# Calculating acceleration due to friction without mass?

• Amber_
In summary, the problem involves a car traveling at 28.4 m/s that brakes 0.505 seconds later, with the car in front also braking at the same time. The coefficient of friction is 0.719 and the acceleration of gravity is 9.8 m/s^2. The task is to calculate the acceleration of the car in front when it brakes, with the given information.
Amber_

## Homework Statement

Here is the problem:
You are driving at the speed of 28.4 m/s
(63.5426 mph) when suddenly the car in
front of you (previously traveling at the same
speed) brakes. Considering an average human
reaction, you press your brakes 0.505 s later.
Assume that the brakes on both cars are fully
engaged and that the coeﬃcient of friction is
0.719 between both cars and the road.
The acceleration of gravity is 9.8 m/s 2

Calculate the acceleration of the car in front
of you when it brakes.
Answer in units of m/s 2

Note: this is the first part of a multipart question.

2. The attempt at a solution

I know exactly how I would do this problem, were the masses of the cars given. I honestly have no idea how you would get the acceleration due to friction without knowing the mass of the car. Is it possible that this is a mistake in the problem, or am I missing something?

Amber_ said:
I know exactly how I would do this problem, were the masses of the cars given.

Ok, I give you the mass. It is equal to m.

I thought of that, but . . . oh. Oops.

Clearly I didn't think hard enough before because I didn't realize the m's should cancel out. Okay I get it now! Thanks for that.

## 1. How do you calculate acceleration due to friction without mass?

The formula for calculating acceleration due to friction without mass is a = μg, where μ is the coefficient of friction and g is the acceleration due to gravity (9.8 m/s^2). This formula assumes that the mass of the object is canceled out by the mass of the surface it is moving on.

## 2. What is the coefficient of friction?

The coefficient of friction is a dimensionless number that represents the amount of friction between two surfaces. It is a measure of the roughness or smoothness of the surfaces in contact and is used to calculate the force of friction.

## 3. How does the surface affect the acceleration due to friction?

The surface has a significant impact on the acceleration due to friction. The coefficient of friction varies depending on the type of surface, with smoother surfaces having a lower coefficient of friction and rougher surfaces having a higher coefficient of friction. This means that the force of friction will be greater on rougher surfaces, resulting in a higher acceleration due to friction.

## 4. Can the acceleration due to friction be negative?

Yes, the acceleration due to friction can be negative. This occurs when the frictional force is acting in the opposite direction to the motion of the object. In this case, the friction is slowing down the object's motion, resulting in a negative acceleration.

## 5. How does the mass of the object affect the acceleration due to friction?

The mass of the object does not directly affect the acceleration due to friction. However, it does play a role in determining the amount of force required to overcome the frictional force and accelerate the object. Generally, a heavier object will require more force to overcome friction and accelerate compared to a lighter object.

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