Hooke's Law - Section 12A

**1. **The largest
meteorite of lunar origin reportedly has a mass of 19 g. If the meteorite placed on a scale whose spring constant is 83 N/m, what is
the compression of the spring?

**2. **In 1952, a great
rainfall hit the island of Reunion in the Indian Ocean. In less than 24 h, 187 kg of rain fell on each square meter of soil. If a
187 kg mass is placed on a scale that has a spring constant of 1.53 x 10^{4} N/m, how far is the spring compressed?

**3. **The largest tigers,
and therefore the largest members of the cat family, are the Siberian tigers. Male Siberian tigers are reported to have an
average mass of about 389 kg. By contrast, a variety of very small cat that is
native to India has an average adult mass of only 1.5 kg. Suppose this small cat is placed on a spring scale, causing the spring to be extended from
its equilibrium position by 1.2 mm. How far would the spring be extended if a typical male Siberian tiger were placed on the same scale?

**4. **The largest known
crab is a giant spider crab that had a mass of 18.6 kg. The distance from the end of one of this crab’s claws to the end of the other claw measured about 3.7 m. If this particular giant spider crab were hung from an elastic band so that the elongation of the band was equal to the crab’s claw span, what would be the spring constant of the elastic band?

**5. **The CN Tower in
Toronto, Canada, is 533 m tall, making it the world’s tallest free-standing structure. Suppose an unusually long bungee cord
is attached to the top of the CN Tower. The equilibrium length of the cord is equal to one-third the height of the tower. When a test mass of 70.0
kg is attached, the cord stretches to a length that equals two-thirds of
the tower’s height. From this information, determine the spring constant of the bungee cord.

**6. **The largest ruby in
the world may be found in New York. This ruby is 109 mm long, 91 mm wide, and 58 mm thick, making its volume about 575 cm^{3} . (By comparison, the world’s largest
diamond, the Star of Africa, has a volume of just over 30 cm 3 .

a. If the ruby is attached to a vertically hanging spring with a
spring constant of 2.00 x 10^{2} N/m so that the spring is stretched
15.8 cm what is the gravitational force pulling the spring?

b. What is the mass of the jewel?

**7. **Mauna Kea on the
island of Hawaii stands 4200 m above sea level. How-ever, when measured from the island’s sea-submerged base, Mauna Kea has a height of 10 200 m, making it the tallest single mountain in the world. If you have a 4.20
x 10^{3} m elastic cord with a spring constant
of 3.20 x 10^{-2} N/m, what force would stretch
the spring to 1.02 x 10^{4} m?

**8. **Rising 348 m above
the ground, La Gran Piedra in Cuba is the tallest rock on Earth. Suppose an elastic band 2.00
x 10^{2} m long hangs vertically off the top of La Gran Piedra. If the band’s spring constant is 25.0
N/m, how large must a mass be if, when it is attached to the band, it causes
the band to stretch all the way to the ground?