Dynamics Question (First-Year)

[dekoi]

How should I approach this question:

You are driving at a constant velocity of 25 m/s.
You have antiques in the back of your pick-up truck.
You see a giant hole in the road, 55 m ahead of you.
Coefficients of friction for the antiques: μs=0.6 and μk=0.3.

Can you stop without the antiques sliding and being damaged? (Hint: You're not trying to stop in the shortest possible distance.)


All I have found so far was the acceleration if you were to stop right before the giant hole. The value I calculated is a = -5.68 m/s2. I can't figure out what to do with the coefficients of static and kinetic friction, however.

Thank you.

 

[Tom Mattson]

dekoi: I've moved this out of the Physics section. Any and all homework goes here, not there.

I can't figure out what to do with the coefficients of static and kinetic friction, however.

Start here:

You want to furniture to not slide. That means you want it to move with the truck, so you assume that the furniture has the same acceleration as the truck, then calculate the frictional force on the furniture.

 

[dekoi]

Is the following the correct method of completing the question? :

(x-direction)

Fnet= ma
Fnet= -μsmg

→ ma=-μsmg
a=-μsg=-(0.6)(9.8)
a=-5.88 m/s^2

→ v2^2=v1^2+2ad
d=v2^2-v1^2
¨¨¨¨¨2a
d=(0-25^2) / (2)(-5.88)
d=53 m

→ The car stops in time without the antiques breaking since 53 m < 55 m.

 

[dekoi]

... .

 

[mukundpa]

Looks good if the truck tyres can provide required frictional force.

 

[dekoi]

I'm confused because I did not use the coefficient of KINETIC friction in my answer, but it was given to me.

 

[Tom Mattson]

They gave you the coefficient of kinetic friction in case the furniture started sliding. If they hadn't given it you you, it would have been a dead giveaway of the answer!

 

[dekoi]

Oh, that makes sense now.

Thanks.