Toy 1, which has a mass of 2 kg, is moving to the right at 3 m/s, and Toy 2, whose mass is unknown, is moving to the left at 3 m/s. After the two toys collide, each object's speed is 3 m/s. What could be Toy 2's mass (choose 2 answers)?
A. 1 kg
B. 3 kg
C. 2 kg
D. Negligible mass
2*3-m*3=(2+m)3
6m=6-6
mass m= neg
Would there also be a second answer? I didn't include that it was a head-on collision.
No second answer
To determine the mass of Toy 2 after the collision, we need to use the principle of conservation of momentum.
The principle of conservation of momentum states that the total momentum of a closed system remains constant before and after a collision, assuming no external forces are acting on the system.
Mathematically, we can express this principle as:
(initial momentum of Toy 1) + (initial momentum of Toy 2) = (final momentum of Toy 1) + (final momentum of Toy 2)
The momentum of an object is defined as the product of its mass and velocity. Therefore, we can write the equation as:
(2 kg * 3 m/s) + (unknown mass of Toy 2 * -3 m/s) = (2 kg * 3 m/s) + (unknown mass of Toy 2 * 3 m/s)
Simplifying the equation, we get:
(6 kg * m/s) - (unknown mass of Toy 2 * 3 m/s) = (6 kg * m/s) + (unknown mass of Toy 2 * 3 m/s)
We can now solve for the unknown mass of Toy 2.
By canceling out the similar terms on both sides of the equation, we are left with:
-unknown mass of Toy 2 * 3 m/s = unknown mass of Toy 2 * 3 m/s
Since we know that both objects have a final velocity of 3 m/s, the difference in momentum between the two objects is zero. This means the unknown mass of Toy 2 can be any value without affecting the equation. In other words, it could have any mass.
Therefore, the correct answers are:
A. 1 kg
B. 3 kg