1. The problem statement, all variables and given/knowndata A 5kg box is started
ID: 1757513 • Letter: 1
Question
1. The problem statement, all variables and given/knowndataA 5kg box is started at the top of a spiral slide at t=0 with aspeed of 15m/s. The spiral has a radius, r=2m, and it's height isgiven by z=-.4 where z is in meters and is inradians. The slide has a wall and a floor with a coe. of friction of .3
a) With no friction, what is the speed of mass when=2pi?
b)With no friction, what is the speed of the mass when t=.5s?
c)With friction only between the floor and mass where does the massstop and at what time?
e)With friction only between the wall and the mass, what is thefinal speed of the mass?
2. Relevant equations
z=-.4
W=?Fds
W=1/2mv^2-1/2mv^2
Explanation / Answer
a)the initial angular velocity of the box is wo = (u/r) u = 15 m/s and r = 2 m the displacement of the box is z = ut + (1/2)at2 --------(1) z = -.4 where = 2 radian or z = -.4 * 2 = -.4 * 2 * 3.14 = -2.512 m a = (u2/r) solving equation (1) for t the speed of the mass when =2 radian is v = u + at b)the displacement of the mass when t = .5 s is z1 = ut + (1/2)at2 we know that v2 - u2 = 2az or v = (u2 + 2az)1/2 c)the forces acting on the mass when it slides down the spiralis Fx = F - fk = F -k * n F = (m * u2/r) or Fx = (m * u2/r) -k * n and Fy = n + (-w) = 0 or n = w or Fx = (m * u2/r) -k * w or m * ax = (m * u2/r) -k * m * g or ax = (u2/r) - k * g--------(2) when the mass stops then its final speed is zero therefore weget v = u + at v = 0 or u + at = 0 or t = -(u/a) the value of a is obtained from equation (2) the mass stops at a distance S = ut + (1/2)at2 d)the final speed of the mass when there is friction betweenthe wall and the mass is v2 - u2 = 2aS or v = [u2 + 2aS]1/2 d)the final speed of the mass when there is friction betweenthe wall and the mass is v2 - u2 = 2aS or v = [u2 + 2aS]1/2Related Questions
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