in a nasa shuttle two identical springs make a v shape and

in a nasa shuttle , two identical springs make a v shape and hold a mass of 7.00kg. at the top, a horiontal distance of 70.0 cm sperates the springs. The unstreched length of each spring is 30.0 cm. A)when the shuttle isnt moving and is parked on earth , the angle between the top springs is 90 degrees. What extra Distance is the spring streched?

B) if the shuttle isnt moving, and the angle between the springs is 90 degrees, what is the spring constant?

C) during an early stage of takeoff from earth, the angle of the springs increases to 160 degrees. what is the acceleration ?

D) on the moon where gravity is 1.62 m/s ^2 how much does the mass of weigh ?

Solution

A) suppose new length of spring is L\' then

for right angle traingle,

L\'^2 + L\'^2 = 70^2

L\' = 49.5 cm

Stretch in spring deltaL = L\' - L = 49.5 - 30 = 19.5 cm = 0.195 m

B) Balancing forces in vertical,

kx cos45 + kx cos45 - mg = 0

2k(0.195)cos45 = 7 x 9.8

k = 248.76 N/m

C) angle of each spring with vertical = 160/2 = 80 deg

so L\'sin80 = (70/2) = 35 cm

L\' = 35.54 cm

deltaL = x = 35.54 - 30 = 5.54 cm = 0.0554 m

Using Fnet = ma on mass

mg - 2kxcos80 = ma

7 x 9.8 - (2 x 248.76 x 0.0554 x cos80) = 7a

a = 9.12 m/s^2

D) Weight = mg = 7 x 1.62 = 11.34 N