Answer:
a) mass of cart 2 = 2.59kg
b) Vf2 = 1.703m/s
c) Vcom = 0.85m/s
Explanation:
Complete question: a) what is the mass of cart 2? b) What is its speed of impact? c) What is the speed of the two cars' centre of mass?
The collision is elastic. Using law of conservation of momentum
M1V1 = M1Vf1 + M2Vf2
This equation has two unknowns, so we use the equation of conservation of kinetic Energy
1/2M1Vvi^2 = 1/2M1zvf1^1 + 1/2 M2Vf^2
M2= M1( Vi1 - Vf1)/Vf2
= M1(Vi1 - Vf1)/ Sqrt(M1(Vi1^2 - Vf2^2)/M2
M2 = M1(Vi1- Vf1)^2/ (Vi1^2 - Vf1^2)
M2 = 4.9(1.3- 0.4)^2/(1.3^2- 0.4^2)
M2= 4.9(0.9)^2/ (1.69 - 0.16)
M2 = 3.969/1.53
M2 = 2.59kg
b) Velocity of cart 2 after collision
Vf2 = M1(Vi1 - Vf1)/M2
Vf2 = 4.9( 1.3 - 0.4)/ 2.59
Vf2 = 4.9(0.9)/2.59
Vf2 = 4.41/2.59 = 1.703m/s
c) From conservation of momentum, the speed of the center of mass has to be equal to that after collision, therefore:
VCom = (Vf1M1 + Vf2M2)/ (M1 + M2)
Vcom= [(0.4 × 4.9) + (1.70× 2.59)]/(4.9 + 2.59)
Vcom = 6.37/7.49
Vcom = 0.85m/s
