Need help with a Force problem involving friction.

In summary, a student is trying to find the coefficients of static and kinetic friction between a box and a plank by gradually raising one end of the plank until the box starts to slip. The static friction coefficient is 0.73, but the kinetic friction coefficient cannot be calculated using the provided formulas without the mass of the box. After some trial and error, the student realizes that the mass is negligible and finds the correct answer.
  • #1
frankfjf
168
0
A student wants to determine the coefficients of static friction and kinetic friction between a box and a plank. She places the box on the plank and gradually raises one end of the plank. When the angle of inclination with the horizontal reaches 36 degrees, the box starts to slip, and it then slides 2.2 m down the plank in 1.5 s at constant acceleration. What are (a) the coefficient of static friction and (b) the coefficient of kinetic friction between the box and the plank?

I've solved part a for 0.73 as the static friction coefficient, but cannot get b using the formulas the student guide provided. What am I doing wrong?

It suggests using:

mg(sin(theta)) - f = ma

f = ukmgcos(theta)

a = 2d/t^2

Where uk is the variable for the coefficient of kinetic friction. However how can I apply these formulas if the problem does not provide the mass? I tried making the mass negligible (Setting m to 1) but that doesn't produce the right answer. What am I doing wrong?
 
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  • #2
Sorry, nevermind, I figured it out.
 
  • #3


It seems like you are on the right track with using the equations provided, but there may be a slight error in your calculations. Let's break down the problem and go through the steps together:

1. First, we need to identify the known values in the problem. We are given the angle of inclination (36 degrees), the distance traveled (2.2 m), and the time it took to travel that distance (1.5 s). We also know that the acceleration is constant, so we can use the formula a = 2d/t^2 to calculate the acceleration.

2. Next, we can use the formula mg(sin(theta)) - f = ma to solve for the force of friction. In this case, the force of friction is the only unknown variable in the equation. We can substitute in the known values and solve for f.

3. Now, we can use the formula f = ukmgcos(theta) to solve for the coefficient of kinetic friction. Again, we can substitute in the known values and solve for uk.

4. To check our answer, we can plug in the values for uk and f into the original equation f = ukmgcos(theta) and see if it balances out. If it does, then our calculations are correct.

Remember, the mass of the box is not provided in the problem, but it does not affect the calculation of the coefficients of friction. As long as you use the correct formula and substitute in the known values correctly, you should be able to solve for both coefficients. If you are still having trouble, I recommend double-checking your calculations and making sure you are using the correct units for each variable.
 

1. What is friction and how does it affect force?

Friction is a force that acts in the opposite direction of an object's motion. It is caused by the microscopic irregularities of surfaces rubbing against each other. Friction can either help or hinder an object's motion, depending on the direction of the force.

2. How do you calculate the force of friction?

The force of friction can be calculated using the formula F = μN, where F is the force of friction, μ is the coefficient of friction, and N is the normal force. The coefficient of friction depends on the types of surfaces in contact and can be found in tables or experimentally determined.

3. What is the difference between static and kinetic friction?

Static friction is the force that keeps an object at rest when a force is applied to it, while kinetic friction is the force that opposes the motion of an object that is already in motion. The coefficient of static friction is usually higher than that of kinetic friction.

4. How does the weight of an object affect the force of friction?

The weight of an object does not directly affect the force of friction. However, the weight does affect the normal force, which in turn affects the force of friction. The greater the weight of an object, the greater the normal force, and therefore the greater the force of friction.

5. Can friction ever be eliminated?

No, friction cannot be completely eliminated. Even in the smoothest of surfaces, there will always be microscopic irregularities that will cause friction. However, friction can be reduced by using lubricants, such as oil or grease, or by using smoother surfaces.

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