After being struck by a bowling ball, a 1.4kg bowling pin sliding to the right at 4.5 m/s collides head-on with another 1.4 kg bowling pin initially at rest. Find the final velocity of the second pin in the following situations: a)The first pin moves to the right after the collision at 0.7 m/s.
To find the final velocity of the second pin, we can use the principle of conservation of linear momentum. According to this principle, the total momentum before the collision should be equal to the total momentum after the collision.
The momentum of an object is defined as the product of its mass and velocity. Mathematically, momentum (p) is given by:
p = m * v
Where:
p = momentum
m = mass
v = velocity
Let's calculate the initial momentum (P_initial) and the final momentum (P_final) of the system.
For the first pin:
Initial momentum (P_initial1) = mass1 * velocity1 = 1.4 kg * 4.5 m/s
For the second pin:
Initial momentum (P_initial2) = mass2 * velocity2 = 1.4 kg * 0 m/s (since it's at rest)
After the collision, the first pin moves to the right at 0.7 m/s. So we have:
Final momentum (P_final1) = mass1 * velocity1_after_collision = 1.4 kg * 0.7 m/s
For the second pin, let's assume its final velocity is v_final2. So we have:
Final momentum (P_final2) = mass2 * v_final2
Since momentum is conserved, we can set up an equation:
P_initial1 + P_initial2 = P_final1 + P_final2
Substituting the values we have:
1.4 kg * 4.5 m/s + 1.4 kg * 0 m/s = 1.4 kg * 0.7 m/s + 1.4 kg * v_final2
Simplifying the equation:
6.3 kg·m/s = 0.98 kg·m/s + 1.4 kg·v_final2
Rearranging the equation:
6.3 kg·m/s - 0.98 kg·m/s = 1.4 kg·v_final2
5.32 kg·m/s = 1.4 kg·v_final2
Dividing both sides by 1.4 kg:
5.32 kg·m/s / 1.4 kg = v_final2
The final velocity of the second pin is approximately 3.8 m/s.