homework 11 – ALGHAMDI, ALI – Due: Nov 13 2017, 11:00 pm (Central time) 1

Question 1, chap 113, sect 1.

part 1 of 1 10 points

Military specifications often call for elec- tronic devices to be able to withstand accel- erations of 10 g. To make sure that their products meet this specification, manufactur- ers test them using a shaking table that can vibrate a device at various specified frequen- cies and amplitudes. The acceleration of gravity is 9.81 m/s2. If a device is given a vibration of amplitude

9.9 cm, what should be its frequency in order to test for compliance with the 10 g military specification? Answer in units of Hz.

Question 2, chap 113, sect 2.

part 1 of 1 10 points

When a mass of 28 g is attached to a certain spring, it makes 18 complete vibrations in 3.6 s. What is the spring constant of the spring?

Answer in units of N/m.

Question 3, chap 113, sect 2.

part 1 of 2 10 points

Given: G = 6.67259 × 10−11 N m2/kg2

An object of mass 144 kg moves in a smooth straight tunnel dug through the center of a planet of mass 8.78×1024 kg and radius 2.21× 106 m as shown in the figure.

x

y

F

m

planet

r

Determine the effective force constant k of the harmonic motion; i.e., use Hook’s Law

F = −k x . Answer in units of N/m.

Question 4, chap 113, sect 2.

part 2 of 2 10 points

Find the maximum speed of the object. Answer in units of m/s.

Question 5, chap 113, sect 2.

part 1 of 1 10 points

An m = 4.8 kg lead ball is hanging from a k = 559 N/m spring. The ball is pulled 23 cm below the equilibrium position and released with zero initial velocity. What is the speed of the ball 2.09 s after it

was released? (Mind the units.) Answer in units of m/s.

Question 6, chap 113, sect 3.

part 1 of 1 10 points

A solid cylinder of mass M = 5.7 kg and radius R = 6.7 cm is yoked to a spring as shown in the figure below:

742.3 N/m 6.7 cm

5.7 kg

To be precise, the axle of the cylinder is at- tached to a horizontal spring of force constant k = 742.3 N/m. The cylinder rolls back-and- forth on a horizontal base without slipping. For simplicity, assume that the spring, the axle and the yoke which connects them have negligible masses compared to the cylinder itself. What is the angular frequency of the cylin-

der rolling back-and-forth around the equlib- rium position? Answer in units of rad/s.

Question 7, chap 113, sect 3.

part 1 of 1 10 points

A large block with mass 26 kg executes

homework 11 – ALGHAMDI, ALI – Due: Nov 13 2017, 11:00 pm (Central time) 2

horizontal simple harmonic motion as it slides across a frictionless surface with a frequency 2.17 Hz . Block smaller block with mass 8 kg rests on it, as shown in the figure, and the coefficient of static friction between the two is µs = 0.609 . The acceleration of gravity is 9.8 m/s2 .

k

26 kg

µs = 0.609

8 kg

What maximum amplitude of oscillation can the system have if the block is not to slip? Answer in units of cm.

Question 8, chap 113, sect 3.

part 1 of 1 10 points

A uniform plank of mass M = 7.9 kg and length L = 32 cm is pivoted at one end. A vertical spring of force constant k = 420 N/m is attached to the plank at a distance ℓ = 21 cm from the pivot end, as shown in the figure below:

32 cm 7.9 kg

21 cm θ

4 2 0 N / m

The height of the pivot has been adjusted so that the plank will be in equilibrium in the horizontal position θ = 0. Find the period of small oscillation of the

plank about the equilibrium point. Answer in units of s.

Question 9, chap 113, sect 4.

part 1 of 1 0 points

Given: Icm = 2

5 m r2 for a solid sphere.

A solid sphere has mass 5 kg , radius 4 cm . The sphere rolls without slipping in a spheri- cal bowl of radius 32 cm . The acceleration of gravity is 9.8 m/s2 .

32 cm

4 cm

Determine (for small displacements from equilibrium) the period of harmonic oscilla- tion which the sphere undergoes. Answer in units of s.

Question 10, chap 113, sect 5.

part 1 of 1 10 points

A visitor to a lighthouse wishes to deter- mine the height of the tower. The visitor ties a spool of thread to a small rock to make a simple pendulum, then hangs the pendulum down a spiral staircase in the center of the tower. The period of oscillation is 9.42 s. The acceleration of gravity is 9.81 m/s2 . What is the height of the tower?

Answer in units of m.

Question 11, chap 113, sect 6.

part 1 of 1 10 points

A uniform disk of radius 4.1 m and mass 3.7 kg is suspended from a pivot 1.189 m above its center of mass. The acceleration of gravity is 9.8 m/s2 .

axis

Find the angular frequency ω for small os- cillations. Answer in units of rad/s.

homework 11 – ALGHAMDI, ALI – Due: Nov 13 2017, 11:00 pm (Central time) 3

Question 12, chap 113, sect 99.

part 1 of 4 10 points

Consider a mass M = 4.9 kg hanging from a spring with force constant k = 6900 N/m. Let x denote the vertical coordinate of the mass; the mass is inequilibrium at x = 0; positive direction is up. At time t0 = 0 the mass is moved to x0 =

+5 cm and given initial speed v0 = −1.4 m/s. (Mind the units!) Subsequently, it oscillates according to

x(t) = A × sin(ωt + ϕ0).

What is the amplitude A of this oscillation? Answer in units of cm.

Question 13, chap 113, sect 99.

part 2 of 4 10 points

What is the initial phase ϕ0? Give an answer between −π and +π. Answer in units of rad.

Question 14, chap 113, sect 99.

part 3 of 4 10 points

What is the total energy of the oscillation? Answer in units of J.

Question 15, chap 113, sect 99.

part 4 of 4 0 points

When is the kinetic energy of the oscillator is equal to twice the potential energy — K = 2U — for the first time (after T0 = 0)? Answer in units of s.

Question 16, chap 112, sect 10.

part 1 of 1 10 points

A steel piano wire 1.47 m long has a cross- sectional area of 0.00459 cm2. The Young’s modulus for the wire is 2 × 1011 N/m2. When under a tension of 89.6 N , how much does it stretch? Answer in units of mm.

Question 17, chap 112, sect 10.

part 1 of 1 10 points

A solid metal sphere of volume 1.24 m3 is lowered to a depth in the ocean where the water pressure is equal to 1.3 × 107 N/m2. The bulk modulus of the metal from which the sphere is made is 9.69 × 109 N/m2. Given: The atmospheric pressure is

101300 Pa. What is the change in the volume of the

sphere? Answer in units of m3.

Question 18, chap 112, sect 11.

part 1 of 1 10 points

The distortion of the Earth’s crystal plates is an example of shear on a large scale. A particular crystal rock has a shear modulus of 1.8 × 1010 Pa. What shear stress is involved when a 9 km

layer of this rock is sheared through a distance of 4.6 m? Answer in units of Pa.

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