Names: ________________________
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Worksheet 1
1. If an equation is dimensionally correct, does this mean that the equation must be
true? Explain your answer.
2. If an equation is not dimensionally correct, does this mean that the equation can’t
be true? Explain your answer.
3.
Acceleration is the rate of change of speed: the change in speed divided by the
time interval. What are the units of acceleration?
Some people measure speed in miles per hour, while others use meters per
second. Estimate the acceleration of a car starting from a stop light.
Convert your result into the units involving meters and seconds.
4. One of the fundamental laws of motion states that the acceleration of an object is
directly proportional to the resultant force on it and inversely proportional to its
mass. (a) If the proportionality constant is defined to have no dimensions,
determine the dimensions of force.
(b) The newton (N) is the SI unit of force. According to the results of (a), how can
you express a force having units of Newtons by using the fundamental units of
mass, length, and time?
5. The displacement of an object moving under uniform acceleration is some
function of time and the acceleration. Suppose we write the displacement as
𝑠 = 𝑘𝑎! 𝑡 ! , where k is a dimensionless constant, a is acceleration, t is time and s
is displacement. Show by dimensionless analysis that this expression is satisfied if
m = 1 and n = 2. Can the analysis give the value of k?
6. A painter is to cover the walls in a room that is 8.0 ft high and 12 ft long along a
side. What surface area (in square meters) must she cover?