When you pull out a stuck drawer, the force of static friction causes it to stick in place. This causes the drawer to jerk outwards, sometimes violently. Assume that you apply a constant force just large enough to “unstick” the drawer, but that when the drawer comes loose, you can’t immediately stop applying the force due to your reaction time. Estimate how far the drawer will move before it comes to rest.
How would I go about finding the the distance the drawer moves for this problem? Am I correct to assume that I need to use kinematic equations to do this? And do I need to use kinetic friction in my calculations, since the drawer would be moving?
The "jerk" depends on the difference between static friction (the stickiness) and kinetic friction. The former is always greater than (perhaps or equal to) the kinetic friction.
You need to estimate the mass m of the drawer, the force F required to overcome the static friction, the static and kinetic frictions, and finally the reaction time.
Then you would use kinematics equations to find the acceleration of the drawer during the reaction time, and finally the time it takes for that motion to stop.
To find the distance the drawer moves before coming to rest, you can indeed use the kinematic equations. However, in this case, you don't need to consider kinetic friction since you are assuming a constant force just large enough to "unstick" the drawer.
First, let's analyze the forces acting on the drawer. Initially, the force of static friction opposes your applied force, preventing the drawer from moving. Once the static friction is overcome, the only force acting on the drawer is the force you applied.
Since the force is constant, we can use the second law of motion, which states that the net force acting on an object is equal to its mass multiplied by its acceleration. In this case, the acceleration of the drawer is given by Newton's second law as:
F = ma
where F is the applied force and m is the mass of the drawer.
Now, to find the distance the drawer moves, we can use the kinematic equation for motion given a constant acceleration:
s = ut + (1/2)at^2
where s is the distance traveled, u is the initial velocity (which is zero in this case, as the drawer starts from rest), a is the acceleration, and t is the time.
We need to find the time it takes for the drawer to come to rest. To do this, we can divide the force by the static friction coefficient (μ_s) to get the maximum static friction that could oppose the applied force. Then, we can divide this maximum static friction by the mass of the drawer to find the maximum static friction acceleration.
Now, once the static friction is overcome, the drawer will continue moving with this acceleration until it comes to rest. Hence, the acceleration in the kinematic equation will be the maximum static friction acceleration.
Finally, you can substitute the value of time into the kinematic equation to find the distance the drawer moves before coming to rest.
Remember to use consistent units throughout your calculations and ensure you have the necessary values for the applied force, mass of the drawer, and the static friction coefficient.