Math Is Fun Forum

jimi70

Member

Registered: 2012-04-04

Posts: 22

Reaction forces problem

A particle of mass 0.5 kg is moving at constant speed on a rough horizontal table in the direction of the constant unit vector i. The particle is acted on by three forces, namely (i) its weight, (ii) an appiled force P and (iii) the total reaction of the table R. Given that P = (3i + 8j) N, where j is a unit vector vertically downwards, and taking g = 9.8 m s[sup]-2[/sup], determine R in the form R = (ki + lj) N, where k and l are numbers. Hence determine the coefficient of friction between the particle and the table, to 2 decimal places.

Now, the part I need clarification on is the part where the question asks for R in the form (ki + lj). I thought that the normal reaction always acted perpendicularly to the surface of contact, in which case there would be no horizontal component, i.e. k would be zero. My book disagrees. Am I confused or missing something?

Bob

Administrator

Registered: 2010-06-20

Posts: 10,164

Re: Reaction forces problem

hi jimi70

Welcome to the forum! 

It is a rough table and friction isn't mentioned as separate force so I think 'total reaction' means the normal reaction combined with a frictional force.  You are right to query this as reaction is usually reserved for the normal force.

I haven't actually tried the question yet, but I'd start by calling the two forces there, F and let's say S.  That keeps it clear what all the forces are.

Then you can do the usual equilibrium stuff (constant velocity => no accelerating force required) and go for mu = F/R

Post again if you need more help.

Bob

ps.  looked up the definition on Wolfram Alpha:

reaction:   (mechanics) the equal and opposite force that is produced when any force is applied to a body

Which I guess means it doesn't have to be normal to the surface.

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

jimi70

Member

Registered: 2012-04-04

Posts: 22

Re: Reaction forces problem

Thanks bob

Yes, I'm pretty sure now that you're right, i.e. 'total reaction' in the question is the resultant of the normal reaction and friction.