A spring with k=170 N/m is at the top of a frictionless incline that has an angl

Question

A spring with k=170 N/m is at the top of a frictionless incline that has an angle of 37°. The end of the spring is 1m from bottom of the incline when it is uncompressed. A 2.00kg canister is pushed against the spring until it is compressed 0.200m. (A) How much work was done to the canister at this point? (B) What is the speed of the canister when it leaves the spring at the equilibrium point? (C) If the surface now has a coefficient of friction of 0.35, what is the speed of the block when it reaches the bottom of the 1m ramp? (D) How much thermal energy is lost?

Explanation / Answer

A) work done=( k*x^2)/2=(170*0.2^2)/2=3.4J

B)when it leaves the equilibrium point the kinetic energy is equal to potential energy

(m*V^2)/2=(k*x^2)/2

V=(k*x^2)/m

V=(170*0.2^2)/2=3.4=1.844m/s

C) V=(0.35*170*1*1)/2=29.75=5.454m/s

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