Answer to Question #83692 in Mechanics | Relativity for Ahuose Oko

Question

a horizontal spring whose constant a 600 Newtons per meter is compressed 0.29 meters and then released. The spring constant contacts a 0.300 kilogram ball at A transferring 100% of the Springs energy to the ball. what is the height of point B if the ball is traveling at 5.0 meters per second at that point. what is the velocity of the ball at Point C

Answer 1

According to law of conservation of energy (assume that Δx=0.29,Δl is distance from the point of the highest compression to the point A):

(kΔx^2)/2=(kΔl^2)/2+(mv^2)/2+mgh,

h=k(Δx^2-Δl^2 )/2mg-v^2/2g=7.3-102.04Δl^2.

Suppose that the point C is H metres high above the spring level and velocity to find is u:

(kΔx^2)/2=(kΔl^2)/2+(mu^2)/2+mgH,

u=√(k(Δx^2-Δl^2 )/m-2gH)=√(168.2-2000Δl^2-19.6H).

According to law of conservation of energy (assume that Δx=0.29,Δl is distance from the point of the highest compression to the point A):

(kΔx^2)/2=(kΔl^2)/2+(mv^2)/2+mgh,

h=k(Δx^2-Δl^2 )/2mg-v^2/2g=7.3-102.04Δl^2.

Suppose that the point C is H metres high above the spring level and velocity to find is u:

(kΔx^2)/2=(kΔl^2)/2+(mu^2)/2+mgH,

u=√(k(Δx^2-Δl^2 )/m-2gH)=√(168.2-2000Δl^2-19.6H).