Question

A spring with a constant k=400n/m shoots a 1.00kg ball up a frictionless incline after being compressed 0.150m. What is the maximum height reached by the ball?

Answer 1

the maximum height reached by ball is 0.45m.

how to calculate the maximum height ?

Given :-

spring constant ( k ) = 400N/m

mass of ball = 1kg

spring compressed ( x )= 0.150m

we calculate height by using mechanical energy conservation According to the principle of conservation of mechanical energy, The total mechanical energy of a system is conserved .

Mechanical energy is the sum of the potential and kinetic energies in a system :-

K₀ + U₀ = K + U    (eq 1)                    

where,

           K₀ = initial kinetic energy = 0

           U₀ = initial potential energy = $\frac{1}{2} kx^{2}$

           K = final kinetic energy when it reaches at its max height =0

           U = final potential energy when it reaches at its max height =mgh

The elastic potential energy is = $\frac{1}{2} kx^{2}$

                                                     =  0.5 × 400 × 0.15 × 0.15

                                                     = 4.5 J.  

putting value in eq 1 :-

                                    0 + 4.5 = 0 + mgh

                                     4.5 = 10h

                                      h=0.45m

Thus from the above conclusion we can say that the maximum height reached by the ball is 0.45m.

Learn more about the energy conservation here : https://brainly.com/question/20626677

#SPJ4