Question

Two objects, A and B, initially at rest, are "exploded" apart by the release of a coiled spring that was compressed between them. As they move apart, the velocity of object A is 5 m/s, and the velocity of object B is 2 m/s. The ratio of the mass of object A to the mass of object B, mA/mB, is

a) 5/2
b) 2/5
c) 5/7
d) 7/5

Answer 1

In an elastic collision, the velocity and kinetic energy are conserved. Using the conservation of momentum formula and the given velocities, we can find the final velocity of mass B. The final velocity of mass B is 2 m/s in the +x direction.

Step-by-step explanation:

For elastic collisions, momentum and kinetic energy are conserved. In this case, mass A is initially moving with a velocity of 5 m/s in the +x direction, and mass B is initially at rest. After the collision, mass A has a velocity of 3 m/s in the -x direction. To find the velocity of mass B after the collision, we can use the conservation of momentum formula:

mAvAi + mBvBi = mAvAf + mBvBf

Since mass A is moving in the -x direction, its velocity is negative. Plugging in the given values, we have:

mA(5 m/s) + mB(0 m/s) = mA(3 m/s) + mBvBf

Simplifying, we get:

5mA = 3mA + mBvBf

Since mass A = mass B, we can further simplify to:

5 = 3 + vBf

Solving for vBf, we find that the final velocity of mass B is 2 m/s in the +x direction.