Answer:
(a) The initial gravitational potential energy of the lead can be calculated using the formula:
E = mgh
where E is the potential energy, m is the mass, g is the acceleration due to gravity, and h is the height. Substituting the given values, we get:
E = (0.5 kg) × 10 m/s² × 25 m = 125 J
Therefore, the initial gravitational potential energy of the lead is 125 J.
(b) When the lead reaches the ground, all of its potential energy is converted into kinetic energy. The kinetic energy can be calculated using the formula:
E = (1/2)mv²
where E is the kinetic energy, m is the mass, and v is the velocity. At the moment of impact, the lead has a velocity of:
v = √(2gh) = √(2 × 10 m/s² × 25 m) = 10 m/s
Substituting the given values, we get:
E = (1/2) × 0.5 kg × (10 m/s)² = 25 J
Therefore, the kinetic energy of the lead on reaching the ground is 25 J.
(c) The energy gained by the lead due to the impact is converted into internal energy, which raises the temperature of the lead. The amount of energy required to raise the temperature of the lead can be calculated using the specific heat capacity formula:
Q = mcΔT
where Q is the energy gained, m is the mass, c is the specific heat capacity, and ΔT is the change in temperature. The specific heat capacity of lead is 128 J/kg°C. Substituting the given values, we get:
125 J - 25 J = (0.5 kg) × 128 J/kg°C × ΔT
ΔT = (100 J) / (64 J/kg°C) = 1.56°C
Therefore, the rise in temperature of the lead is 1.56°C.
(d) The energy transfers that have occurred from the moment the lead strikes the ground until it has cooled to air temperature again are:
Conversion of potential energy to kinetic energy upon impact
Conversion of kinetic energy to internal energy upon impact, raising the temperature of the lead
Transfer of heat energy from the lead to the surrounding air, as the lead cools down to air temperature