of friction on a ramp?

The coefficient of friction on a ramp is a measurement of the resistance to motion between two surfaces in contact. It is represented by the symbol μ and can range from 0 to 1, with lower values indicating less friction and higher values indicating more friction.

Why is it important to find the coefficient of friction on a ramp?

Finding the coefficient of friction on a ramp is important because it helps us understand the amount of force needed to overcome the friction between two surfaces. This information is crucial in designing structures and equipment that need to move or support objects on a ramp.

How do you calculate the coefficient of friction on a ramp?

The coefficient of friction on a ramp can be calculated by dividing the force required to move an object on the ramp by the weight of the object. This can be done by measuring the angle of the ramp and using the formula μ = tanθ, where θ is the angle of the ramp.

What factors can affect the coefficient of friction on a ramp?

The coefficient of friction on a ramp can be affected by various factors, such as the type of surface materials, the weight of the object, the angle of the ramp, and the presence of any lubricants or contaminants on the surfaces.

How can the coefficient of friction on a ramp be reduced?

The coefficient of friction on a ramp can be reduced by using materials with lower coefficients of friction, such as smooth and slippery surfaces, or by adding lubricants to the surfaces. Additionally, reducing the weight of the object or decreasing the angle of the ramp can also decrease the coefficient of friction.

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