ASVAB Mechanical Comprehension Practice Test 247654 Results

	Your Results	Global Average
Questions	5	5
Correct	0	2.94
Score	0%	59%

Review

1 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?

48% Answer Correctly

	0.1
	-6.7
	0.27
	0.3

Solution

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.

2 If you lift a 6 lbs. rock 21 ft. from the ground, how much work have you done?

70% Answer Correctly

	0 ft⋅lb
	3 ft⋅lb
	27 ft⋅lb
	126 ft⋅lb

Solution

Work is force times distance. In this case, the force is the weight of the rock so:
\( W = F \times d \)
\( W = 6 \times 21 \)
\( W = 126 \)

3 The radius of the axle is 7, the radius of the wheel is 8, and the blue box weighs 60 lbs. What is the effort force necessary to balance the load?

53% Answer Correctly

	15 lbs.
	8.14 lbs.
	52.63 lbs.
	9.12 lbs.

Solution

The mechanical advantage of a wheel and axle is the input radius divided by the output radius:

MA = \( \frac{r_i}{r_o} \)

In this case, the input radius (where the effort force is being applied) is 8 and the output radius (where the resistance is being applied) is 7 for a mechanical advantage of \( \frac{8}{7} \) = 1.14

MA = \( \frac{load}{effort} \) so effort = \( \frac{load}{MA} \) = \( \frac{60 lbs.}{1.14} \) = 52.63 lbs.

Which of these is the formula for kinetic energy?

67% Answer Correctly

	\(KE = {m \over v^2 }\)
	\(KE = mgh\)
	\(KE = {1 \over 2}mv^2\)
	\(KE = {1 \over 2}mh^2\)

Solution

Kinetic energy is the energy of movement and is a function of the mass of an object and its speed: \(KE = {1 \over 2}mv^2\) where m is mass in kilograms, v is speed in meters per second, and KE is in joules. The most impactful quantity to kinetic energy is velocity as an increase in mass increases KE linearly while an increase in speed increases KE exponentially.

5 If the green box weighs 10 lbs. and 75 lbs. of force is applied 3 ft. from the fulcrum at the blue arrow, how far from the fulcrum would the green box need to be placed to balance the lever?

55% Answer Correctly

	7.5 ft.
	90 ft.
	11.25 ft.
	22.5 ft.

Solution

To balance this lever the torques at the green box and the blue arrow must be equal. Torque is weight x distance from the fulcrum so the equation for equilibrium is:

R_ad_a = R_bd_b

where a represents the green box and b the blue arrow, R is resistance (weight/force) and d is the distance from the fulcrum.

Solving for d_a, our missing value, and plugging in our variables yields:

d_a = \( \frac{R_bd_b}{R_a} \) = \( \frac{75 lbs. \times 3 ft.}{10 lbs.} \) = \( \frac{225 ft⋅lb}{10 lbs.} \) = 22.5 ft.