ASVAB Mechanical Comprehension Practice Test 150198 Results

	Your Results	Global Average
Questions	5	5
Correct	0	2.88
Score	0%	58%

Review

1 The radius of the axle is 5, the radius of the wheel is 8, and the blue box weighs 35 lbs. What is the effort force necessary to balance the load?

53% Answer Correctly

	21.88 lbs.
	12.8 lbs.
	13 lbs.
	6.6 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 5 for a mechanical advantage of \( \frac{8}{5} \) = 1.6

MA = \( \frac{load}{effort} \) so effort = \( \frac{load}{MA} \) = \( \frac{35 lbs.}{1.6} \) = 21.88 lbs.

2 If the force applied at the blue arrow over 4 ft. moves the green box 0.57 ft., what is the mechanical advantage of this lever?

56% Answer Correctly

	7
	6.3
	21
	9

Solution

Mechanical advantage (MA) can be calculated knowing only the distance the effort (blue arrow) moves and the distance the resistance (green box) moves. The equation is:

MA = \( \frac{E_d}{R_d} \)

where E_d is the effort distance and R_d is the resistance distance. For this problem, the equation becomes:

MA = \( \frac{4 ft.}{0.57 ft.} \) = 7

You might be wondering how having an effort distance of 7 times the resistance distance is an advantage. Remember the principle of moments. For a lever in equilibrium the effort torque equals the resistance torque. Because torque is force x distance, if the effort distance is 7 times the resistance distance, the effort force must be \( \frac{1}{7} \) the resistance force. You're trading moving 7 times the distance for only having to use \( \frac{1}{7} \) the force.

3 If this lever is in equilibrium with an effort force of 20.0 ft. lb. at the blue arrow and a resistance force of 6 ft. lb. at the green box, what is its mechanical advantage?

48% Answer Correctly

	0.27
	0.45
	1.8
	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 = \( \frac{F_r}{F_e} \) = \( \frac{6 ft.}{20.0 ft.} \) = 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.

Connected gears of different numbers of teeth are used together to change which of the following charasteristics of the input force?

66% Answer Correctly

	rotational direction
	energy
	torque
	force

Solution

Connected gears of different numbers of teeth are used together to change the rotational speed and torque of the input force. If the smaller gear drives the larger gear, the speed of rotation will be reduced and the torque will increase. If the larger gear drives the smaller gear, the speed of rotation will increase and the torque will be reduced.

5 If the green box weighs 20 lbs. and is 9 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 6 ft.?

63% Answer Correctly

	90 lbs.
	30 lbs.
	60 lbs.
	15 lbs.

Solution

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:

R_ad_a = R_bd_b

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 R_b, our missing value, and plugging in our variables yields:

R_b = \( \frac{R_ad_a}{d_b} \) = \( \frac{20 lbs. \times 9 ft.}{6 ft.} \) = \( \frac{180 ft⋅lb}{6 ft.} \) = 30 lbs.