Exam 10: Simple Harmonic Motion and Elasticity

A pendulum is transported from sea-level, where the acceleration due to gravity g is 9.80 m/s², to the bottom of Death Valley. At this location, the period of the pendulum is decreased by 3.00%. What is the value of g in Death Valley?

The position of a simple harmonic oscillator is given by where t is in seconds. What is the maximum velocity of this oscillator?

When a 0.20-kg block is suspended from a vertically hanging spring, it stretches the spring from its original length of 0.040 m to 0.045 m. The same block is attached to the same spring and placed on a horizontal, frictionless surface as shown. The block is then pulled so that the spring stretches to a total length of 0.15 m. The block is released at time t = 0 s and undergoes simple harmonic motion. -Complete the following statement: In order to increase the frequency of the motion, one would have to

The radius of a sphere of lead (B = 4.2 × 10¹⁰ N/m²) is 1.000 m on the surface of the earth where the pressure is 1.01 × 10⁵ N/m². The sphere is taken by submarine to the deepest part of the ocean to a depth of 1.10 × 10⁴ m where it is exposed to a pressure is 1.25 × 10⁸ N/m². What is the volume of the sphere at the bottom of the ocean?

A 0.750-kg object hanging from a vertical spring is observed to oscillate with a period of 1.50 s. When the 0.750-kg object is removed and replaced by a 1.50-kg object, what will be the period of oscillation?

A block is suspended from the ceiling by a long, thin strip of tungsten metal. The strip behaves as a spring. To produce a 0.25 m horizontal deflection of the block, a force of 6.5 N is required. Calculate the spring constant for the tungsten strip.

When a 0.20-kg block is suspended from a vertically hanging spring, it stretches the spring from its original length of 0.040 m to 0.045 m. The same block is attached to the same spring and placed on a horizontal, frictionless surface as shown. The block is then pulled so that the spring stretches to a total length of 0.15 m. The block is released at time t = 0 s and undergoes simple harmonic motion. -What is the frequency of the motion?

Which one of the following statements concerning Hooke's law is false?

A relaxed spring protrudes from an opening 0.0500 meters as shown in Figure A. A 1.00-kg block is found to just force the spring completely into the opening as shown in Figure B. -Determine the spring constant k.

The brick shown in the drawing is glued to the floor. A 3500-N force is applied to the top surface of the brick as shown. If the brick has a shear modulus of 5.4 × 109 N/m², how far to the right does the top face move relative to the stationary bottom face?

The maximum compressional stress that a bone can withstand is 1.6 × 10⁸ N/m² before it breaks. A thighbone (femur), which is the largest and longest bone in the human body, has a cross sectional area of 7.7 × 10^-4 m². What is the maximum compressional force that can be applied to the thighbone?

When a 0.20-kg block is suspended from a vertically hanging spring, it stretches the spring from its original length of 0.040 m to 0.045 m. The same block is attached to the same spring and placed on a horizontal, frictionless surface as shown. The block is then pulled so that the spring stretches to a total length of 0.15 m. The block is released at time t = 0 s and undergoes simple harmonic motion. -What is the speed of the block each time the spring is 5.0 cm long?

A cable stretches by an amount d as it supports a crate of mass M. The cable is cut in half. What is the mass of the load that can be supported by either half of the cable if the cable stretches by an amount d?

When a 0.20-kg block is suspended from a vertically hanging spring, it stretches the spring from its original length of 0.040 m to 0.045 m. The same block is attached to the same spring and placed on a horizontal, frictionless surface as shown. The block is then pulled so that the spring stretches to a total length of 0.15 m. The block is released at time t = 0 s and undergoes simple harmonic motion. -What is the total mechanical energy of the system at any instant?

A cable stretches by an amount d when it supports a crate of mass M. The cable is then cut into three equal pieces. If the same crate is supported by any one of these pieces, by how much will the cable stretch?

A thin, circular hoop with a radius of 0.32 m is hanging on a nail. Adam notices that the hoop is oscillating back and forth through small angles like a physical pendulum. The moment of inertia of the hoop for the rotational axis passing through the nail is I = 2mr². What is the period of the hoop?

The position of a simple harmonic oscillator is given by where t is in seconds. What is the period of the oscillator?

A certain spring compressed 0.20 m has 10 J of elastic potential energy. The spring is then cut into two halves and one of the halves is compressed by 0.20 m. How much potential energy is stored in the compressed half of the spring?

When a 0.20-kg block is suspended from a vertically hanging spring, it stretches the spring from its original length of 0.040 m to 0.045 m. The same block is attached to the same spring and placed on a horizontal, frictionless surface as shown. The block is then pulled so that the spring stretches to a total length of 0.15 m. The block is released at time t = 0 s and undergoes simple harmonic motion. -Which one of the following expressions gives the displacement of the block as a function of time? Let x be in cm and t in seconds.

What are the SI units of the shear modulus?