Question

3
(a)
before the spring was released during step 1, the marble
was at rest and had
a kinetic energy.
b elastic potential energy.
c gravitational potential energy.
(b) the types of energy in the system changed during step 1.
before the spring was released during step 1, the spring
was at rest and had
a chemical potential energy
b motion energy
c elastic potential energy
d gravitational potential energy

Explanation:

• Part (a):
• Kinetic energy is the energy of motion. Since the marble was at rest (\(v = 0\)), by the formula \(K=\frac{1}{2}mv^{2}\) (where \(m\) is mass and \(v\) is velocity), its kinetic energy \(K = 0\).
• Gravitational potential energy \(U = mgh\) (where \(m\) is mass, \(g\) is the acceleration due to gravity, and \(h\) is height). There is no information suggesting a height change relevant to the marble's energy in the context of the spring - marble system before spring release (assuming a horizontal spring - marble setup, which is a common problem setup unless stated otherwise).
• Elastic potential energy of a spring is given by \(U_s=\frac{1}{2}kx^{2}\) (where \(k\) is the spring constant and \(x\) is the displacement from the equilibrium position). When a spring is compressed or stretched (a common pre - release state for a spring - marble system to launch the marble), it stores elastic potential energy. The marble, as part of the system where the spring is deformed, has the system's elastic potential energy associated with it before release.
• Part (b):
• Chemical potential energy is related to chemical bonds (e.g., in batteries or fuel), which is not relevant to a spring.
• Motion energy is another term for kinetic energy. The spring was at rest (\(v = 0\)), so \(K=\frac{1}{2}Mv^{2}=0\) (where \(M\) is the mass of the spring, assuming \(M>0\), but \(v = 0\)).
• As mentioned above, for a spring, the relevant potential energy when it is deformed (compressed or stretched) is elastic potential energy \(U_s=\frac{1}{2}kx^{2}\).
• Gravitational potential energy for the spring \(U = Mgh\) (where \(M\) is spring mass, \(g\) is acceleration due to gravity, \(h\) is height). There is no indication of a height change relevant to energy transformation in the spring - marble launch context (assuming a horizontal setup) before spring release.

Answer:

(a) B. elastic potential energy
(b) C. Elastic Potential Energy