NAME(s)____
BALLS COLLIDE (HONORS)
1)Where to make them collide?
You
are given two ramps at different slope facing one another. ( A short ramp at a
steep angle, and a long ramp at a shallower angle) You are given a ball. You
will roll the ball down each ramp and make measurements. Then the balls will be
taken away from you. Using only your information and formulas, predict where to
put TWO balls, one on each ramp, so they will collide at the bottom (when let
go at the same time). Have teacher verify results.
Hint: Get acceleration of each ramp first. Vi=0, A=2D/T^{2}.^{}
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2)Where
will they collide????
You
are given one ball and a ramp. You will roll the ball down the ramp and make
measurements. THEN, you will be given a second ball. BEFORE you are given the second
ball, you will be asked to predict where a ball from the top and the middle of
the ramp will collide along the floor, if at all. Show your work and
calculations. (HINT: you can use algebra, calculus, or the good old graphing
method. Assume that the ball after the ramp goes a constant speed D=VfT). Have
teacher verify results
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^{ t= 0 t=t2 t = t1 t=tafter + td}
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^{ two equations, two unknowns, solve for distance after ramp, or time after ramp . **** Extra, use algebra to show that you never even needed to time anything!}
^{MEASUREMENTS:}
^{D1= TOTAL DISTANCE on ramp for Ball1}
^{T1= Time for ball 1}
^{**Calculations (in order):}
^{A= Acceleration of ramp (both balls)}
^{Vf1=Final velocity ball1 on ramp=velocity on floor ball1}
^{D2= distance on ramp ball 2 (=1/2D1)}
^{T2=time on ramp ball2}
^{Vf2=Final velocity ball2 on ramp=velocity on floor ball2}
^{TD=time difference…. =time ball 2 spent on floor before ball1 on floor Df2= distance ball 2 on floor before ball2}
^{T= time ball1 on floor (1 unknown), D= distance ball1 on floor (2nd unknown) 2 equations and 2 unknowns! (T? and D? time and dis ball1 on floor)}
^{ }NAME________
BALLS COLLIDE (ACADEMIC)
Where to make them collide? (Same Place, Same Time)
You
are given two ramps at different slope facing one another. ( A short ramp at a
steep angle, and a long ramp at a shallower angle) You are given a ball. You
will roll the ball down each ramp and make measurements. Then the balls will be
taken away from you. Using only your information and formulas, predict where to
put TWO balls, one on each ramp let go at the same time, so they will collide
at the bottom. Have teacher verify results
_{(Vi = 0)}
SteepRAMP1 LENGTH (same each
time) TIME











time avg= 
D=1/2AT^{2} A1
= 2D/T^{2}

_{(Vi = 0) start ball at top of ramp for this, just to calculate the acceleration for the shallow ramp.}
ShallowRAMP2
LENGTH (same each time) TIME











time avg= 
D=1/2AT^{2} A2
=2D/T^{2}
^{}^{}
^{To make them collide….. keep ramp 1 the same, fill in the dis, time, and calculate its acceleration. When they meet, the TIME will be the same, so for ramp 2, use the same time as ramp1, the acceleration you calculated from measurements, and get the new distance up ramp2. Check results!!!}
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^{SteepRamp1 ShallowRamp2}
^{Distance1 up ramp_________ *Acceleration2_________ (from measurements) with original D,T}
^{*Time1 down ramp_______ }^{à}^{ *New Time1 down ramp ________ (same as ramp1=T1) }
^{*Acceleration1_________(from measurements) *NewDistance up ramp2_______________ }D=1/2AT^{2}
^{ }NAME________
BALLS COLLIDE (ACADEMIC)
^{Where will they collide?}
Where will they collide???? (Same Place Same time)
You
are given one ball and a ramp. You will roll the ball down the ramp and make
measurements. THEN, you will be given a second ball. BEFORE you are given the
second ball, you will be asked to predict where a ball from the top and the
middle of the ramp will collide along the floor, if at all. Show your work and
calculations. (HINT: you can use algebra, calculus, or the good old graphing
method. Assume that the ball after the ramp goes a constant speed). Have
teacher verify results
_{(Vi = 0)}
SRAMP1 LENGTH
(same each time) TIME











time avg= 
D=1/2AT^{2} Vf^{2}=2AD D^{after}=Vf*T_{after}
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^{ t= 0 t=t2 t = t1 t=tafter + td}
^{* = calculations}
^{BALL1: BALL2:}
^{Length of ramp:__ ___ D1 Length down ramp (half of ball one)__ _ D2 = 1/2D1}
^{Time1 down ramp__ ___T1_ *Acceleration of ramp (same as ball1)__ __=A}
^{*Acceleration of ramp__ __ }D_{1}=1/2AT_{1}^{2}^{ *Time2 down ramp__ ___ }D_{2}=1/2AT_{2}^{2}^{ }
^{*Velocity1 at bottom of ramp__ _} Vf_{1}^{2}=2AD_{1}^{ *Velocity2 at bottom of ramp__ _ } Vf_{2}^{2}=2AD_{2}2^{}
^{ *Time difference(Time along floor before ball1) TD= (T1  T2)}
^{Distance along floor=Velocity1 * Time after ramp Distance along floor=Velocity2 *( Time after ramp + Time difference)}
^{ D? = V1 * T? D? = V2 ( T? + TD)}
^{ two equations, two unknowns, solve for distance after ramp. D? and T? are the same for them to collide.}
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