VCE (Victoria) Physics — practice by topic

1. Rearranging F = -k x gives k = F / x, so k carries the units of force divided by the units of length. 2. Force is measured in newtons and displacement in meters, so k is measured in newtons per meter. 3. The units of k are newtons per meter (N/m). 4. Joules per meter would be an energy gradient and meters per newton is the reciprocal of a force constant, so neither fits. _Source: OpenStax College Physics (CC BY 4.0), Ch 16 "Oscillatory Motion and Waves", section 16.1 Hooke's Law: Stress and Strain Revisited_

1. While the car sits still, the restoring force from the springs equals the passenger's weight. 2. Weight w = m g = (90.0 kg)(9.80 m/s squared) = 882 N. 3. Convert the settling distance: 1.50 cm = 1.50 x 10^-2 m. 4. From k = F / x, k = 882 N / (1.50 x 10^-2 m) = 5.88 x 10^4 N/m. 5. Dividing 882 N by 1.50 without converting to meters gives 5.88 x 10^2 N/m, which is the trap in one option. 6. Multiplying weight by displacement instead of dividing gives 13.2 N m, an energy, not a force constant. _Source: OpenStax College Physics (CC BY 4.0), Ch 16 "Oscillatory Motion and Waves", section 16.1 Hooke's Law: Stress and Strain Revisited_

1. Elastic potential energy stored in a Hooke's law system is PE = (1/2) k x squared. 2. Convert the compression: 4.00 cm = 0.0400 m. 3. Square it: (0.0400 m) squared = 1.60 x 10^-3 m squared. 4. PE = (1/2)(250 N/m)(1.60 x 10^-3 m squared) = 0.200 J. 5. Forgetting to square the displacement gives 5.00 J, and dropping the factor of one half gives 0.400 J, so both shortcuts mislead. _Source: OpenStax College Physics (CC BY 4.0), Ch 16 "Oscillatory Motion and Waves", section Energy in Hooke's Law of Deformation_