Acceleration of two Objects after Collision

[Riman643]

Homework Statement

Two bikes collide on a street and travel a distance away from each other before coming to rest. The first bike is 20 kg and the second bike is 15 kg. The coefficient of kinetic friction is 0.5. What is the magnitude of acceleration of each.

Relevant Equations

F = ma
f[SUB]k[/SUB] = Nμ[SUB]k[/SUB]

This seems like a fairly simple problem but I got the same answer for both so I'm unsure if I am doing it right.

I found the accelerations as such

a₁ = (f_k)/(m_a) = (98/20) = 4.9 m/s²
a₂ = (f_k)/(m_a) = (73.5/15) = 4.9 m/s²

Am I doing something wrong or is this problem just that simple?

 

[SammyS]

Problem Statement: Two bikes collide on a street and travel a distance away from each other before coming to rest. The first bike is 20 kg and the second bike is 15 kg. The coefficient of kinetic friction is 0.5. What is the magnitude of acceleration of each.
Relevant Equations: F = ma
f_k = Nμ_k

This seems like a fairly simple problem but I got the same answer for both so I'm unsure if I am doing it right.

I found the accelerations as such

a₁ = (f_k)/(m_a) = (98/20) = 4.9 m/s²
a₂ = (f_k)/(m_a) = (73.5/15) = 4.9 m/s²

Am I doing something wrong or is this problem just that simple?

It could work out like that.

See if that makes sense.

What all goes into determining f_k ?

What goes into getting N, the normal force, for this problem?

 

[Riman643]

I got the Normal force by knowing that it is equal to the force of gravity of each object. I then multiplied the normal force by the kinetic coefficient to get the force of friction.

 

[SammyS]

I got the Normal force by knowing that it is equal to the force of gravity of each object. I then multiplied the normal force by the kinetic coefficient to get the force of friction.

OK.
So, for motorcycle 1: (f_k)₁= μ_kN₁ = μ_k(m₁ g)
Then what do you do to find a₁ ?
Divide that by m₁. Right?

 

[Riman643]

OK.
So, for motorcycle 1: (f_k)₁= μ_kN₁ = μ_k(m₁ g)
Then what do you do to find a₁ ?
Divide that by m₁. Right?

Correct. That's the only way I could think of to find the acceleration.

 

[SammyS]

Correct. That's the only way I could think of to find the acceleration.

It's a pretty good way.

Doing it symbolically:
## a_1=\dfrac{\mu_k (m_1 g)}{m_1}##

Does that show you that the acceleration of bike 1 is independent of its mass ?

 

[PeroK]

Correct. That's the only way I could think of to find the acceleration.

Do you think this problem makes sense? What has kinetic friction to do with a bicycle?

 

[Riman643]

It's a pretty good way.

Doing it symbolically:
## a_1=\dfrac{\mu_k (m_1 g)}{m_1}##

Does that show you that the acceleration of bike 1 is independent of its mass ?

I think so. The mass on top would cancel with the mass on the bottom.

 

[SammyS]

I think so. The mass on top would cancel with the mass on the bottom.

Right.
So now, is it surprising that both bikes have the same magnitude of acceleration?

 

[Riman643]

Do you think this problem makes sense? What has kinetic friction to do with a bicycle?

Kinetic friction would be the force slowing them down to a rest.

 

[Riman643]

Right.
So now, is it surprising that both bikes have the same magnitude of acceleration?

Yeah now that I see it algebraically it makes more sense.

 

[PeroK]

Kinetic friction would be the force slowing them down to a rest.

1) Wouldn't a bike slow down somewhat and then fall over?

2) Why would kinetic friction slow a bike? If kinetic friction of ##0.5## was acting on a bike, then it would be almost impossible to get it to move.

3) E.g. you have calculated a deceleration of ##4.9m/s^2##. Does that seem realistic? A bicycle traveling at about ##5m/s## would come to a halt in ##1s## - almost as soon as you stop pedalling?

 

[Riman643]

1) Wouldn't a bike slow down somewhat and then fall over?

2) Why would kinetic friction slow a bike? If kinetic friction of ##0.5## was acting on a bike, then it would be almost impossible to get it to move.

3) E.g. you have calculated a deceleration of ##4.9m/s^2##. Does that seem realistic? A bicycle traveling at about ##5m/s## would come to a halt in ##1s## - almost as soon as you stop pedalling?

As for the logistics of the question I am not sure. I think these were just randomly generated numbers. I am just curious if the way I went about solving the problem was correct.

 

[PeroK]

As for the logistics of the question I am not sure. I think these were just randomly generated numbers. I am just curious if the way I went about solving the problem was correct.

But Physics must relate to the real physical phenomena. It's not a random invention. Either a bike slides to a halt like a box or it rolls. And if it rolls, then kinetic friction is not acting. Otherwise, the wheel would have been a poor invention.

My problem is not with the way you tackled the problem, but the people who set these questions divorce physics from reality and engineering.

For your information, if you slam on the brakes on a bike (or a car) and it skids, then that is kinetic friction. If you brake properly, then that is actually static friction (although that takes a bit of explaining). And, if a bike or a car rolls to a stop without braking, then that is a combination of air resistance and rolling resistance. The fact that rolling resistance is so low compared to friction is why the wheel, bikes and cars are so efficient.

If it was all just friction then you might as well have square wheels on your car.