- #1

PhysicsNoob2

- 2

- 3

- Homework Statement
- You create a banked track of 12 degrees, now what's the maximum linear velocity?

And how would this change if a child was driving the kart instead?

- Relevant Equations
- F=mv^2/r

F=mg sin(theta)

This is a UK A-Level question that I'm really struggling with, and can't seem to find any resources online that explain it well.

I've been given the following details:

mass of gokart + driver = 520kg

radius of track = 42m

Maximum frictional force between tyres and road on flat track F = 20% weight of kart+driver (104kg)

Bank of track = 12 degrees

And I've calculated the following in earlier questions:

Coefficient of friction = F/N = 0.0204

Angular velocity (Flat track) w = sqrt (F/mr) = 0.069 rad/s

Linear velocity (Flat track) v = sqrt (Fr/m) = 2.898 m/s

Here is my working out for the question I'm stuck on so far:

F (Force down the slope) = mg sin (theta)

F = 520 * 9.8 * sin(12)

F = 1059.51...

v = sqrt (Fr/m)

v = sqrt (1059.51... * 42 / 520)

v = 9.25 m/s (2dp)

I'm certain that I'm doing something wrong here, as this is using the force down the slope and not the centripetal force towards the centre of the track. But I've never seen anywhere that shows me how to calculate this? Or have I got this right and am worrying about nothing?

And when calculating a lighter kart (Taking in to account the child driving), I get the same maximum linear velocity. Is this correct? As intuition would suggest that the kart would move faster with a child in it than with an adult?

Thanks in advance

I've been given the following details:

mass of gokart + driver = 520kg

radius of track = 42m

Maximum frictional force between tyres and road on flat track F = 20% weight of kart+driver (104kg)

Bank of track = 12 degrees

And I've calculated the following in earlier questions:

Coefficient of friction = F/N = 0.0204

Angular velocity (Flat track) w = sqrt (F/mr) = 0.069 rad/s

Linear velocity (Flat track) v = sqrt (Fr/m) = 2.898 m/s

Here is my working out for the question I'm stuck on so far:

F (Force down the slope) = mg sin (theta)

F = 520 * 9.8 * sin(12)

F = 1059.51...

v = sqrt (Fr/m)

v = sqrt (1059.51... * 42 / 520)

v = 9.25 m/s (2dp)

I'm certain that I'm doing something wrong here, as this is using the force down the slope and not the centripetal force towards the centre of the track. But I've never seen anywhere that shows me how to calculate this? Or have I got this right and am worrying about nothing?

And when calculating a lighter kart (Taking in to account the child driving), I get the same maximum linear velocity. Is this correct? As intuition would suggest that the kart would move faster with a child in it than with an adult?

Thanks in advance

Last edited: