NAME
Rec. Day:
W Th
Rec. Time: 8 9 10 11 12 1 2 3 4
TA Name:
Physics 1110
Homework 7: Waterslide Wipeout
and the Effect of Friction
Last week, you investigated the physics of the
Megawoosh video, where a person is shown sliding down
a huge waterslide in the Alps, flying through the air, and
landing safely in a child’s pool. You showed that the
physics in the video was consistent with Newton’s laws,
if friction was neglected.
The Mythbusters busted this video, however, by
constructing a full size model of the ramp and showing
that the speed they achieved was insufficient. Friction
makes the jump (as shown) physically impossible!
A series of clips from the Mythbusters show can be found here (check out both!):
https://www.youtube.com/watch?v=iHu6LVg-0Hs
http://www.discovery.com/tv-shows/mythbusters/videos/waterslide-wipeout.htm
Your goal now is to introduce sliding friction into your analysis (still assume that air resistance is
zero). Recall the simplified picture of the ramp from last week. Here, only consider Adam’s slide
down the larger triangle with base x1. The parameters are θ1 = 24°, L1 = 50 m, x1 = 45.7 m, and
h1 = 20.3 m. We'll use a coordinate system with the x-axis positive down the ramp and the y-axis
positive upward, normal to the ramp, as shown above.
1. Last week you showed that (ignoring friction) the magnitude of Adam’s acceleration down the
slide would be a = g sinθ1. Assuming that Adam starts from rest at the top of the ramp and that
you ignore the effect of friction, how fast would he be moving when he reaches the bottom of
the ramp (i.e., after he has slid a distance L1 = 50 m)? Present your reasoning.
2. Now let’s include sliding friction! In the space below, draw a careful free-body diagram for
Adam when he is partway down the ramp. Include sliding friction, and label all the forces.
(Remember, in a free body diagram, Adam is represented as a dot, and all forces are drawn with
their tails starting at that dot)
1
Name__________________________
3. Use your free body diagram (and Newton’s 2nd law) to derive Adam’s acceleration down the
ramp (assume coefficient of kinetic friction µk) Show your reasoning – do the derivation
yourself and show it below.
(A) g(sin θ1 − µ k cosθ1 )
(D) g(sin θ1 − µ k sin θ1 )
(B) g(sin θ1 + µ k cosθ1 )
(E) g(sin θ1 + µ k sin θ1 )
(C) g(cosθ1 − µ k sin θ1 )
4. In the Mythbusters show, Adam suggests that Jamie may go faster down the slide because
Jamie weighs more than Adam. Based on your result in #2, is this true? Present your
reasoning.
(A) No
p. 2
(B) Yes
(C) Can't be determined
Name__________________________
5. Suppose Adam starts from rest, slides a distance L1 to the bottom of the ramp, ending at a
known (measured!) speed v. Which expression tells us the coefficient of kinetic friction?
Present your reasoning; show the algebra.
(A)tan θ1
(B)tan θ1 +
v2
2gL1
(C)tan θ1 −
v2
2gL1
(D)tan θ1 +
v2
v2
(E)tan θ1 −
2gL1 cosθ 1
2gL1 cosθ 1
6. In the Mythbusters video, we’re told that Adam attains a maximum speed of about 30 mi/h at
the bottom of the ramp. Use part 5 to calculate the coefficient of kinetic friction down the
Mythbuster’s water slide. (Remember to convert 30 mi/h into m/s.) Present your reasoning.
Look
up
some
common
friction
coefficients
online
(for
example
at
http://www.engineershandbook.com/Tables/frictioncoefficients.htm). Does your number seem
reasonable for a water slide? Briefly discuss.
p. 3