Question

A car of mass M = 1400kg traveling at 65.0km/hour enters a banked turn covered with ice. The road is banked at an angle θ = 20degrees, and there is no friction between the road and the car's tires. What is the acceleration?

Answer 1

i got \[\Sigma x = nsin(\theta)=ma \]
and \[\Sigma y=ncos(\theta)=mg\]

so n =1460.

a should then be \[1460\sin(20)/1400\]=.95

but mastering physics says it's wrong. says it's 3.57. what did i do wrong?

Answer 2

ok, seriously? wtf....a=v^2/r, so if the velocity is 65 km/hr makes it 1083m/s^2/3.57=r, right? if a=3.57 as mastering physics said? but that answer is wrong too!!! this is bull!!!

Answer 3

Are you having trouble finding r? mv^2/r = centripetal force

Answer 4

Is the question for radius or acceleration?

Answer 5

both. it has multiple parts. wants you to find acceleration first then radius

Answer 6

i've gone through the hints and i got the sum of the forces right. it led me up until getting the actual acceleration...gave me the sum of the forces and the normal force. it was simple algebra to solve for a, or so i thought.

Answer 7

\[\sum F(x) =\frac{ mv^2 }{ r } = nsin \theta \]
\[\sum F(y) = ncos \theta - mg = 0 \implies n = \frac{ mg }{ \cos \theta }\]

\[\frac{ mv^2 }{ r } = \frac{ mg }{ \cos \theta } \sin \theta \implies r = \frac{ v^2 }{ gtan \theta }\]

Answer 8

masses cancel out there leaving acceleration being g*sin(theta)/cos(theta) which gives me the wrong answer still. what the hell am i missing???

Answer 9

a=gsin(theta)/cos(theta)=21.9, not 3.57 which is what the answer is supposed to be...this is really pissing me off.

Answer 10

a=9.8tan(20)=21.9...........................mastering physics says a should equal 3.57.......................

Answer 11

check your calculation
http://www.wolframalpha.com/input/?i=tan%2820%29*9.8

Answer 12

i did it in a calculator....

Answer 13

are you in degree mode?

Answer 14

i thought i was....not sure how it got switched over.....i had it in degrees when i was doing homework yesterday.....

Answer 15

thanks. makes more sense now

Answer 16

yw

Answer 17

\[\frac{ 1 km }{ 1000m } \times \frac{ 3600s }{ 1 h }\]

Answer 18

oh god, i feel stupid. 60 seconds in an hour.......this is what happens when i'm frustrated. stupid mistakes ensue.......thanks

Answer 19

That's for converting m/s to km/h, just go backwards for m/s.

Haha no worries :) it happens. I was looking at your problem and was like how the heck did you get 65 km/h to become 3x the speed of sounds haha, but yeah I hope it makes sense now.