Exam 13: Elasticity and Vibrations

Which of these types of units is used when measuring hydraulic stress?

The meaning of a large Young's modulus is that a small force can produce large deformation of a material.

A simple harmonic system maintains constant frequency, whereas a dumped system's frequency decreases.

A simple harmonic system and a particle moving in uniform circular motion have the same period. The angular frequency of the oscillating system is the same as the angular velocity of the rotational system.

Stress, twisting, and hydraulic stress, all three apply only to solids and liquids.

If the amplitude of a simple harmonic oscillator is tripled, which of these quantities does NOT change?

The period of harmonic motion is independent of amplitude.

The bulk modulus is a unitless coefficient.

An object with a mass of 1.2 kg is pushed down on a vertical spring, compressing it 20 cm. When we release the spring, the object will fly up to a height of 2 m. What is the spring constant?

Calculate the period of oscillation of a hydrogen atom in a water molecule (H₂O). The mass of a hydrogen atom is m = 1.67 × 10^-27 kg. The spring constant for the H-O bond is k = 780 N/m.

Which of the following quantities does tensile stress correspond to?

Figure 13.3 The figure shows a relaxed spring and a body sliding down an incline. -See Fig. 13.3. A crate of a mass 0.5 kg slides down a 30° incline and compresses a spring having a spring constant k = 150 N/m by 20 cm, coming to a stop. What is the length of the sliding path of the crate along the incline?

For an object oscillating while attached to a horizontal spring, at what fraction of maximal velocity is it moving when it passes exactly half way from the equilibrium toward maximum extension?

At what point can we say that the response of an object to stretching is elastic?

Figure 13.2 Stress-strain relation for compact bone. The graph includes both tensile stress (the bone is stretched) and compressive stress (the bone is compressed). -Fig. 13.2 shows the stress-strain curve for compact bone. In addition to the coordinate system origin (0,0), the graph includes four points, (i) to (iv), along the curve. Describe the response of the compact bone in each interval, that is, whether it is elastic or not fully elastic.

Which of these statements applies to a material with a large bulk modulus?

A 30 kg block is at rest while attached to a spring with a spring constant of k = 1500 N/m. A 4 g bullet hits the block and remains in the block. As a result of the collision, the block compresses the spring by 1.8 cm. What was the speed of the bullet?

A horse with a mass of 520 kg has a front leg cannon bone that is 38 cm long. The bone has a circumference of 23 cm. The two front legs support 65% of the horse's weight. If the Young's modulus of a bone is 1.5 × 10¹⁰ Pa, what is the compression of the bone due to the horse's weight?

An object of mass 20 g is attached to a horizontal spring with a spring constant of 150 N/m. What is the speed of the object at 1/3 the amplitude? The spring was initially stretched by 4 cm.

Resonance occurs in a system with no damping when the frequency of the driving force is the same as the natural frequency of the system