A farmer drives a 0.100 kg iron spike with a 2.00 kg sledge hammer. The sledge hammer moves at a constant speed of 3.99 m/s until it comes to rest on the spike after each swing. Assuming all the energy is absorbed by the nail, and ignoring the work done by the nail on the hammer, how much would the nail's temperature rise after 10 successive swings?
work done on hammer in 10 swings
= 10(1/2) m v^2 = 5(2)(3.99)^2
= 159 Joules
I do not know specific heat of iron off hand
159 Joules = Ciron (2 kg) (delta T)
E=Q
Q=mct
E=1/2mv^2*10
5mv^2=mct
5*2*3.99^2=0.1*450*t
T=3.53. C
To calculate the rise in temperature of the nail after 10 successive swings, we can use the principle of conservation of energy.
1. The kinetic energy (KE) of the sledgehammer before it comes to rest is given by the equation KE = (1/2)mv^2, where m is the mass of the sledgehammer (2.00 kg) and v is the speed of the sledgehammer (3.99 m/s). Plugging in the values, we get KE = (1/2)(2.00 kg)(3.99 m/s)^2 = 15.936 J.
2. The potential energy (PE) of the sledgehammer after it comes to rest is given by the equation PE = mgh, where m is the mass of the sledgehammer (2.00 kg), g is the acceleration due to gravity (9.8 m/s^2), and h is the height through which the sledgehammer is dropped. Since the sledgehammer moves at a constant speed, h does not change, so the change in potential energy is zero.
3. The work done by the sledgehammer on the nail is equal to the change in kinetic energy, which is given by W = KE_final - KE_initial = 0 J - 15.936 J = -15.936 J. Note that work is negative since the sledgehammer loses energy.
4. By the principle of conservation of energy, the work done on the nail is equal to the increase in thermal energy (heat) of the nail. So, the increase in thermal energy is given by Q = -W = 15.936 J.
5. To calculate the increase in temperature, we can use the equation Q = mcΔT, where Q is the thermal energy absorbed (15.936 J), m is the mass of the nail (0.100 kg), c is the specific heat capacity of iron (450 J/kg°C), and ΔT is the change in temperature.
6. Rearranging the equation, we can solve for ΔT: ΔT = Q / (mc).
Calculating the change in temperature:
ΔT = 15.936 J / (0.100 kg * 450 J/kg°C) = 354.08°C.
Therefore, after 10 successive swings, the nail's temperature would rise by approximately 354.08°C.
To find the temperature rise of the nail after 10 successive swings, we need to calculate the amount of energy transferred to the nail during each swing and then add up the total energy transferred over 10 swings.
The amount of energy transferred to the nail can be calculated using the work-energy principle, which states that the work done on an object is equal to the change in its kinetic energy. In this case, the work done on the nail is equal to the kinetic energy of the hammer before it comes to rest on the nail.
The kinetic energy of the hammer can be calculated using the formula:
KE = (1/2) * mass * velocity^2
Given that the mass of the hammer is 2.00 kg and the velocity is 3.99 m/s, we can calculate the kinetic energy of the hammer for each swing.
KE = (1/2) * 2.00 kg * (3.99 m/s)^2
= 15.94 J
Since all the energy is transferred to the nail, the amount of energy transferred to the nail during each swing is 15.94 J.
Now, to find the total energy transferred over 10 swings, we multiply the energy transferred per swing by the number of swings:
Total energy transferred = Energy per swing * Number of swings
= 15.94 J * 10
= 159.4 J
The rise in temperature of the nail can be calculated using the specific heat capacity formula:
Q = m * c * ΔT
where Q is the heat energy transferred, m is the mass of the nail, c is the specific heat capacity of iron, and ΔT is the change in temperature.
Since the mass of the nail is 0.100 kg and the specific heat capacity of iron is 450 J/kg°C, we can rearrange the formula to solve for ΔT:
ΔT = Q / (m * c)
Plugging in the values:
ΔT = 159.4 J / (0.100 kg * 450 J/kg°C)
= 3.54 °C
Therefore, the temperature of the nail would rise by 3.54 °C after 10 successive swings.