Question # 1 A 55.0 kg skateboarder wants to just make it to the upper edge of a
ID: 1601943 • Letter: Q
Question
Question # 1
A 55.0 kg skateboarder wants to just make it to the upper edge of a "quarter pipe," a track that is one-quarter of a circle with a radius of 2.50 m .
What speed does he need at the bottom?
Question # 2
A 56 kg student is standing atop a spring in an elevator that is accelerating upward at 3.4 m/s2 . The spring constant is 3000 N/m
By how much is the spring compressed?
Question # 3
A 11 kg runaway grocery cart runs into a spring with spring constant 240 N/m and compresses it by 56 cm .
What was the speed of the cart just before it hit the spring?
Explanation / Answer
Q1)
total energy at the bottom Ei = (1/2)*m*v^2
total energy at the top Ef = m*g*R
from enrgy conservation
Ef = Ei
m*g*R = (1/2)*m*v^2
v = sqrt(2*g*R)
v = sqrt(2*9.8*2.5) = 7 m/s <<<--------asnwer
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Q2)
Fnet = m*a
kx - mg = m*a
3000*x - (56*9.8) = 56*3.4
x = 0.25 m/s^2 <<<-----answer
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Q3)
kinetic energy before hitting = elastic potential ensergy of spring
(1/2)*m*V^2 = (1/2)*k*x^2
v = x*sqrt(k/m)
v = 0.56*sqrt(240/11)
v = 2.62 m/s <<<<---------answer