8. a billiard ball rolling across a table at 1.50 m/s makes a head - on elastic collision with an identical…

8. a billiard ball rolling across a table at 1.50 m/s makes a head - on elastic collision with an identical ball. find the speed of each ball after the collision (a) when the second ball is initially at rest, (b) when the second ball is moving toward the first at a speed of 1.00 m/s. (10 points)

8. a billiard ball rolling across a table at 1.50 m/s makes a head - on elastic collision with an identical ball. find the speed of each ball after the collision (a) when the second ball is initially at rest, (b) when the second ball is moving toward the first at a speed of 1.00 m/s. (10 points)

Answer

Explanation:

Step1: Recall elastic - collision formulas

For a one - dimensional elastic collision between two objects of equal mass (m_1 = m_2=m), the velocity formulas are (v_{1f}=\frac{(m_1 - m_2)v_{1i}+2m_2v_{2i}}{m_1 + m_2}) and (v_{2f}=\frac{(m_2 - m_1)v_{2i}+2m_1v_{1i}}{m_1 + m_2}). Since (m_1 = m_2), these simplify to (v_{1f}=v_{2i}) and (v_{2f}=v_{1i}).

Step2: Solve part (a)

Given (v_{1i}=1.50\ m/s) and (v_{2i} = 0\ m/s). Using the simplified elastic - collision formulas for equal - mass objects, we have (v_{1f}=0\ m/s) and (v_{2f}=1.50\ m/s).

Step3: Solve part (b)

Given (v_{1i}=1.50\ m/s) and (v_{2i}=- 1.00\ m/s) (negative because it's moving towards the first ball). Using (v_{1f}=v_{2i}), we get (v_{1f}=-1.00\ m/s). Using (v_{2f}=v_{1i}), we get (v_{2f}=1.50\ m/s).

Answer:

(a) (v_{1f}=0\ m/s), (v_{2f}=1.50\ m/s) (b) (v_{1f}=-1.00\ m/s), (v_{2f}=1.50\ m/s)