The collision between a hammer and a nail can be considered to be approximately elastic. Estimate the kinetic energy acquired by a 15 g nail when it is struck by a 550 g hammer moving with an initial speed of 5.1 m/s.
To estimate the kinetic energy acquired by the nail, we can use the law of conservation of kinetic energy in an elastic collision. In an elastic collision, the total kinetic energy before the collision is equal to the total kinetic energy after the collision.
The kinetic energy (KE) of an object is given by the equation KE = (1/2)mv^2, where m is the mass of the object and v is its velocity.
First, let's calculate the initial kinetic energy of the hammer before the collision:
mass of the hammer (m_hammer) = 550 g = 0.55 kg
initial velocity of the hammer (v_hammer) = 5.1 m/s
Initial kinetic energy of the hammer (KE_hammer_initial) = (1/2) * m_hammer * v_hammer^2
Next, let's calculate the final kinetic energy of the hammer and nail after the collision. Since the collision is considered approximately elastic, the final velocity of the hammer and the nail will be the same. Let's call it v_final.
Initial kinetic energy of the hammer and nail system (KE_initial) = KE_hammer_initial
Final kinetic energy of the hammer and nail system (KE_final) = (1/2) * (m_hammer + m_nail) * v_final^2
= (1/2) * (0.55 kg + 0.015 kg) * v_final^2 (where m_nail is the mass of the nail, which is 15 g = 0.015 kg)
Since the total kinetic energy before the collision is equal to the total kinetic energy after the collision, we can equate the initial and final kinetic energies:
KE_initial = KE_final
(1/2) * m_hammer * v_hammer^2 = (1/2) * (m_hammer + m_nail) * v_final^2
Now we can solve for v_final:
v_final^2 = (m_hammer * v_hammer^2) / (m_hammer + m_nail)
v_final^2 = (0.55 kg * (5.1 m/s)^2) / (0.55 kg + 0.015 kg)
Once we have the value of v_final, we can calculate the final kinetic energy of the hammer and nail system.
KE_final = (1/2) * (m_hammer + m_nail) * v_final^2
Substituting the known values into the equations, you can calculate the final kinetic energy acquired by the nail in this collision.