Calculating acceleration due to friction without mass?

AI Thread Summary
To calculate the acceleration of a car due to friction without knowing its mass, it's essential to recognize that mass cancels out in the equations of motion. The problem involves a car braking with a coefficient of friction of 0.719 and gravity at 9.8 m/s². The initial confusion stemmed from the assumption that mass was necessary for the calculation. Once clarified, the acceleration can be determined using the formula a = μg, where μ is the coefficient of friction. Understanding this principle allows for the correct calculation of acceleration due to friction.
Amber_
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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?
 
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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.
 
Kindly see the attached pdf. My attempt to solve it, is in it. I'm wondering if my solution is right. My idea is this: At any point of time, the ball may be assumed to be at an incline which is at an angle of θ(kindly see both the pics in the pdf file). The value of θ will continuously change and so will the value of friction. I'm not able to figure out, why my solution is wrong, if it is wrong .
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