Exam 10: Elasticity and Oscillations

Diatomic molecules such as H₂ and O₂ undergo simple harmonic motion with frequencies that obey Hooke's Law with the effective mass being half the atomic mass.If the mass of a hydrogen atom is 1.67 $\times$ 10^-27 kg and the observed frequency of oscillation is 125 $\times$ 10¹² Hz,what is the effective spring constant associated with the bond between the hydrogen atoms?

A nail projects 25.0 mm horizontally outward from a wall.A 400 N picture is hung from the end of the nail and the nail deflects downward by 2.00 $\times$ 10^-5 m.If the shear modulus is 3.40 $\times$ 10¹⁰ N/m²,then what is the diameter of the nail?

A 120.0 N picture hangs from a nail in the wall.The maximum shear stress the nail can sustain is 1.000 $\times$ 10⁶ N/m².The smallest diameter the nail can be is

A force of 100 N is applied to a rod with a diameter of 6.00 mm.The stress in the rod is

A pendulum is made with a 4.00 kg mass suspended at the end of a 75.0 cm thin rod.The pendulum is started at an angle of 20.0 degrees with the vertical.What is the velocity of the pendulum as it passes through the origin?

A 10.0 kg mass is attached to the end of a 2.00 m brass rod with a 1.00 mm diameter.If the tensile modulus of brass is 9.10 $\times$ 10¹⁰ N/m²,then the period of the simple harmonic motion of the mass is

A rod with a diameter of 2.00 mm,projects 20.0 mm horizontally outward from a wall.A 10.0 N weight is hung from the end of the rod and the rod deflects downward by 4.00 $\times$ 10^-6 m.The shear strain of the rod is

A cube is subjected to a pressure of 12 atmospheres.The un-squeezed length of one side of the cube is 10.000 cm.The squeezed length of one side of the cube is 9.999 cm.The bulk strain on the cube is

A 1.0 kg mass is connected to a spring with a spring constant of 9.00 N/m.If the initial velocity is 4.0 cm/s and the initial displacement is 2.0 cm,then what is the maximum spring potential energy of the simple harmonic motion?

Diatomic molecules such as H₂ and O₂ undergo simple harmonic motion with frequencies that obey Hooke's Law with the effective mass being half the atomic mass.If the mass of a hydrogen atom is 1.627 $\times$ 10^-27 kg and that of fluorine is 3.17 $\times$ 10^-26 kg,what is the ratio of oscillation frequencies of H₂ to that of F₂,assuming that the bond strength between the atoms of hydrogen is the same as that between fluorine atoms?

A nail projects 40.0 mm horizontally outward from a wall.A 25.0 N coat is hung from the end of the nail and the nail deflects downward by 2.50 $\times$ 10^-6 m.The shear strain of the nail is

A 2.00 kg mass is connected to a spring with a spring constant of 900 N/m.The displacement is given by the expression x(t) = 12.0 cm sin( $\omega$ t).What is the frequency of the simple harmonic motion?

A physical pendulum is composed of a disc whose center of gravity is attached to a thin rod.The disc has a moment of inertia of 1/2 MR².The mass of the disc is 500 gm and has a radius of 4.00 cm.The length of the rod is 50.0 cm.The period of the physical pendulum is

A pendulum is made with a 4.00 kg mass suspended at the end of a thin rod.The period of the small motion simple harmonic motion is 1.00 sec.What is the length of the thin rod?

An astronaut measures her mass by means of a device consisting of a chair attached to a large spring.The period of oscillation she undergoes when set into motion is used to determine her mass.If her mass together with the chair is 172 kg and the time required for her to undergo 10 full oscillations is 27 seconds,what is the spring constant?

A wire has a strain of 0.10%.If the wire has an un-stretched length of 5.00 m,then the change in length of the wire is

A block is placed in oscillation on a frictionless horizontal surface attached to a spring that is also attached to a wall.If,when stretched away from equilibrium by 15 cm and released,it oscillates with a period of 0.25s,and if the mass of the block is 15 kg,what force was required to stretch the spring by the initial 15 cm?

A mass is suspended vertically from a spring so it is at rest at the equilibrium position.The mass is pulled straight down to an extension x and released so that it oscillates about the equilibrium position.The acceleration is greatest in magnitude and directed upward when the mass is

A wire is 1.50 m long and has a diameter of 1.50 mm.The tensile modulus of the wire is 6.20 $\times$ 10¹⁰ N/m².If a force of 400 N is applied to end of the wire,then the increase in length of the wire is

A spring-powered launcher has a spring with a spring constant of 50.0 N/cm.The launcher is prepared to launch a projectile by compressing the spring by 5.00 cm.If the mass of the projectile is 10.0 grams,then what is the velocity of the projectile when it is launched from the launcher?