A level mechanics help. F=ma and coefficients of friction?!?

Question

A stone slides in a straight line across a frozen pond. given that the initial speed of the stone is 5ms-1 and that it slides 20m before coming to rest, calculate the coefficient of friction between the stone and the surface of the frozen pond.

Using the equations of motion i've calculated deceleration to be -0.625ms-2

Not sure what the contact force is, or how to work out horizontal force seeing as i don't have mass in

F= muR

Could you please explain, step by step.

Thanks!

Answer 1

You have to use conservation of Energy. not F=MA in this case.



What happens when you use conservation of energy you get an equation in which you can factor the mass out.



We get this equation by understanding the Energy of the system of the beginning is equal to 1/2mv^2 and at the end the energy of the system is equal to zero. Along the way the system looses energy in the form of work by moving the rock over the ice.



.5mv^2 - mgxf = 0



What this equation says:



half mass X velocity squared - mass X distance X gravity X coefficient of friction = 0



You can factor out and divide both sides by M to make it disappear.



You know G and you know X and that just leaves you with the coefficient.

Answer 2

U^2 = 2as where: a = deceleration , s = distance, U = initial speed

25 = 2 x a x 20

40a = 25

a = 25/40 = 0.625m/s/s

this deceleration a represents the coefficient of friction

Answer 3

a) A particle "is desperate in action" ability "is made to start shifting". once you communicate approximately that s = 4 + 5t - 2t^2 its velocity v = v(t) is given via ability of ds/dt = v(t) = 5 - 4t consequently at t =a million v(a million) = 5-4 = a million m/s - travels indoors the +ve x journey and at t = 2 v(2) = 5 - 8 = - 3 m/s - travels indoors the -ve x journey b) To be at loosen up one might want to have v(t) = 0 or v(t) = 5 - 4t = 0 consequently t = 5/4 = a million.25 s c) Acceleration = a(t) = dv/dt = - 4 m/s^2 = consistent and so does now no longer undergo in ideas on the time. it is going to likely be an identical at t =a million and t=2. d) The particle starts at a place s(0) = 4 m from the initiating of OX with velocity v(0) = 5m/s and destructive acceleration = decceleration = - 4m/s^2. At t = a million.25 s it reverses it is velocity and travels in path of the initiating of OX .