You use a spring loaded dart gun to launch a 25 g rubber dart upward at an angle

Question

You use a spring loaded dart gun to launch a 25 g rubber dart upward at an angle (not straight upward). The spring has a spring constant of 100 N/m and an uncompressed length of 15 cm. When the dart is loaded into the gun, the spring is 5 cm long. At the highest point in Its (tight, the dart moves at 5 m/s. Ignore friction and air resistance, and assume the initial height of 0 m. Insert a relevant sketch here: Full points will be awarded for the correct answer to the following question: What Is the height of the highest point In the flight? If the full credit cannot be awarded, then partial credit will be awarded for the correct answers to the following questions What Is the initial compression of the spring? What is the initial potential energy of the spring before the spring is released? What is the initial kinetic energy of the dart before the spring is released? What is the initial gravitational energy of the dart before the spring is released? What is the total energy of the system before the spring is released? What is the total energy of the system once the dart is at the highest point? What is the final potential energy of the spring when the dart is at the highest point? What is the final kinetic energy of the dart at the highest point? What is the final gravitational potential energy of the dart when it is at the highest point? What is the height of the dart at the highest point?

Explanation / Answer

i) initial compression = 15 -5 =10 cm   or 0.10 m

ii) Spring PEi = k x^2 /2 = 100 (0.10^2) /2 = 0.5 J

iii) KEi = 0

iv) Gravitational PEi = 0

v) total energy = 0.5 J

vi)From energy conservation , total energy wil not change.

hence final total energy = 0.5 J

vii) Spring potential Energy = 0

viii) KEf = 0

ix) total energy = spring PE + KE + gravt PE

0.5 = 0 + 0 + Pe

PE = 0.5 J

x) 0.5 = m g h

0.5 = (25 /1000 kg) (9.8) (h)

h = 2.04 m

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