Air Track Problem with friction

[Wishingwell]

Homework Statement

An air-track glider of mass 0.109 kg is attached to the end of a horizontal air track by a spring with force constant 22.5 N/m

(a) With the air track turned off, the glider travels 8.8 cm before it stops instantaneously. How large would the coefficient of static friction μs have to be to keep the glider from springing back to the left?

(b) If the coefficient of static friction between the glider and the track is μs= 0.55, what is the maximum initial speed v1 that the glider can be given and remain at rest after it stops instantaneously? With the air track turned off, the coefficient of kinetic friction is μk= 0.54.

Homework Equations

PE = .5kx^2
F = -kx

The Attempt at a Solution

My main problem with this is that I have no idea how to set up the problem when friction is involved. I assumed it was μmg from earlier problems but that was dead wrong. Can anyone help me out?

 

[kuruman]

Reason it out. If the glider travels 8.8 cm, the spring is extended by 8.8 cm. Can you find the force that the spring exerts on the glider? If so, then the maximum force of static friction must be at least that much to prevent the glider from being pulled back.

 

[kerimek]

I would approach this problem by first identifying the key variables and equations needed to solve it. In this case, we are dealing with an air-track glider with a mass of 0.109 kg, a spring with a force constant of 22.5 N/m, and a coefficient of static friction μs. The equations that we can use to solve this problem are the potential energy equation (PE = .5kx^2) and the force equation (F = -kx).

For part (a), we are looking for the coefficient of static friction μs that would keep the glider from springing back to the left. To solve this, we can use the force equation and set it equal to the maximum static friction force (F = μsN). We can then substitute in the values given for the force constant and the distance travelled (8.8 cm or 0.088 m) to solve for μs.

For part (b), we are given the coefficient of static friction μs and the coefficient of kinetic friction μk, and we are asked to find the maximum initial speed v1 that the glider can be given and remain at rest after it stops instantaneously. To solve this, we can use the potential energy equation and set it equal to the kinetic energy equation (KE = 0.5mv^2). We can then substitute in the values given for the coefficients of friction and the mass of the glider to solve for v1.

In both cases, it is important to keep track of units and to use consistent units throughout the calculations. Additionally, it is always a good idea to check your solutions and make sure they make sense in the context of the problem.