applesjgtl
A 1200 kg racecar is driven along a frictionless horizontal surface at a speed of 65 km/hr. If a horizontal cord brings the car to rest in a distance of 2.2 m, what is the elasticity constant (k) of this spring?
Delete
Share
This Question is Closed
Shane_B
Best Response
You've already chosen the best response.
1
Do you have any idea where to start?
applesjgtl
Best Response
You've already chosen the best response.
0
Not really.
applesjgtl
Best Response
You've already chosen the best response.
0
65km/hr=18.06m/s
Shane_B
Best Response
You've already chosen the best response.
1
I'd start by converting the velocity to m/s. Then calculate the KE of the racecar using:\[KE=\frac{1}{2}mv^2\]
Shane_B
Best Response
You've already chosen the best response.
1
Since the racecar comes to a rest you know that the change in KE will be the amount of work done on the car and: \[W=\frac{1}{2}kx^2\]
applesjgtl
Best Response
You've already chosen the best response.
0
1/2(1200kg)(18.06m/s)^2=195698.16J
Shane_B
Best Response
You've already chosen the best response.
1
So:\[KE=\frac{1}{2}(1200kg)(18.06m/s)^2=195698J=Work\space done\]\[195698J=\frac{1}{2}k(2.2m^2)\]Now just solve for k.
Shane_B
Best Response
You've already chosen the best response.
1
Small correction there...it should have been:\[195698J=\frac{1}{2}k(2.2m)^2\]
applesjgtl
Best Response
You've already chosen the best response.
0
Oh, because it's not the unit that's being squared.
Shane_B
Best Response
You've already chosen the best response.
1
Yep
Shane_B
Best Response
You've already chosen the best response.
1
Looking at that last equation, what do you get for k?
applesjgtl
Best Response
You've already chosen the best response.
0
k=80867.01
applesjgtl
Best Response
You've already chosen the best response.
0
What's that unit?
Shane_B
Best Response
You've already chosen the best response.
1
It's a constant...no unit. You also have to consider significant figures in your calcs but that's how you solve it.
applesjgtl
Best Response
You've already chosen the best response.
0
Not overly concerned with significant figures in this case, but you make a good point. Thanks!
Shane_B
Best Response
You've already chosen the best response.
1
no problem :)