finding height by applying work energy theorem

Question

  A block is released from rest at point A and slides down a curved slope to point B, then continues until it comes to rest at point C. There is no friction from point A to point B, but there is friction from point B to point C. It stops in a time t as it travels from B to C. The vertical height of A is h above point B, and point C is horizontal distance x from point B. (you can find a diagram of this by searching up this question, unable to insert image)

Write an expression for h. Your answer should be in terms of x, t, and g (9.80 m/s2). (Apply the work-energy theorem to the block’s motion from A to B.)

Answer 1

Hello Jule,

Hope this should work

Work done gravitational force from At B = mgh

There is a loss of potential energy and gain in Kinetic energy from A to B ( so work done is positive)

at B

KE = 1/2 (mvb^2) Which becomes zero at C due to friction

Force of friction = µmg , where µ = Coefficient of kinetic friction

Work done = - µmgx , wher x = distance moved under force of friction

Also 1/2 mvb^2 = µmgx

So vb = sqrt (2 µgx), g= 9.8

so Vi = vb = sqrt (2 µgx) , vf = 0

Use vb -0 = Acceleration *t

vb = √( (2 µgx) = at

a= Acceleration , t= time to stop from B to C

a= µg ( Deceleration )

Now vb^2 = 2ax

or vb^2 = 2µg x