Car changing speed around a corner - find tangential and radial accel

  • Thread starter Thread starter Phys121VIU
  • Start date Start date
  • Tags Tags
    Car Radial Speed
AI Thread Summary
A car is changing speed while turning, with a velocity of 19 m/s at a 45° angle south of east and a total acceleration of 3.0 m/s² at 20° north of east. To find the radial and tangential components of acceleration, the relationship between these components and their angles relative to the total acceleration must be utilized. The tangential acceleration is aligned with the velocity direction, while the radial acceleration is perpendicular to it. The calculations involve using the sine law to determine the magnitudes of the tangential and radial accelerations, ensuring that they adhere to the given total acceleration. The discussion emphasizes the importance of understanding the geometric relationships between the vectors involved in the problem.
Phys121VIU
Messages
17
Reaction score
0

Homework Statement



A car changes speed as it turns from traveling due south to heading due east. When exactly halfway around the curve, the cars velocity is 19m/s at 45° south of east. At this moment, the cars total acceleration is 3.0 m/s2 at 20° north of east.

Calculate the radial and tangential components of the cars acceleration, then calculate the radius of the turn


Homework Equations



Radial acceleration is v2/R

and tangential/centripetal acceleration is Δ|v|/Δt



The Attempt at a Solution



I can't use either of these formulas to find either acceleration. Radius isn't given to find radial acceleration, and time isn't given to find tangential accel.

So from there I tried using the given total acceleration: 3.0m/s and 20° with
either the sine or cosine laws to find the acceleration components.

I ended up with some numbers that seemed unlikely (I need to figure out how to post formulas better..) so I am doubting that is how to solve the question.

What i do know is that once I find radial acceleration I can use that formula to find the Radius.
 
Physics news on Phys.org
How about finding the angle between your acceleration vector given and the direction of the expected centripetal acceleration vector. Same, what is the angle between the expected tangential acceleration vector and the acceleration vector given?
 
r0wbrt said:
How about finding the angle between your acceleration vector given and the direction of the expected centripetal acceleration vector. Same, what is the angle between the expected tangential acceleration vector and the acceleration vector given?

How would I find the angle of the expected radial accel vector with just the knowledge of the total accel vector being 20° north of east? Are the tangential accel and radial accel vectors perpendicular to each other? Therefore making it possible to use sin/cosine laws to find the missing angles/magnitudes?

If i use the sine law:

For tangential accel:

3m/s2/sin90° = b/sin70° so b would = 2.597m/s2

And for radial/centripetal accel:

3m/s2/sin90° = c/sin20° so c = 3.064m/s2

But these numbers don't seem right..when i check the numbers my using

a2 = b + c2

i come out with 4.01m/s2 which doesn't = the given total accel...please help!
 
You're given both the direction of the velocity vector (45° south of east) and the acceleration vector (20° north of east). Use this information to determine the relative angle between velocity and acceleration.
 
Last edited:
tangential acceleration is in the direction of velocity, so the angle between tangential accel and total accel is 20+45=65 degrees.
centripetal acceleration is perpendicular to velocity and makes 45-20=25 degrees.
so you get 3sin65 and 3sin25 as answers
btw tangential and radial are by definition perpendicular directions.And also check your answer! c=3sin20##\neq##3.024
 
TL;DR Summary: I came across this question from a Sri Lankan A-level textbook. Question - An ice cube with a length of 10 cm is immersed in water at 0 °C. An observer observes the ice cube from the water, and it seems to be 7.75 cm long. If the refractive index of water is 4/3, find the height of the ice cube immersed in the water. I could not understand how the apparent height of the ice cube in the water depends on the height of the ice cube immersed in the water. Does anyone have an...
Thread 'Variable mass system : water sprayed into a moving container'
Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...

Similar threads

Back
Top