A 4.0-kg metal ball with an initial momentum of 20 kg m/s, collides with a 1.0-kg metal ball initially at rest. After collision, the final momenta of the 4.0-kg and 1.0-kg metal balls are 16 kg m/s and 4.0 kg m/s, respectively. What is the change in energy of the system? Is the collision elastic or inelastic?
initial energy=1/2 *4*5^2=50joules
final energy= 1/2 *4*4^2+1/2*1*4^2=1/2(5*16)=40Joules
inelastic
To find the change in energy of the system, we need to calculate the initial and final kinetic energies.
The initial kinetic energy can be found using the formula: K_i = 1/2 * m_1 * v_1^2 + 1/2 * m_2 * v_2^2, where m_1 and m_2 are the masses of the respective balls, and v_1 and v_2 are their initial velocities.
For the 4.0-kg metal ball:
m_1 = 4.0 kg
v_1 = 20 kg m/s
K_1i = 1/2 * 4.0 kg * (20 kg m/s)^2 = 800 J
For the 1.0-kg metal ball:
m_2 = 1.0 kg
v_2 = 0 m/s (initially at rest)
K_2i = 1/2 * 1.0 kg * (0 m/s)^2 = 0 J
The final kinetic energy can similarly be calculated using the formula: K_f = 1/2 * m_1 * v_1f^2 + 1/2 * m_2 * v_2f^2, where v_1f and v_2f are the final velocities of the balls.
For the 4.0-kg metal ball:
v_1f = 16 kg m/s
K_1f = 1/2 * 4.0 kg * (16 kg m/s)^2 = 512 J
For the 1.0-kg metal ball:
v_2f = 4.0 kg m/s
K_2f = 1/2 * 1.0 kg * (4.0 kg m/s)^2 = 8 J
Now, to find the change in energy of the system (ΔE), we subtract the initial kinetic energy from the final kinetic energy: ΔE = K_f - K_i.
ΔE = (K_1f + K_2f) - (K_1i + K_2i)
= (512 J + 8 J) - (800 J + 0 J)
= 520 J - 800 J
= -280 J
The change in energy of the system is -280 J, indicating a decrease in energy.
To determine if the collision is elastic or inelastic, we need to compare the initial and final kinetic energies. In an elastic collision, the total kinetic energy of the system is conserved, while in an inelastic collision, some kinetic energy is lost.
If the change in energy is zero (ΔE = 0), it would indicate an elastic collision. However, since the change in energy is -280 J in this case, it indicates that some energy is lost during the collision, making it an inelastic collision.