With the same block-spring system from above, imagine doubling the displacement of the block to start the motion. By what factor would the following change? A. Kinetic energy when passing through the equilibrium position.
B. Speed when passing through the equilibrium position.

A)     K / K₀ = 4   b)     v / v₀ = 4

Explanation:

A) For this exercise we can use the conservation of mechanical energy

in the problem it indicates that the displacement was doubled (x = 2xo)

starting point. At the position of maximum displacement

      Em₀ = Ke = ½ k (2x₀)²

final point. In the equilibrium position

      = K = ½ m v²

        Em₀ = Em_{f}

        ½ k 4 x₀² = K

        (½ K x₀²) = K₀

         K = 4 K₀

          K / K₀ = 4

B) the speed value

          ½ k 4 x₀² = ½ m v²

          v = 4 (k / m) x₀

if we call

           v₀ = k / m x₀

          v = 4 v₀

         v / v₀ = 4

(a )    

(b)   7507.57 m/s

Explanation:

Given information :

Potential difference=

Charge transferred = 31 C.

Mass to accelerated the car= 1100 kg

(a) The change in energy is determined by the following formula

where E= change in Energy

Q=Potential difference

V= Charge transferred

Putting the value of Potential difference and charge transferred in the given equation we get

(b) Kinetic energy can be determined by the given formula

Putting the value of m and k in the previous equation

v=7507.57 m/s