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VICPhysicsQuick questions
Unit 3: How do fields explain motion and electricity?
Quick questions on Banked tracks and the banking angle: VCE Physics Unit 3
11short Q&A pairs drawn directly from our worked dot-point answer. For full context and worked exam questions, read the parent dot-point page.
What is free-body diagram on a frictionless banked track?Show answer
Consider a car of mass $m$ on a banked curve of radius $r$ at angle $\theta$ to the horizontal, moving at speed $v$. Two forces act:
What is the design speed?Show answer
Dividing the horizontal equation by the vertical equation:
What is above and below the design speed?Show answer
At the design speed. Friction is zero. The road feels smooth; passengers feel pushed into their seats but not sideways.
What is why engineers bank curves?Show answer
Highway off-ramps, velodromes, race tracks and railway curves are banked so that vehicles can take the curve safely at the typical traffic speed without relying on friction. This reduces tyre wear, lowers the risk of skidding on wet roads, and is more comfortable for passengers because no sideways force is felt.
What is at the design speed?Show answer
Friction is zero. The road feels smooth; passengers feel pushed into their seats but not sideways.
What is below the design speed?Show answer
The horizontal component of the normal force is more than needed for the (smaller) required centripetal force. The car tends to slide down the bank (inward); friction must act up the bank to prevent it.
What is above the design speed?Show answer
The horizontal component of the normal force is not enough for the (larger) required centripetal force. The car tends to slide up the bank (outward); friction must act down the bank to keep the car on the curve.
What is resolving forces along the slope instead of horizontally and vertically?Show answer
The centripetal acceleration is horizontal (toward the centre of the circle), so resolve along horizontal and vertical axes, not along and perpendicular to the slope.
What is including friction in the design-speed calculation?Show answer
The whole point of the design speed is that friction equals zero.
What is confusing the direction of the friction force?Show answer
Below the design speed, friction acts up the slope; above, it acts down. The car tendency is opposite to the friction.
What is quoting an angle that depends on mass?Show answer
$\tan\theta = \frac{v^2}{rg}$ has no mass term; the design speed is the same for a motorbike and a truck.