Final answer:
To find the maximum speed of a pinball released by a spring, equate the spring's potential energy at maximum compression to the pinball's kinetic energy at maximum speed and solve for the speed variable.
Step-by-step explanation:
To calculate the maximum speed at which a pinball of mass 40g can be released by the spring in a pinball machine with a spring constant of 60N/m and a compression distance of 10cm, we can use the principle of conservation of energy. The potential energy stored in the spring when compressed is equal to the kinetic energy of the pinball at its maximum speed.
Spring potential energy (PE_spring) is calculated using the formula PE_spring = (1/2)kx², where k is the spring constant and x is the displacement from equilibrium (compression distance). Using the given values, PE_spring = (1/2)(60 N/m)(0.1 m)².
Kinetic energy (KE) of the pinball is given by KE = (1/2)mv², where m is the mass of the pinball and v is the maximum speed.
Setting the potential energy equal to the kinetic energy and solving for v, we find the maximum speed v of the pinball when it is released by the spring. The mass of the pinball needs to be in kilograms, so we convert 40g to 0.040 kg.