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

• courtney1121
In summary, the problem of estimating the minimum amount of time to slow down without the box sliding off the seat onto the floor requires the coefficient of static friction to be known. Without this information, the time cannot be accurately calculated. One must draw a free body diagram of the box and apply Newton's 2nd law to start solving the problem.
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.

courtney1121 said:
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.

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.

## What is the equation for calculating time to slow down with static friction?

The equation for calculating time to slow down with static friction is t = v/μg, where t is the time in seconds, v is the velocity in meters per second, μ is the coefficient of static friction, and g is the acceleration due to gravity (9.8 m/s^2).

## How do you determine the coefficient of static friction for a specific road surface?

The coefficient of static friction for a specific road surface can be determined by conducting experiments where a car is driven at a constant speed and then brakes to a stop on the surface. The coefficient of static friction can be calculated by dividing the maximum frictional force by the weight of the car.

## What factors can affect the time to slow down with static friction?

The time to slow down with static friction can be affected by factors such as the velocity of the car, the coefficient of static friction of the road surface, the weight of the car, and any external forces acting on the car (e.g. wind resistance).

## How does the time to slow down with static friction differ from the time to slow down with kinetic friction?

The time to slow down with static friction is typically longer than the time to slow down with kinetic friction. This is because static friction is stronger than kinetic friction, meaning it takes longer for the car to overcome the initial resistance and start slowing down.

## What are some safety precautions to consider when calculating the time to slow down with static friction?

When calculating the time to slow down with static friction, it is important to consider the condition of the road surface, the speed of the car, and any potential hazards or obstacles that may affect the car's braking distance. It is also important to ensure that the car's brakes and tires are in good condition to ensure maximum effectiveness when slowing down.

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