A ballistic pendulum (like (he one we studied in lab) can be used lo measure the

Question

A ballistic pendulum (like (he one we studied in lab) can be used lo measure the initial velocity of a projectile. One such pendulum has a 2.50 kg mass held by a massless length 55.0 cm. A 150 g projectile is tired from a launcher, and is caught by the pendulum which then deflects by 65degree. a What is the kinetic energy of the pendulum projectile immediately alter the impact? (This wilt require a bit of trigonometry.) b. What is the initial velocity of the projectile? c. What % of the kinetic energy is lost in the collision?

Explanation / Answer

Given:-

Mass of the pendulum,M=2.50 kg

Length of the pendulum,L=0.55

Mass of the projectile, m=0.150kg

Angle= 650

a] Applying conservation of Energy

Ke initial= Ke of projectile+Ke of pendulum= 1/2mvi2+ 0= 1/2*0.150kg*vo2=0.075vo2

Pe initial= 0

Te initial= Ke initial +Pe initial= 0.075vo2

Ke final= Combined Ke of projectile+pendulum= 1/2[ m+M]vf2= 1/2[2.50+0.150]vf2= 1.325vf2

Pe final = [ m+M]gh= [2.50+0.150]*9.8*0.55*[1-cos 650]=2.65*9.8*0.3176= 8.25J [ h=L(1-costheta) ]

Te final=Ke final+Pe final =1.325vf2 + 8.25J

Applying conservation of Energy

Te inital= Te final

0.075vo2=1.325vf2 + 8.25J

Ke final= [0.075vo2- 8.25]J------------------------Combined Ke of projectile/pendulum after the impact

b]

0.075vo2=1.325vf2 + 8.25J

vo2=17.67 vf2 +110

vo=[17.67 vf2 +110]1/2------------------------Initial velocity of the projectile

c]

Ke lost in the collision= Ke initial- Kefinal=0.075vo2- 1.325vf2= 8.25J

% of  Ke lost in the collision= 8.25/100= 0.0825 J

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