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Sample Practice Test Questions
If the green box weighs 20 lbs. and is 1 ft. from the fulcrum, how much weight would need to be placed at the blue arrow to balance the lever if the arrow's distance from the fulcrum is 8 ft.?
To balance this lever the torques on each side of the fulcrum must be equal. Torque is weight x distance from the fulcrum so the equation for equilibrium is:
Rada = Rbdb
where a represents the left side of the fulcrum and b the right, R is resistance (weight) and d is the distance from the fulcrum.Solving for Rb, our missing value, and plugging in our variables yields:
Rb = \( \frac{R_ad_a}{d_b} \) = \( \frac{20 lbs. \times 1 ft.}{8 ft.} \) = \( \frac{20 ft⋅lb}{8 ft.} \) = 2.5 lbs.
Measuring tools provide a convenient and easy way to compare object dimensions against:
a standard
Measuring tools give easy access to the wide variety of standard dimensions that are used to categorize and classify objects.
The transfer of heat by the circulation or movement of the heated parts of a liquid or gas is called:
convection
Convection is the transfer of heat by the circulation or movement of the heated parts of a liquid or gas. Examples of heat transfer by convection include water coming to a boil on a stove, ice melting, and steam from a cup of coffee.
If \( \left|x + 9\right| \) - 3 = 7, which of these is a possible value for x?
First, solve for \( \left|x + 9\right| \):
\( \left|x + 9\right| \) - 3 = 7
\( \left|x + 9\right| \) = 7 + 3
\( \left|x + 9\right| \) = 10
The value inside the absolute value brackets can be either positive or negative so (x + 9) must equal + 10 or -10 for \( \left|x + 9\right| \) to equal 10:
| x + 9 = 10 x = 10 - 9 x = 1 | x + 9 = -10 x = -10 - 9 x = -19 |
So, x = -19 or x = 1.
What is the next number in this sequence: 1, 7, 13, 19, 25, __________ ?
The equation for this sequence is:
an = an-1 + 6
where n is the term's order in the sequence, an is the value of the term, and an-1 is the value of the term before an. This makes the next number:
a6 = a5 + 6
a6 = 25 + 6
a6 = 31
The formula for acceleration is which of the following?
\(\vec{a} = { \vec{F} \over m }\)
Newton's second law of motion leads to the formula for acceleration which is a measure of the rate of change of velocity per unit time and, if you solve for positive acceleration, reveals how much net force is needed to overcome an object's mass. The formula for acceleration is \(\vec{a} = { \vec{F} \over m }\) or, solving for force, \(\vec{F} = m\vec{a}\).
Atoms of an element whose atoms can vary in the number of neutrons in their nucleus are called which of the following?
isotopes
The atomic mass of an element listed in the Periodic Table represents the average mass of a single atom of that element and is measured in atomic mass units (amu). This number is an average as some elements have isotopes with atoms that vary in their number of neturons and, therefore, differ in weight.
What is the first step to solving a problem where multiple forces are acting on an object?
calculate the net force
In mechanics, multiple forces are often acting on a particular object and, taken together, produce the net force acting on that object. Like force, net force is a vector quantity in that it has magnitude and direction.
A ramp is an example of which kind of simple machine?
inclined plane
An inclined plane is a simple machine that reduces the force needed to raise an object to a certain height. Work equals force x distance and, by increasing the distance that the object travels, an inclined plane reduces the force necessary to raise it to a particular height. In this case, the mechanical advantage is to make the task easier. An example of an inclined plane is a ramp.
If this lever is in equilibrium with an effort force of 10.0 ft. lb. at the blue arrow and a resistance force of 3 ft. lb. at the green box, what is its mechanical advantage?
Mechanical advantage (MA) is the ratio by which effort force relates to resistance force. If both forces are known, calculating MA is simply a matter of dividing resistance force by effort force:
MA = \( \frac{F_r}{F_e} \) = \( \frac{3 ft.}{10.0 ft.} \) = 0.3
In this case, the mechanical advantage is less than one meaning that each unit of effort force results in just 0.3 units of resistance force. However, a third class lever like this isn't designed to multiply force like a first class lever. A third class lever is designed to multiply distance and speed at the resistance by sacrificing force at the resistance. Different lever styles have different purposes and multiply forces in different ways.