Calculate Time to Slow Down w/Static Friction on I-79 Exit 147A

[courtney1121]

A box full of fragile objects is on the back seat of your car. You are driving at 65 mph (29 m/s) on I-79. As you get off at exit 147A for Meadville, you must slow down to 0 mph. Estimate the minimum amount of time should you take to slow down (based on the appropriate acceleration) without the box sliding off the seat onto the floor on the car.

any thoughts on where to start?

we got acceleration due to gravity and velocity. We will have acceleration going in the opposite direction of motion.

 

[PhanthomJay]

A box full of fragile objects is on the back seat of your car. You are driving at 65 mph (29 m/s) on I-79. As you get off at exit 147A for Meadville, you must slow down to 0 mph. Estimate the minimum amount of time should you take to slow down (based on the appropriate acceleration) without the box sliding off the seat onto the floor on the car.

any thoughts on where to start?

we got acceleration due to gravity and velocity. We will have acceleration going in the opposite direction of motion.

You are missing some data. The problem cannot be solved unless you know the coefficient of static friction between the box and the seat. Was this info given? Otherwise, the time will have to be expresed as a function of the static friction coefficient. For starters, draw a FBD of the box and apply Newton's 2nd law.

 

[kyle8921]

We can use the equation vf = vi + at to calculate the time it takes to slow down to 0 mph. However, we also need to take into account the static friction force between the box and the car seat. This force will act in the opposite direction of motion and will help keep the box from sliding off the seat. We can use the equation Ff = μN to calculate the maximum static friction force, where μ is the coefficient of static friction and N is the normal force between the box and the seat. We can then use this force in the equation ΣF = ma to calculate the acceleration needed to overcome the static friction force and slow down the car. Once we have the acceleration, we can use the first equation mentioned to calculate the time needed to slow down to 0 mph. It is important to note that the coefficient of static friction depends on the materials of the box and the car seat, so it may be necessary to do some research or testing to obtain an accurate value. Overall, the time needed to slow down will depend on the specific situation and the amount of friction present, but using these equations can help estimate a minimum amount of time needed to safely slow down without the box sliding off the seat.