A ball with a mass of #6 kg# moving at #4 m/s# hits a still ball with a mass of #7 kg#. If the first ball stops moving, how fast is the second ball moving?

Question

A ball with a mass of #6 kg# moving at #4 m/s# hits a still ball with a mass of #7 kg#.  If the first ball stops moving, how fast is the second ball moving?

Isabella Alvarez · Accepted Answer

#v_2^'=3.43" "m/s" rounded the two decimal place"# #"Momentum before collision"# #".........................................."# #m_1=6 " "kg" " "'mass of the first object'"# #v_1=4 " "m/s" ""'velocity of the first object'"# #vec P_1=m_1*v_1=6*4=24" " kg*m/s" Momentum of the first object"# #m_2=7" "kg" 'mass of the second object'"# #v_2=0" velocity of the second object"# #vec P_2=m_2*v_2=7*0=0" Momentum of the second object"# #Sigma vec P_b=vec P_1+vec P_2" vectorial sum of the momentums before collision"# #Sigma vec P_b=24+0=24 " "kg*m/s# #"Momentum after collision"# #"........................................."# #m_1=6" "kg# #v_1^'=0" the first ball is stopping"# #vec P_1^'=m_1*v_1^'=6*0=0" Momentum of the first object"# #m_2=7 " "kg# #v_2^'=?" velocity of the second ball"# #vec P_2^'=m_2*v_2^'=7v_2^'# #"The conservation of momentum"# #"..................................................."# #Sigma vec P_b=Sigma vec P_a# #24=0+7v_2^'# #v_2^'=24/7# #v_2^'=3.43" "m/s" rounded the two decimal place"#

Parker Abbott · Answer

undefined Using the principle of conservation of momentum, the total momentum before the collision is equal to the total momentum after the collision.

Total momentum before collision: m1 * v1 + m2 * v2, where m1 is the mass of the first ball (6 kg), v1 is the initial velocity of the first ball (4 m/s), m2 is the mass of the second ball (7 kg), and v2 is the initial velocity of the second ball (0 m/s since it is still).

Total momentum after collision: (m1 + m2) * v_final, where v_final is the final velocity of both balls after the collision.

Since the first ball stops moving (v1 = 0 m/s), the total momentum before and after the collision is:

Total momentum before collision: 6 kg * 4 m/s + 7 kg * 0 m/s = 24 kg·m/s

Total momentum after collision: (6 kg + 7 kg) * v_final = 13 kg * v_final

Setting the two equal:

24 kg·m/s = 13 kg * v_final

Solve for v_final:

v_final = 24 kg·m/s / 13 kg ≈ 1.85 m/s

So, the second ball is moving at approximately 1.85 m/s after the collision.