Answer: 2.12 kg
Explanation:
Since the 1.3 kg object moves to the west after the collision, the other object will move to the east after the collision.
In an elastic collision, the relative velocity after the collision is the opposite of the relative velocity before the collision. Since the 1.3 kg object’s velocity before the collision is 6.7 m/s greater than the other object, after the collision, its velocity will be 6.7 m/s less than the other object. To determine the other object’s velocity, use the following equation.
v = 1.7 – 7.1 = -5.4 m/s
The negative sign means it is moving eastward. Let’s use this number is a momentum equation to determine its mass.
Initial momentum = 1.3 * 7.1 = 9.23 east
For the 1.3 object, final momentum = 1.3 * 1.7 = 2.21 west
To determine the final momentum of the other object, add these two numbers.
Final momentum = 11.44 east
To determine its mass, use the following equation.
m * 5.4 = 11.44
m = 11.44 ÷ 5.4 = 2.12 kg
To make sure that kinetic energy is conserved, let’s round this number to 2 kg and determine the final kinetic energies.
For the 1.3 object, KE = 1/2 * 1/3* 1.7^2 = 0.48
For the 2 kg object, KE = 1/2* 2 * 5.4^2 = 29.64
Total final KE = 29.64
Initial KE = 0.5* 1.3 * 7.1^2 = 32.77
Since I rounded the mass up to 2kg, this proves that kinetic energy is conserved and the mass is correct!
