Answer: 4.87 m/s
Explanation:
According to the law of conservation of energy, the total amount of energy in a system cannot be created nor destroyed. This means that the box's total elastic potential energy (U) is equivalent to its total kinetic energy (K).
Therefore, U = K.
The formula for elastic potential energy is given as:
U = [tex]\frac{1}{2}kx^{2}[/tex], where:
- k is the spring constant (N/m)
- x is the change in position or how much the spring is stretched (m)
Let's calculate the elastic potential energy when k = 145 and x = 0.06 (6 cm = 0.06 m):
U = [tex]\frac{1}{2}kx^{2}[/tex]
U = [tex]\frac{1}{2}(145)(0.06)^{2}[/tex]
U = 0.261J
Since U = K, 0.261 = K.
The formula for kinetic energy is given as:
K = [tex]\frac{1}{2}mv^{2}[/tex], where:
- m is the mass of the object (kg)
- v is the velocity of the object (m/s)
We can replace this formula for K in our equation 0.261 = K:
0.261 = [tex]\frac{1}{2}mv^{2}[/tex]
Since m is 0.022 kg (22 g = 0.22 kg):
0.261 = [tex]\frac{1}{2}(0.022)v^{2}[/tex]
Solving for v:
[tex]\frac{2(0.261)}{0.022}[/tex] = v²
v = [tex]\sqrt {\frac{2(0.261)}{0.022}}[/tex]
v = 4.87
The velocity of the box is 4.87 m/s when the box's entire elastic potential energy is converted to its entire kinetic energy.
Learn more about the law of conservation of energy here: https://brainly.com/question/41690512
