Answer :
Final answer:
The spring constant is given as 143 N/m. The total mechanical energy of the spring-mass system in a frictionless environment without any displacement or velocity specified would be the sum of kinetic and elastic potential energies. The exact value cannot be calculated without additional information on the mass's displacement or velocity.
Explanation:
The question pertains to a physics problem involving a mass-spring system on a frictionless surface. The student asks two questions: (a) Determine the spring constant and (b) Determine the total mechanical energy of the spring-mass system.
(a) Determining the Spring Constant
The spring constant, also known as the force constant, is given in the problem as 143 N/m. This value is a measure of the stiffness of the spring and is denoted by the symbol 'k'. Therefore, the spring constant is 143 N/m.
(b) Total Mechanical Energy of the Spring-Mass System
The total mechanical energy in a spring-mass system can be found by considering the energy stored in the spring when it is either compressed or stretched. For a spring on a frictionless surface, the total mechanical energy is purely elastic potential energy when the spring is at its maximum compression or extension, denoted as:
PEelastic = (1/2)kx2
Where k is the spring constant and x is the displacement from the equilibrium position. However, the total mechanical energy also includes kinetic energy when the mass is moving. Without friction or other external forces, the total mechanical energy is conserved and can be calculated at any point during the oscillation using the formula:
TE = (1/2)mv2 + (1/2)kx2
Since the question does not specify the displacement or velocity, the exact value of the total mechanical energy cannot be determined without additional information. If the mass is at rest at the maximum displacement, the total mechanical energy is equal to the elastic potential energy at that point.
