** PLEASE follow this 5 box format and CLEARLY state the situation and variables

Question

** PLEASE follow this 5 box format and CLEARLY state the situation and variables(draw diagram), what we are finding, the answer, the strategy to obtain the answer, and the steps for the calculation**
You are in charge of testing/designing a new amusement park ride. At the end of the ride, the 1200 kg cart (including people) goes down a hill that is angled at 30o from the horizontal. The starting height of the cart is 20 m above the ground, and it is going 5 m/s at the top of the hill. There is a constant force of friction of 30 N on the cart the entire ride. At the bottom of the hill, the cart travels 50 m before being stopped by a spring that is compressed by 2 m. What is the spring constant of the spring? Note: the 50 m traveled includes the 2 m of spring compression

Explanation / Answer

situation:
a cart of weight 1200 kg.
hill with angle 30 degree with horizontal.
starting height of the cart=20 m
starting velocity=5 m/s

friction force=30 N (constant force)

at the bottom , it travelled 50 m
spring compressed by 2 m

strategy:

as there is change from potential to kinetic to spring energy, the best method to implement is energy method.

calculation:

initial total energy=potential energy+kinetic energy=1200*9.8*20+0.5*1200*5^2=250200 J

total length travelled let be h.

then sin 30=20/h

h=20/sin(30)=40 m

so work done against friction=friction force*distance=30*(40+50)=2700 J

rest of the energy is converted to spring potential energy.

so if spring constant is k,

then 0.5*k*2^2=250200-2700

k=123750 N/m

answer:

spring constant=123750 N/m

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