Answer:
A) m2 = 98.71g
B) v_f2 = 1.86 m/s
Explanation:
We are given;
Mass of cart; m1 = 340g
Initial speed; v_i1 = 1.2 m/s
Final speed; v_f1 = 0.66 m/s
A)Since the collision is elastic, we can simply apply the conservation of momentum to get;
m1•(v_i1) = m1•(v_f1) + m2•(v_f2) - - - - - (eq1)
From conservation of kinetic energy, we have;
(1/2)m1•(v_i1)² = (1/2)m1•(v_f1)² + (1/2)m2•(v_f2)² - - - - eq(2)
Let's make v_f2 the subject in eq 2;
Thus,
v_f2 = √([m1•(v_i1)² - m1•(v_f1)²]/m2)
v_f2 = √([m1((v_i1)² - (v_f1)²)]/m2)
Let's put this for v_f2 in eq1 to obtain;
m2 = {m1((v_i1) - (v_f1))}/√([m1((v_i1)² - (v_f1)²)]/m2)
Let's square both sides to give;
(m2)² = {m1•m2((v_i1) - (v_f1))²}/([(v_i1)² - (v_f1)²]
This gives;
m2 = {m1((v_i1) - (v_f1))²}/([(v_i1)² - (v_f1)²]
Plugging in the relevant values to get;
m2 = {340((1.2) - (0.66))²}/([(1.2)² - (0.66)²]
m2 = 98.71g
B) from equation 1, we have;
m1•(v_i1) = m1•(v_f1) + m2•(v_f2)
Making v_f2 the subject, we have;
v_f2 = m1[(v_i1) - (v_f1)]/m2
Plugging in the relevant values to get;
v_f2 = 340[(1.2) - (0.66)]/98.71
v_f2 = 1.86 m/s
