A 1.60-g bullet, moving at 542 m/s, strikes a 0.249-kg piece of wood at rest on a frictionless table. The bullet sticks in the wood, and the combined mass moves slowly down the table.
(a) Find the speed of the combination after the collision.
m/s
(b) Find the kinetic energy of the bullet before the collision.
J
(c) Find the kinetic energy of the combination after the collision.
J
(d) How much kinetic energy did the bullet lose?
J
(e) What percent of the bullet's original kinetic energy is lost?
%
m1 = 0.0016 kg, v1 = 542 m/s, m2 =0.249, v2 = 0, u = ?
(a) m1•v1 +m2•v2 = (m1+m2) •u
u = m1•v1/(m1+m2).
(b) KE1 =m1•v1²/2.
(c) KE = ((m1+m2) •u²/2
(d) ΔKE = KE1 – KE.
(e) (ΔKE/KE1) •100%
I have never used these equations before, can you explain/ show me
To solve this problem, we can use the law of conservation of momentum and the law of conservation of kinetic energy.
(a) To find the speed of the combination after the collision, we need to calculate the final velocity.
Using the law of conservation of momentum:
Initial momentum of the bullet = Final momentum of the combination
The momentum, p, is given by the product of mass and velocity.
Initial momentum of the bullet (before collision) = mass of the bullet * velocity of the bullet
Final momentum of the combination (after collision) = (mass of the bullet + mass of the wood) * velocity of the combination
Since the bullet sticks in the wood, the mass of the bullet and the wood will combine.
Substituting the values:
(0.00160 kg * 542 m/s) = (0.00160 kg + 0.249 kg) * V_f
0.872 kg⋅m/s = 0.2516 kg * V_f
Solving for V_f:
V_f = 0.872 kg⋅m/s / 0.2516 kg
V_f = 3.4637 m/s
Therefore, the speed of the combination after the collision is 3.4637 m/s.
(b) The kinetic energy of the bullet before the collision can be calculated using the formula:
Kinetic energy = 1/2 * mass * velocity^2
Substituting the values:
Kinetic energy of the bullet before the collision = 1/2 * 0.00160 kg * (542 m/s)^2
Calculating:
Kinetic energy of the bullet before the collision = 0.464 J (rounded to three decimal places)
Therefore, the kinetic energy of the bullet before the collision is 0.464 J.
(c) The kinetic energy of the combination after the collision can also be calculated using the same formula:
Kinetic energy = 1/2 * mass * velocity^2
Substituting the values:
Kinetic energy of the combination after the collision = 1/2 * (0.00160 kg + 0.249 kg) * (3.4637 m/s)^2
Calculating:
Kinetic energy of the combination after the collision = 0.274 J (rounded to three decimal places)
Therefore, the kinetic energy of the combination after the collision is 0.274 J.
(d) The kinetic energy lost by the bullet can be calculated by finding the difference between the initial and final kinetic energies of the bullet.
Kinetic energy lost by the bullet = Kinetic energy of the bullet before the collision - Kinetic energy of the combination after the collision
Substituting the values:
Kinetic energy lost by the bullet = 0.464 J - 0.274 J
Calculating:
Kinetic energy lost by the bullet = 0.190 J (rounded to three decimal places)
Therefore, the bullet lost 0.190 J of kinetic energy.
(e) To find the percentage of the bullet's original kinetic energy lost, we need to calculate the percentage using the formula:
Percentage = (Kinetic energy lost / Kinetic energy before collision) * 100%
Substituting the values:
Percentage = (0.190 J / 0.464 J) * 100%
Calculating:
Percentage = 40.948 % (rounded to three decimal places)
Therefore, approximately 40.948% of the bullet's original kinetic energy is lost.