This question requires you to consider the units of each quantity in order to follow the calculation.
In order to reduce its diameter, a wire is pulled through a small hole in a metal plate. The wire is made of metal whose specific heat capacity is 400 J kg⁻¹ °C⁻¹ and, on emerging from the hole, has a mass per unit length of 5 g per m. A steady force of 600 N is required. If all the heat generated is retained in the wire, we can calculate the rise in temperature of the wire.
Calculate all quantities using SI units (metre, kilogram, second).
a) Draw a simple sketch of the situation and mark on it the force applied to the thin wire.
b) What is the value of the work done on one metre length of the wire?
c) How much work is done on one kilogram of wire?
d) Assuming all of the work done is converted into heat calculate the temperature rise of the wire.
If, however, the temperature of the wire were kept constant by spraying it with cold water, then we can calculate what mass of water would be needed.
Specific heat capacity of water is 4,200 J kg⁻¹ °C⁻¹
e) Calculate the mass of wire, in kilograms, that is produced each second if it emerges from the hole at a speed of 8.4 ms⁻¹.
f) Using your answer from part (c), calculate the work done on the wire each second.
g) If the temperature rise of the water were to be 12 °C, calculate the mass of water used each second to keep the temperature constant.