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In this lesson, we will learn how to use dimensional analysis to solve real-life problems.

Q1:

If 1 foot is about 30 centimetres and 1 yard is about 90 centimetres, approximately how many feet are there in a yard?

Q2:

Which quantities could be sized to determine the fuel efficiency of a car?

Which of the following is an appropriate unit for the fuel efficiency?

Q3:

Mona wants to convert kg/m^{3} into meters per second

Which of the following is correct?

What does she find?

Q4:

Adam wants to convert 50 m/s into kilometres per hour.

He starts by writing the speed as a ratio of distance to time. What would this look like?

Next, he works out how many metres would be covered in 1 hour, which is equal to s. What does he find?

Finally, he converts his result in (2) to kilometres. What speed does he find?

Considering units as algebraic quantities, which of the following is equivalent to Adam’s conversion?

Q5:

If the density of a material is 𝑑 g/cm^{3}, what is its density expressed in kg/m^{3}?

Q6:

Convert 1 m/s into kilometers per hour, giving your answer as a fraction in its simplest form.

Convert 𝑎 m/s into kilometers per hour.

Q7:

The density 𝐷 of a material can be measured in kilograms per cubic meter, often written as kg/m^{3}. Use dimensional analysis to determine which of the following formulas is correct to calculate the density of a given object, where 𝑚 is its mass and 𝑉 its volume.

Q8:

When heating up a meal, some parts of the meal can be hot before some others. For instance, chicken will heat up faster than broccoli. This is because different substances have different specific heat capacities, which is the energy needed to raise the temperature of one kilogram of a substance by one degree Celsius. The specific heat capacity is often expressed in joules per kilogram and per degree Celsius (or J/(kg⋅°C)). Using dimensional analysis, find the formula for the amount of energy 𝑄 needed to raise the temperature of a mass 𝑚 of a substance of specific heat capacity 𝑐 by Δ 𝑇 degrees.

Q9:

The amount of pressure an object is exerting is given by 𝑃 = 𝐹 𝐴 , where 𝐹 is the force exerted by the object and 𝐴 is the surface area on which the force is spread. When 𝐹 is measured in newtons, which can be expressed as kg⋅m/s^{2}, and 𝐴 is measured in square meters, the pressure is measured in pascals. Which of the following is the expression of pascals in terms of the base units kilograms, meters, and seconds?

Q10:

Convert 1 km/h into meters per second, giving your answer as a fraction in its simplest form.

Convert 𝑎 km/h into meters per second.

Q11:

If the density of a material is 𝑑 kg/m^{3}, what is its density expressed in g/cm^{3}?

Q12:

Yasmine wants to convert 30 km/h into meters per second

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