ASVAB Mechanical Comprehension Practice Test 762910 Results

	Your Results	Global Average
Questions	5	5
Correct	0	3.09
Score	0%	62%

Review

1 If the green box weighs 10 lbs. and is 7 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

	3.89 lbs.
	11.67 lbs.
	35 lbs.
	1 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 = \( \frac{R_ad_a}{d_b} \) = \( \frac{10 lbs. \times 7 ft.}{6 ft.} \) = \( \frac{70 ft⋅lb}{6 ft.} \) = 11.67 lbs.

2 If the green box is 6 ft. from the fulcrum and a certain force applied 9 ft. from the fulcrum at the blue arrow balances the lever, what is the mechanical advantage?

61% Answer Correctly

	1.65
	4.5
	3
	1.5

Solution

Because this lever is in equilibrium, we know that the effort force at the blue arrow is equal to the resistance weight of the green box. For a lever that's in equilibrium, one method of calculating mechanical advantage (MA) is to divide the length of the effort arm (E_a) by the length of the resistance arm (R_a):

MA = \( \frac{E_a}{R_a} \) = \( \frac{9 ft.}{6 ft.} \) = 1.5

When a lever is in equilibrium, the torque from the effort and the resistance are equal. The equation for equilibrium is R_ad_a = R_bd_b where a and b are the two points at which effort/resistance is being applied to the lever.

In this problem, R_a and R_b are such that the lever is in equilibrium meaning that some multiple of the weight of the green box is being applied at the blue arrow. For a lever, this multiple is a function of the ratio of the distances of the box and the arrow from the fulcrum. That's why, for a lever in equilibrium, only the distances from the fulcrum are necessary to calculate mechanical advantage.

If the lever were not in equilibrium, you would first have to calculate the forces and distances necessary to put it in equilibrium and then divide E_a by R_a to get the mechanical advantage.

3 What's the mechanical advantage of a wedge that's 2 inches wide and 8 inches long?

83% Answer Correctly

	1
	4
	8
	7

Solution

The mechanical advantage (MA) of a wedge is its length divided by its thickness:

MA = \( \frac{l}{t} \) = \( \frac{8 in.}{2 in.} \) = 4

4 If the radius of the axle is 7 and the radius of the wheel is 12, what is the mechanical advantage of this wheel and axle configuration?

52% Answer Correctly

	7
	5
	-5
	1.71

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 12 and the output radius (where the resistance is being applied) is 7 for a mechanical advantage of \( \frac{12}{7} \) = 1.71

Which class of lever is used to increase force on an object in the same direction as the force is applied?

52% Answer Correctly

	all of these
	third
	first
	second

Solution

A second-class lever is used to increase force on an object in the same direction as the force is applied. This lever requires a smaller force to lift a larger load but the force must be applied over a greater distance. The fulcrum is placed at one end of the lever and mechanical advantage increases as the object being lifted is moved closer to the fulcrum or the length of the lever is increased. An example of a second-class lever is a wheelbarrow.