1. Consider the skateboarder in the figure below. If she has a mass of 54 kg, an initial velocity of 29 m/s, and a velocity of 11 m/s at the top of the ramp, what is the work done by friction on the skateboarder? Ignore the kinetic energy of the skateboard's wheels. H at top of ramp = 5m


2. The roller coaster in the figure below starts with a velocity of 16 m/s. One of the riders is a small girl of mass 27 kg. Find her apparent weight when the roller coaster is at locations B and C. At these two locations, the track is circular, with the radii of curvature given in the figure. The heights at points A, B, and C are
hA = 10 m,
hB = 20 m, r = 10m
and
hC = 0, r = 20m
Assume friction is negligible and ignore the kinetic energy of the wheels. (The figure is not necessarily drawn to scale.)



50fg per correct answer within 3 hours

This post was edited by g4mer on Oct 17 2013 07:16pm

#1 has been solved still looking for #2

prob need the picture

This is all done through conservation of energy

1. .5(54 Kg)[(29 m/s)^2] + Friction= (54 Kg)(9.81 m/s^2)(5m) + .5(54kg)(11 m/s)^2
kinetic energy(initial) +friction= potential energy + kinetic energy(final)
friction= 19.761 kJ

2. Kinetic(initial)= potential(@B)+Kinetic(@B)
.5mv^2=mgh+.5mv^2
they don't give you mass, but it doesn't matter since mass cancels out anyways.
Velocity @ B= 7.73 m/s

Apparent weight of an object is the amount of acceleration felt on an object.
Normal Force= m*v^2/r - mg

Normal Force= -103.53 Newtons, With the Y-axis facing downwards, meaning that there is a feeling of weightlessness. This is intuitive if you've ridden a roller coaster, going fast and reaching the top of the hill you will feel weightless.

For C, you can do the initial energy as the kinetic+potential for either A or B, since it is conserved and friction isn't accounted for it doesn't matter, they're the same.

KE@B+PE@B=KE@C

.5m(7.73)^2+m(9.81)(20m)=.5m(V@c)^2
mass cancels
V@c=21.2639 m/s

F= mv^2/r + mg
This is slightly different than last time, you're adding mg not subtracting because the forces are working together this time. Gravity and the acceleration from the roller coaster both acting to pull downwards.

F= 875.277 newtons

Also, for reference, the small girl at regular gravity is simply F=MA where A is gravity, and that equates to 264.87 newtons.