Exam 1: Physics and Measurement

You measure the height of a building using your knowledge of trigonometry, by measuring the angle to the top of the building from a point on the ground 100.0 m away. You measure an angle θ=20.0°±1.0°. How high is the building?

A 2.00 m by 3.00 m plate of aluminium has a mass of 324 kg. What is the thickness of the plate? (The density of aluminium is 2.70 *103 kg/m3.)

At the end of a year, a motor car company announces that sales of a pickup are down 43% for the year. If sales continue to decrease by 43% in each succeeding year, how long will it take for sales to decrease to zero?

The answer to a question is [MLT-1]. The question is 'What are the dimensions of:

The equation for the change of position of a train starting at x = 0 m is given by $x=\frac{1}{2} a t^{2}+b t^{3}$ . The dimensions of b are:

When doing a physics problem, you were asked to calculate how fast a car was going in a particular situation. You came up with an answer of 230 m/s. You want to check if this is plausible, by converting this number into more familiar units: kilometres per hour. What is 230 m/s when converted into kilometres per hour, and is this a plausible speed for a car?

What is the mass of air in a room that measures 5.0 m * 8.0 m *3.0 m? (The density of air is 1/800 that of water).

The quantity with the same units as force times time, Ft, with dimensions MLT-1 is:

Which of the following quantities has the same dimensions as kinetic energy, $\frac{1}{2} m v^{2}$ ? Note: [a] = [g] = LT-2; [h] = L and [v] = LT-1.

A standard exam page is 210 mm by 297 mm. An exam that is 2.0 mm thick has a volume of:

You are trying to compare the fuel efficiency of two cars, one made in the US and one made in Australia. You know that the Australian car will use 14 litres of fuel per 100 km of driving. The US car has been tested as getting 10 miles per gallon of fuel used. A mile is 1.609 km and a US gallon is 3.785 litres. How many litres will the US car use per 100 km of driving?

Which one of the quantities below has dimensions equal to $\left[\frac{\mathrm{ML}}{\mathrm{~T}^{2}}\right]$ ?

The term $\frac{1}{2} \rho \nu^{2}$ occurs in Bernoulli's equation in Chapter 15, with $\rho$ being the density of a fluid and v its speed. The dimensions of this term are:

Five people measure the length of a car. The values they obtain are 2.38 m, 2.36 m, 2.41 m, 2.36 m and 2.37 m. What is the approximate uncertainty in their measurement of the length of the car?

Two rocket engineers are trying to see whether a changed nozzle design makes their rockets go faster. The first rocket travels at a speed of 1000±3 m/s, while the second rocket travels at a speed of 1005±2 m/s. How much faster is the second rocket?

Which of the following products of ratios gives the conversion factors to convert metres per second $\left(\frac{\mathrm{m}}{\mathrm{~s}}\right)$ to parsecs per year $\left(\frac{\text { Parsec }}{\text { Year }}\right)$ ? A parsec is a unit of distance used in astrophysics, and is equal to 3.26 light years. A light year is 9.46 x 1015 m.

One number has three significant figures and another number has four significant figures. If these numbers are added, subtracted, multiplied, or divided, which operation can produce the greatest number of significant figures?

Spike claims that dimensional analysis shows that the correct expression for change in velocity is $\vec{v}_{f}-\vec{v}_{i}$ , is $\overrightarrow{\mathrm{v}}_{f}-\overrightarrow{\mathrm{v}}_{i}=\frac{m t}{F}$ , where m is mass, t is time, and F is the magnitude of force. Carla says that can't be true because the dimensions of force are $\left[\frac{\mathrm{ML}}{\mathrm{~T}^{2}}\right]$ . Which one, if either, is correct?

A rectangle has a length of 1.323 m and a width of 4.16 m. Using significant figure rules, what is the area of this rectangle?

The density of an object is defined as: