Nate the Skate was an avid physics student whose main non-physics interest in li
ID: 1433753 • Letter: N
Question
Nate the Skate was an avid physics student whose main non-physics interest in life was high-speed skateboarding. In particular, Nate would often don a protective suit of Bounce-Tex, which he invented, and after working up a high speed on his skateboard, would collide with some object. In this way, he got a gut feel for the physical properties of collisions and succeeded in combining his two passions.* On one occasion, the Skate, with a mass of 121 kg, including his armor, hurled himself against a 871-kg stationary statue of Isaac Newton in a perfectly elastic linear collision. As a result, Isaac started moving at 1.37 m/s and Nate bounced backward. What were Nate's speeds immediately before and after the collision? (Enter positive numbers.) Ignore friction with the ground. Before:
Explanation / Answer
ELASTIC COLLISION ONE DIMENSIONAL
m1 = 121 kg m2 = 871 kg
speeds before collision
u1 = ? u2 = 0 m/s
speeds after collision
v1 = ? v2 = 1.37
initial momentum before collision
Pi = m1*u1 + m2*u2
after collision final momentum
Pf = m1*v1 + m2*v2
from momentum conservation
total momentum is conserved
Pf = Pi
m1*u1 + m2*u2 = m1*v1 + m2*v2 .....(1)
from energy conservation
total kinetic energy before collision = total kinetic energy after collision
KEi = 0.5*m1*u1^2 + 0.5*m2*u2^2
KEf = 0.5*m1*v1^2 + 0.5*m2*v2^2
KEi = KEf
0.5*m1*u1^2 + 0.5*m2*u2^2 = 0.5*m1*v1^2 + 0.5*m2*v2^2 .....(2)
solving 1&2
we get
v1 = [ ((m1-m2)*u1) + (2*m2*u2) ] /(m1+m2)
v2 = ( ((m2-m1)*u2) + (2*m1*u1) ) /(m1+m2)
before collision
a)
v2 = ( ((m2-m1)*u2) + (2*m1*u1) ) /(m1+m2)
1.37 = ( ((871-121)*0) + (2*121*u1) ) /(121+871)
u1 = 5.62 m/s
after collision
v1 = ( ((121-871)*5.62) + (2*871*0) ) /(121+871)
v1 = -4.25 m/s
v1 = -20.45 cm/s
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