1. In 0.810 s, a 6.95-kg block is pulled through a distance of 4.20 m on a frict
ID: 1864583 • Letter: 1
Question
1. In 0.810 s, a 6.95-kg block is pulled through a distance of 4.20 m on a frictionless horizontal surface, starting from rest. The block has a constant acceleration and is pulled by means of a horizontal spring that is attached to the block. The spring constant of the spring is 455 N/m. By how much does the spring stretch? _______ m
2. Recall that the spring constant is inversely proportional to the number of coils in the spring, or that shorter springs equate to stiffer springs. An object is attached to the lower end of a 14-coil spring that is hanging from the ceiling. The spring stretches by 0.164 m. The spring is then cut into two identical springs of 7 coils each. As the drawing shows, each spring is attached between the ceiling and the object. By how much does each spring stretch? _________ m
3. A block of mass m = 0.635 kg is fastened to an unstrained horizontal spring whose spring constant is k = 86.0 N/m. The block is given a displacement of +0.120 m, where the + sign indicates that the displacement is along the +x axis, and then released from rest.
(a) What is the force (magnitude and direction) that the spring exerts on the block just before the block is released? _______ N
(b) Find the angular frequency ? of the resulting oscillatory motion. ______ rad/s
(c) What is the maximum speed of the block? _______ m/s
(d) Determine the magnitude of the maximum acceleration of the block. _______ m/s^2
4. An object attached to a horizontal spring is oscillating back and forth along a frictionless surface. The maximum speed of the object is 1.26 m/s, and its maximum acceleration is 6.90 m/s2. How much time elapses between an instant when the object's speed is at a maximum and the next instant when its acceleration is at a maximum? ________ s
5. A heavy-duty stapling gun uses a 0.120 kg metal rod that rams against the staple to eject it. The rod is attached and pushed by a stiff spring called a "ram spring" (k = 33986 N/m). The mass of this spring may be ignored. Squeezing the handle of the gun first compresses. The ram spring is compressed by 3.40 10-2 m from its unstrained length and then releases from rest. Assuming that the ram spring is oriented vertically and is still compressed by 9.90 10-3 m when the downward-moving ram hits the staple, find the speed of the ram at the instant of contact. ________ m/s
6. A simple pendulum is made from a 0.69-m-long string and a small ball attached to its free end. The ball is pulled to one side through a small angle and then released from rest. After the ball is released, how much time elapses before it attains its greatest speed? ______ s
7. Two physical pendulums (not simple pendulums) are made from meter sticks that are suspended from the ceiling at one end. The sticks are uniform and are identical in all respects, except that one is made of wood (mass = 0.15 kg) and the other of metal (mass = 0.80 kg). They are set into oscillation and execute simple harmonic motion. Determine the period of (a) the wood pendulum and (b) the metal pendulum.
(a) T =
(b) T =
8. Tsunamis are fast-moving waves generated by underwater earthquakes. In the deep ocean their amplitude is barely noticeable, but upon reaching shore, they can rise up to the astonishing height of a six-story building. One tsunami, generated off the Aleutian islands in Alaska, had a wavelength of 800 km and traveled a distance of 3700 km in 5.6 h.
(a) What was the speed (in m/s) of the wave? For reference, the speed of a 747 jetliner is about 250 m/s _______ m/s
(b) Find the wave's frequency. ______ Hz
(c) Find the wave's period. _______ s
9. The middle C string on a piano is under a tension of 688 N. The period and wavelength of a wave on this string are 3.82 10-3 s and 1.26 m, respectively. Find the linear density of the string. ______ kg/m
10. A wire is stretched between two posts. Another wire is stretched between two posts that are two times as far apart. The tension in the wires is the same, and they have the same mass. A transverse wave travels on the shorter wire with a speed of 180 m/s. What would be the speed of the wave on the longer wire? ________ m/s
Explanation / Answer
1)since the block starts from rest the acceleration is
a=2S/t^2
=12.80
The force needed to create such acceleration is
F=ma=6.95*12.80=88.98
This force stretches the string by
x=F/k
=88.98/455=0.195m
2)since spring constant is inversely propotional to the no of turns in the spring thus
mg=-kx/14
now the spring is cut into two halves
mg=-2ky/7
equating the two equations we get
y=x/4
=0.16/4=0.4m
3)
a) F=-k x
=-86*0.120=54.61
b)frequency=sqrt(k/m)
=sqrt(135.4)=11.63
c)v = sqrt[kx^2/m]
=sqrt(86*0.120^2/0.635)
=sqrt(1.95)=1.39
d)max acc= max force/mass=88.98/0.635=140.1N
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