Question

A toy dart gun contains a spring with a spring constant of 250 N/m. A 0.059 kg dart is pressed 0.05 m into the gun. a) If the gun is aimed directly upward, how high into the air will the dart travel when shot (measured from the compressed position in the gun)? b) What is the maximum velocity of the dart? c) If the dart got stuck to the spring: i) with what angular frequency will the dart oscillate (neglect friction)? ii) with what frequency will the dart oscillate (neglect friction)? iii) what will be the period of this oscillation?

Answer 1

Griven, K = 250 Nm m = 0.059 lg compression (x) = 0.05m. @ To find: H Use Energy conservation between initial and final! position: At maim height Bit P.Ei & Eft P. Ef [ Nf 2o, ki Efre k x2 = mgH k x2 H = 250 N/m x 6.05² m² 2 xo.059 kg x 9.81m² ang [TH= 0.54m | Ang To & Dart use find : man will have maxim velocity Just after release. ku2 = xmv² losorloor? kaz m 0.059 v 250 3.600s)? [v = 3.25 m/s Jane © Time period (m) = *2 * 59 T= 0.096 Ang frauency (5) t ons 10-442] Ang frequency (wa) = 2X f = 165.09 H2 ) and Time perio 0.059 leg 250N/m AL -