Final answer:
The expansion gap needed for steel railroad rails can be calculated using the linear expansion formula. Big nails can be efficiently counted by weight, dividing the total weight by the weight per nail. The work done by a mule on a barge is calculated with the force, distance, and the angle of the force to the direction of travel.
Step-by-step explanation:
To determine how large an expansion gap should be left between steel railroad rails that may reach a maximum temperature of 35.0°C higher than when they were laid, you need to use the concept of thermal expansion.
The formula for linear expansion is
ΔL = αL₀ΔT,
where ,
ΔL is the change in length,
α is the coefficient of thermal expansion for steel (typically around 1.2×⁴°C⁻¹),
L₀ is the original length, and ΔT is the change in temperature.
For a 10.0 m long rail and a temperature increase of 35.0°C, the calculation would give us the necessary expansion gap size.
When weighing big nails for construction purposes, counting by weight can be efficient. Assuming the weight per big nail is given, you can find the total number of nails by dividing the total weight by the weight of one nail. For example, if the total weight of nails is 1227 g and each nail weighs 0.450 g, you can calculate the number of big nails as 2730 by dividing the total weight by the weight per nail.
In terms of work done by a mule pulling a barge, you'd need to calculate the component of the force in the direction of travel. This can be done by using the cosine of the angle between the force and the direction of travel (cos(20 degrees)) multiplied by the force exerted (1200 N) and the distance (10 km converted to meters).