Question

the two objects shown in the drawing are initially moving in opposite directions. they are on a horizontal frictionless surface, so the net external force acting on them is zero. the objects collide and move apart after the collision. the table shows five possible sets of initial and final momenta for the objects. which is the only set that could occur?
before collision

c
a
d
e
b

Explanation:

Step1: Principle of Conservation of Momentum

According to the law of conservation of momentum, the total initial momentum \(P_{i}\) of the system should be equal to the total final momentum \(P_{f}\). The formula for the total momentum of a system of two objects is \(P = P_{1}+P_{2}\), where \(P_{1}\) and \(P_{2}\) are the momenta of object 1 and object 2 respectively.

Step2: Calculate for each option

• Option a:
• Initial momentum \(P_{i}=+ 16\space kg\cdot m/s+( - 16\space kg\cdot m/s)=0\space kg\cdot m/s\)
• Final momentum \(P_{f}=+8\space kg\cdot m/s + 12\space kg\cdot m/s=20\space kg\cdot m/s\)
• Since \(P_{i}

eq P_{f}\), this option is incorrect.

• Option b:
• Initial momentum \(P_{i}=+16\space kg\cdot m/s+( - 6\space kg\cdot m/s)=10\space kg\cdot m/s\)
• Final momentum \(P_{f}=+4\space kg\cdot m/s+10\space kg\cdot m/s = 14\space kg\cdot m/s\)
• Since \(P_{i}

eq P_{f}\), this option is incorrect.

• Option c:
• Initial momentum \(P_{i}=+12\space kg\cdot m/s+( - 2\space kg\cdot m/s)=10\space kg\cdot m/s\)
• Final momentum \(P_{f}=-4\space kg\cdot m/s + 14\space kg\cdot m/s=10\space kg\cdot m/s\)
• Here \(P_{i} = P_{f}\), so this option satisfies the law of conservation of momentum.
• Option d:
• Initial momentum \(P_{i}=+12\space kg\cdot m/s+( - 28\space kg\cdot m/s)=- 16\space kg\cdot m/s\)
• Final momentum \(P_{f}=-8\space kg\cdot m/s+( - 10\space kg\cdot m/s)=-18\space kg\cdot m/s\)
• Since \(P_{i}

eq P_{f}\), this option is incorrect.

• Option e:
• Initial momentum \(P_{i}=+6\space kg\cdot m/s+( - 14\space kg\cdot m/s)=-8\space kg\cdot m/s\)
• Final momentum \(P_{f}=-6\space kg\cdot m/s+14\space kg\cdot m/s = 8\space kg\cdot m/s\)
• Since \(P_{i}

eq P_{f}\), this option is incorrect.

Answer:

C.