2.6 kg mass
initial velocity of v1 =aˆi,
where a = 5.95 m/s collides with and
sticks to a 1.59 kg mass with an initial velocity
of v1 = bˆj, where b = −4.8 m/s.
Find the final speed of the composite mass.
Answer in units of m/s
Some of the text got garbled, but remember that the momentum of the center of mass for the system stays unchanged.
do a web search for inelastic collisions and you'll find several examples.
To find the final speed of the composite mass after the collision, we can use the principles of conservation of momentum and conservation of kinetic energy.
1. Conservation of momentum:
The total momentum before the collision is equal to the total momentum after the collision. The momentum of an object is defined as the product of its mass and velocity.
Let's calculate the total initial momentum before the collision:
Initial momentum of the first mass (m1):
p1 = m1 * v1
= (2.6 kg) * (5.95 m/s) * i
Initial momentum of the second mass (m2):
p2 = m2 * v2
= (1.59 kg) * (-4.8 m/s) * j
Total initial momentum before the collision:
p_initial = p1 + p2
2. Conservation of kinetic energy:
The total kinetic energy before the collision is equal to the total kinetic energy after the collision. The kinetic energy of an object is defined as half of the product of its mass and the square of its velocity.
Let's calculate the initial kinetic energy of both masses:
Initial kinetic energy of the first mass (KE1):
KE1 = (1/2) * m1 * v1^2
= (1/2) * (2.6 kg) * (5.95 m/s)^2
Initial kinetic energy of the second mass (KE2):
KE2 = (1/2) * m2 * v2^2
= (1/2) * (1.59 kg) * (-4.8 m/s)^2
Total initial kinetic energy before the collision:
KE_initial = KE1 + KE2
Now, after the collision, the masses stick together, so the final velocity of the composite mass is the same for both masses.
Using conservation of momentum, we can equate the total initial momentum to the total final momentum and solve for the final velocity.
p_initial = p_final
p1 + p2 = (m1 + m2) * v_final
Also, using conservation of kinetic energy, we can equate the total initial kinetic energy to the total final kinetic energy and solve for the final velocity.
KE_initial = KE_final
KE1 + KE2 = (1/2) * (m1 + m2) * v_final^2
Now we have two equations, and we can solve them simultaneously to find the final velocity.
Once we have the final velocity, the final speed of the composite mass is the magnitude of the final velocity.
Note: The given values for a and b are not used in the calculations, so please double-check the question or provide the correct values to get an accurate answer.