2108 views

If a car is travelling over a curved hill, what is the maximum speed it can travel before losing contact with the road surface?

This is a question about circular motion that also includes some knowledge of Newton's laws. The car is travelling over a curved surface, which you can imagine as part of the circumference of a circle. In order for the car to be travelling in a circular path, the resultant of all the forces acting on it must provide the centripetal force (which acts towards the centre of the circle). The forces acting on the car are its weight, equal to its mass times the gravitational field strength (mg) acting vertically downwards, and the normal reaction force from the road surface, acting perpendicularly to the road surface. We shall call this R. The resultant of the two forces is equal to mv2 /r, where r is the radius of curvature of the circular path, and this force is the centripetal force. When the car is at the top of the hill, the reaction force is vertically upwards and the weight is vertically downwards, thus the resultant of the two that acts towards the centre of the circular path = mg - R. This resultant force provides the centripetal force and so mg -R = mv2 /r. If the car is to lose contact with the road, then there will no longer be a normal reaction force from the road acting on the car, therefore R=0. When this happens when the car is at the top of the hill, the centripetal force, mv2/r = mg. There is mass (m) present on both sides of the equation here which cancel out, leaving us with v2/r = g. We can rearrange this to make v, the speed at which the car loses contact with the road surface, the subject of the equation. We end up with v= (gr)1/2. The reason this is the maximum speed of the car when it loses contact is because this is when the entirety of the car's weight contributes to the centripetal force (since it acts in the same line as the centripetal force when the car is at the top of the hill) rather than some component of it.)

2 years ago

Answered by Emma, an A Level Physics tutor with MyTutor

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

147 SUBJECT SPECIALISTS

£26 /hr

Degree: Aerospace Engineering PhD Spacecraft Control (Doctorate) - Bristol University

Subjects offered:Physics, Maths+ 4 more

Physics
Maths
Further Mathematics
Extended Project Qualification
.STEP.
.PAT.

“Aerospace Engineering PhD candidate in spacecraft control with 7 years of experience in tutoring.”

£20 /hr

Degree: Engineering (Bachelors) - Warwick University

Subjects offered:Physics, Maths+ 1 more

Physics
Maths
Chemistry

“Hello, I am Ed a dedicated, patient and friendly second-year Engineering student at the University of Warwick.”

MyTutor guarantee

£22 /hr

Degree: Chemical Engineering (Masters) - Bath University

Subjects offered:Physics, Science+ 3 more

Physics
Science
Maths
Further Mathematics
Chemistry

“Hey there! I am Laura and I am currently studying Chemical Engineering at University of Bath. I am really passionate about Science and I am willing to share my knowledge through tutoring you. My passion and expertise in science can be...”

Currently unavailable: for new students

Degree: Earth Sciences (Masters) - Oxford, Exeter College University

Subjects offered:Physics, Science+ 3 more

Physics
Science
Maths
Chemistry
Biology

“Hi I'm Emma, a Masters' student at the University of Oxford who loves all things Maths/ Science!”

You may also like...

Posts by Emma

Describe the structure of DNA

If a car is travelling over a curved hill, what is the maximum speed it can travel before losing contact with the road surface?

Other A Level Physics questions

What is the force on a moving charged particle in a magnetic field, and why is no work done by this force when it accelerates the particle?

What is the Strong Nuclear Force?

Can you explain the ideal gas law?

Use band theory to explain the changes in the resistance of an intrinsic semiconductor as temper changes.

We use cookies to improve your site experience. By continuing to use this website, we'll assume that you're OK with this.