You have been hired to design a spring-launched roller coaster that will carry two passengers per car. The car goes up a 12-m-hi
gh hill, then descends 18 m to the track's lowest point. You've determined that the spring can be compressed a maximum of 2.3 m and that a loaded car will have a maximum mass of 430 kg . For safety reasons, the spring constant should be 13 % larger than the minimum needed for the car to just make it over the top.
a) what spring constant (k) should you specify ?b) What is the maximum speed of a 350 kg car if the spring iscompressed the full amount.
a) what spring constant (k) should you specify ?b) What is the maximum speed of a 350 kg car if the spring iscompressed the full amount.
1 answer:
Answer:
Vmax=11.53 m/s
Explanation:
from conservation of energy
Spring potential energy =potential energy due to elevation
0.5*k*x²= mg=mgh
0.5*k*2.3²= 430*9.81*6
k=9568.92 N/m
For safety reason
k"=1.13 *k= 1.13*9568.92
k"=10812.88 N/m
agsin from conservation of energy
spring potential energy=change in kinetic energy
0.5*k"*x²=0.5*m*
10812.88 *2.3²=430*
=11.53 m/s
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Let the launch velocity be V₀ at an angle of θ relative to the horizontal.
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Also, the time, t, when the missile is at ground level is given by
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Typically, θ=45° to achieve maximum range, so that
This analysis is more applicable to a scud missile rather than a powered, guided missile.
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