To determine the final velocity of the mass when the spring is compressed by 5 cm, we can apply the principle of conservation of mechanical energy. Initially, the mass has kinetic energy due to its initial velocity, and when the spring is compressed, the energy is stored in the potential energy of the spring.
First, let's calculate the initial kinetic energy (K1) of the mass: K1 = (1/2) * m * V0^2
Given: m = 0.05 kg (mass) V0 = 5 m/s (initial velocity)
K1 = (1/2) * 0.05 kg * (5 m/s)^2 K1 = 0.625 J
Now, let's calculate the potential energy (U) stored in the spring when it is compressed by 5 cm: U = (1/2) * k * x^2
Given: k = 10 N/m (spring constant) x = 0.05 m (5 cm converted to meters)
U = (1/2) * 10 N/m * (0.05 m)^2 U = 0.0125 J
Since energy is conserved, the final kinetic energy (K2) of the mass will be equal to the potential energy stored in the spring: K2 = U = 0.0125 J
Now, we can calculate the final velocity (Vf) of the mass using the final kinetic energy: K2 = (1/2) * m * Vf^2
0.0125 J = (1/2) * 0.05 kg * Vf^2 Vf^2 = (0.0125 J * 2) / 0.05 kg Vf^2 = 0.5 J / 0.05 kg Vf^2 = 10 m^2/s^2
Taking the square root of both sides to find Vf: Vf = √(10 m^2/s^2) Vf ≈ 3.16 m/s
Therefore, when the spring is compressed by 5 cm, the mass's velocity will be approximately 3.16 m/s.