A rollercoaster stops at a point with GPE of 10kJ and then travels down a frictionless slope reaching a speed of 10 m/s at ground level. After this, what length of horizontal track (friction coefficient = 0.5) is needed to bring the rollercoaster to rest?

Recognise that the intial potential energy and kinetic energy at 10 m/s position should be identical due to the frictionless slope. 

mgh = 0.5mv2

10kJ = 0.5 x m x 102

10 000 = 0.5 x m x 100

50m = 10 000

m = 200 kg

Recognise that the weight of the rollercoaster is 200g which is equivalent to the vertical reaction force on the horizontal track.

The frictional force is given by the coefficient of friction multiplied by the vertical reaction force:

F = 200g 0.5 = 100g

The rollercoaster comes to rest when its energy is zero and all of the initial kinetic energy (at 10 m/s) has been dissipated by the frictional force. Therefore, we can write the work done by friction, W, in terms of the length of horizontal track, L and equate this to the kinetic energy:

W = L = 100g L = 10 000

L = 10 000 / 100g = 100 / g = 10.2m

The length of track needed is 10.2m

Daniel M. A Level Maths tutor, GCSE Maths tutor

4 months ago

Answered by Daniel, an A Level Maths tutor with MyTutor

Still stuck? Get one-to-one help from a personally interviewed subject specialist


PremiumBarnaby W. A Level Maths tutor, A Level Further Mathematics  tutor, G...
View profile
£24 /hr

Barnaby W.

Degree: Mathematics (Masters) - Southampton University

Subjects offered: Maths, Further Mathematics

Further Mathematics

“ I have always enjoyed tutoring. I find that it gives me real satisfaction to see a child or student you have helped feel much more confident”

Sam E. A Level Maths tutor, GCSE Maths tutor
View profile
£20 /hr

Sam E.

Degree: Computer Science (Masters) - York University

Subjects offered: Maths


“About me: Hello! I'm a first year Computer Science student at the University of York. I offer tutoring for maths at GCSE and A-Level. Despite not studying maths now, it was my original love - the subject which first taught me how to e...”

MyTutor guarantee

PremiumTom J. A Level Economics tutor, IB Economics tutor, GCSE Economics tu...
View profile
£24 /hr

Tom J.

Degree: MSc Ecological Economics (Masters) - Edinburgh University

Subjects offered: Maths, Philosophy+ 2 more


“I have fostered a passion for teaching ever since taking the opportunity to travel to China and teach at an English language school for Chinese pupils.  This experience not only massively broadened my horizons culturally, but also gav...”

About the author

Daniel M. A Level Maths tutor, GCSE Maths tutor
View profile
£20 /hr

Daniel M.

Degree: Engineering (Other) - Durham University

Subjects offered: Maths


“Top tutor from the renowned Russell university group, ready to help you improve your grades.”

MyTutor guarantee

You may also like...

Other A Level Maths questions

What is an Inverse function?

How do I add up the integers from 1 to 1000 without going insane?

How do I integrate ln(x)?

How to find y-intercept on a graphical calculator

View A Level Maths tutors


We use cookies to improve our service. By continuing to use this website, we'll assume that you're OK with this. Dismiss