Exam 10: Elasticity and Oscillations

A force of 10.0 N is applied to a wire with an unstretched length of 4.00 m and a diameter of 5.00 mm. The wire changes length by 1.20 mm as a result of the applied force. What is the stress on the wire?

A 2.0 kg mass is connected to a spring with a spring constant of 9.0 N/m. The displacement is given by the expression x(t) = (12 cm) sin(ω t). What is the amplitude of the motion?

A 1.00 kg mass is connected to a spring with a spring constant of 9.00 N/m. If the initial velocity is 4.00 cm/s and the initial displacement is 0.00 cm, then what is the amplitude of the oscillations?

A vertical spring system with a bob having mass M is set into motion with amplitude A. When the bob is pulled instead to move with amplitude 2A, the following can be concluded:

In simple harmonic motion, the position of the oscillator

A nail with a diameter of 1.00 mm projects 25.0 mm horizontally outward from a wall. A 40.0 N picture is hung from the end of the nail. If the shear modulus is 3.40 × 10¹⁰ N/m², then how much does the nail deflect downward?

A 3.0 kg mass is connected to a spring with a spring constant of 6.0 N/m. The velocity is given by the expression v(t) = (10 cm/s) sin(ω t). What is the maximum velocity of the mass?

A 1.0 kg mass is connected to a spring with a spring constant of 9.0 N/m. If the initial velocity is 4.0 cm/s and the initial displacement is 2.0 cm, then what is the maximum elastic potential energy of the spring?

A force of 15.0 N is applied to a wire with an unstretched length of 4.00 m and a diameter of 5.00 mm. If the wire changed length by 1.20 mm, then the strain in the wire is

A physical pendulum is composed of a sphere whose center of gravity is attached to a thin rod of negligible mass. The sphere has a moment of inertia of 2/5 MR² about its center. The mass of the sphere is 2.00 kg, and it has a radius of 30.0 cm. The length of the rod is 50.0 cm. The period (for small-amplitude oscillations) of the physical pendulum is

A pendulum, which has a period of 0.52 s on Earth, is taken to the surface of a large asteroid. There it is measured to have a period of 1.7 s. What is the value of the gravitational acceleration on the surface of that asteroid?

A force of 500 N is applied to a rod with a diameter of 4.00 mm. The stress on the rod is

A cube is subjected to a pressure of 10.0 atmospheres. The original length of one side of the cube is 1.20 cm. The squeezed length of one side of the cube is 1.18 cm. The volume strain of the cube is

Consider a physical pendulum constructed by attaching a thin, massless rod to the center of a uniform disc of mass 1.00 kg and radius 40.0 cm. The disc has a moment of inertia of ½ MR² about an axis perpendicular to the plane of the disc, through its center. With the rod hung from one end (the pivot), the plane of the disc (attached to the other end) is vertical. If the rod has a length of 50.0 cm, then the period of (small amplitude) oscillations of the pendulum will be

In simple harmonic motion, the position of the oscillator

A steel ball with a diameter of 10 cm is subjected to a pressure that causes the volume of the ball to shrink by 0.01%. The bulk modulus for steel is 1.6 × 10¹¹ N/m². What is the pressure?

An aluminum ball is subjected to a pressure of 7.00 × 10⁶ Pa. The volume strain is −1.0 × 10⁻⁴. What is the bulk modulus?

A 2.00 m brass rod with a 1.00 mm diameter behaves like a spring under stretching or compression. If the elastic modulus of brass is 9.10 × 10¹⁰ N/m², then the spring constant of the rod is

A 2.00 kg mass is connected to a spring with a spring constant of 6.00 N/m. The displacement is given by the expression x(t) = (12.0 cm) sin(ω t). What is the maximum velocity of the mass?

A 2.00 kg mass is connected to a spring with a spring constant of 9.00 N/m. The velocity is given by the expression v(t) = (10.0 cm/s) sin(ω t). What is the maximum acceleration of the mass?