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From what height, h, should a rail-cart fall to complete a loop-the-loop of radius r without falling off a the track? Assume the track on which the rail-cart travels is smooth and express h in terms of r.

This question combines the principles of energy conservation and circular motion. The insight is to realise the condition for which the rail-cart will fall off of the track - when there is no contact forc...

Answered by Benjamin R. • Physics tutor

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A particle, P, moves along the x-axis. The displacement, x metres, of P is given by 0.5t^2(t^2 - 2t + 1), when is P instantaneously at rest

differenciate and then eqate with v = 0.

Answered by Harry S. • Maths tutor

6818 Views

A box initially at rest is on a plank, of length 5m, that is elevated at an angle such that tan(a)=3/4. When it reaches the end of the plank it has velocity 5ms^-1. Calculate the average frictional force on the box.

In physics questions it is useful to not plug numbers in until the end and instead work through algebraically. Let's say the angle of elevation is a, the mass is m, the velocity at the end of the plank is...

Answered by • Physics tutor

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f(x) = sinx. Using differentiation from first principles find the exact value of f' (π/6).

The derivative of the function where x=π/6 is defined asThe limit as h->0 of [sin(h+π/6)-sin(π/6)]/hUsing the double angle formula, sin(h+π/6) = sin(h)cos(π/6) + cos(h)sin(π/6) = √3sin(h)/2 + cos(h)si...

Answered by • Maths tutor

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How do I examine and evaluate the use of melody in set pieces of music?

Melody is one of the main compositional elements which you may be asked to examine when comparing and contrasting different pieces of music. Representing much more than just the main tune of the music, we...

Answered by Lizzie C. • Music tutor

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