The spring of a spring gun has a force constant of 540 N/m andis compressed a di

Question

The spring of a spring gun has a force constant of 540 N/m andis compressed a distance of 32mm. The spring gun is then usedto fire a 30g projectile out of a window at an angle of30o above the horizontal. Neglecting drag force,find the speed of the projectile with which it will strike theground 4.3m below the window. I know that I must first calculate the magnitude of velocityof the projectile as it is fired using spring energy = KE ofthe projectile. Work done W=1/2kx2 The initial velocity is calculated with KE=1/2mv2 ,making v the subject of the formula. I do not understand how to calculate final velocity usingVox and Voy. The spring of a spring gun has a force constant of 540 N/m andis compressed a distance of 32mm. The spring gun is then usedto fire a 30g projectile out of a window at an angle of30o above the horizontal. Neglecting drag force,find the speed of the projectile with which it will strike theground 4.3m below the window. I know that I must first calculate the magnitude of velocityof the projectile as it is fired using spring energy = KE ofthe projectile. Work done W=1/2kx2 The initial velocity is calculated with KE=1/2mv2 ,making v the subject of the formula. I do not understand how to calculate final velocity usingVox and Voy. The initial velocity is calculated with KE=1/2mv2 ,making v the subject of the formula. I do not understand how to calculate final velocity usingVox and Voy.

Explanation / Answer

You are on the right track. Use the relationship energy before and energy after Pes + Pe = Ke Pes = 0.5kx2 Pe= mgh Ke= 0.5mV2 We have 0.5kx2 + mgh = 0.5mV2 Then V= [ (kx2 + 2mgh )/ m] where k= 540 N/m h = 4.3m g= 9.81 m/s2 x= 0.032 m m= 0.030 kg Just plug and play V= [ (540 (0.032)2 + 2 x 0.030 x 9.81 x4.3 )/ 0.030] V= 10.1 m/s

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