show all the equations, steps and work for full rating A block of mass m = 1.0 k
ID: 2116339 • Letter: S
Question
show all the equations, steps and work for full rating
A block of mass m = 1.0 kg, initially at h = 2.0 m, is released and slides along a track. The track is frictionless except from point A to point B, where the length L is 6.0 m and the coefficient of kinetic friction is u k = 0.15. What is the initial gravitational potential energy of the block? What is the speed of the block at point A? How much energy is dissipated as thermal energy when the block passes point B? Find the speed of the block at point B.Explanation / Answer
1) initial gravitational potential energy = m*g*h = 1*2*9.8 = 19.6
2)potential energy is converted into kinetic energy at point A, therefore
mgh=.5*m*v^2
therefore, v at point a = sqrt(2*g*h) = 6.3 m/sec
3)thermal energy dessipated = work done by frictional force = u*m*g*l = .15*1*9.8*6 = 8.82
4)frictinal force causes disceleration from A to B = u*g= .15*9.8=1.47m/sec^2
velocity at point B = sqrt(v^2-(2*a*l)^.5 )= sqrt(6.3^2 - sqrt(2*1.47*6)) = 5.975m/sec
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