Question

Problem 10.69 In a physics lab experiment, a compressed spring launches a 37 g metal ball at a 30 degree angle. Compressing the spring 17 cm causes the ball to hit the floor 1.8 m below the point at which it leaves the spring after traveling 6.0 m horizontally.

Part A What is the spring constant? Express your answer to two significant figures and include the appropriate units.

Answer 1

consider the motion of ball in horizontal direction after launch

x = horizontal distance = 6 m

V_ox = initial velocity = V_o Cos30

t = time of travel

x = V_ox t

6 = (V_o Cos30) t

t = 6 / (V_o Cos30)                 eq-1

consider the motion of ball in vertical direction after launch

V_oy = V_o Sin30

a = - 9.8

Y = vertical displacement = - 1.8

using the equation

Y = V_oy t + (0.5) a t²

- 1.8 = (V_o Sin30) (6 / (V_o Cos30)) + (0.5) (-9.8) (6 / (V_o Cos30))²

V_o = 6.7 m/s

using conservation of energy

spring energy = kinetic energy

(0.5) k x² = (0.5) m V_o²

k (0.17)² = (0.037) (6.7)²

k = 57.5 N/m