Name: /20 marks Module 7: Proficient Level (2 marks) 2) A vertical spring is stretched 60.0 cm by a hanging 5.00 kg mass. a) What is the spring constant? Given ; X = 6010 cm At equilibrium ing = k x K = $1. 75, N / m f= ( 5.00 kg ) ( 9. 81 m / s 2 ) X= 60emm k = mig K= 818. N / m Required : The spring ( m] = 5 KS x constant (10)J KC5 kgx9. 81 m /5 2 ( m ) The spring constant is 81.8 N/ m 60 x 102 b) What will be the frequency of vibration of this spring system? Given: m= 5.60 kq f= 2rev K f= 25 7/ 81.75 N/m /= 1.55s 5. 00 kg 12 = 81.75 N/ m - 1.55 = 6.644 Hz Required: frequency of vibration (f ) The frequency of vibration for this spring system is 0.64 4HZ. * Module 7: Exemplary Level (2 marks) 3) An astronaut on the surface of a 6.50 X 1029 kg planet determines that an 80 cm pendulum requires 162 s to swing 50 cycles. What is the radius of the planet? Given : Mass of T= 2 ST VR T = 257/ R3 planet ( m ) = 6.50 * 10 Kq GM ( C . 6 2 0 1x 16 , 5 x 10 1 x 15 2 1 ) Length of pendulum : 9= GM RS = GMT 2 800 m R 2 4 s+ 2 R: 2 28 x 10 m Required: Radius of planet (r ) R = GMT 2 13 T = ? T= 1625 50 S 1 = / / 6.67 x 10-" NIM kqz ) ( 6.5 x 10 29 keg ) ( 3. 24 ) 2 3 T = 3.245 4 71 2 R = ( 11. 5284 x10 18) 3 m 12 = 2, 24 x 10 'm The radius of the planet is 2.24 x10'm