ASVAB Mechanical Comprehension Practice Test 613174 Results

	Your Results	Global Average
Questions	5	5
Correct	0	2.97
Score	0%	59%

Review

1 A 300 lb. barrel is rolled up a 8 ft. ramp to a platform that's 3 ft. tall. What effort is required to move the barrel?

53% Answer Correctly

	123.8 lbs.
	56.3 lbs.
	120.5 lbs.
	112.5 lbs.

Solution

This problem describes an inclined plane and, for an inclined plane, the effort force multiplied by the effort distance equals the resistance force multipied by the resistance distance:

F_ed_e = F_rd_r

Plugging in the variables from this problem yields:

F_e x 8 ft. = 300 lbs. x 3 ft.
F_e = \( \frac{900 ft⋅lb}{8 ft.} \) = 112.5 lbs.

2 If a 35 lbs. weight is placed 7 ft. from the fulcrum at the blue arrow and the green box is 8 ft. from the fulcrum, how much would the green box have to weigh to balance the lever?

61% Answer Correctly

	15.31 lbs.
	7.66 lbs.
	245 lbs.
	30.63 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_a, our missing value, and plugging in our variables yields:

R_a = \( \frac{R_bd_b}{d_a} \) = \( \frac{35 lbs. \times 7 ft.}{8 ft.} \) = \( \frac{245 ft⋅lb}{8 ft.} \) = 30.63 lbs.

3 If the green box is 2 ft. from the fulcrum and a certain force applied 4 ft. from the fulcrum at the blue arrow balances the lever, what is the mechanical advantage?

61% Answer Correctly

	2.2
	0.67
	-2
	2

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 = \( \frac{E_a}{R_a} \) = \( \frac{4 ft.}{2 ft.} \) = 2

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.

Coplanar forces:

62% Answer Correctly

	act in a common plane
	act along the same line of action
	have opposite dimensions
	pass through a common point

Solution

Collinear forces act along the same line of action, concurrent forces pass through a common point and coplanar forces act in a common plane.

The work done by the sum of all forces acting on a particle equals the change in the kinetic energy of the particle. This defines which of the following?

60% Answer Correctly

	conservation of mechanical energy
	work-energy theorem
	Pascal's law
	mechanical advantage

Solution

The work-energy theorem states that the work done by the sum of all forces acting on a particle equals the change in the kinetic energy of the particle. Simply put, work imparts kinetic energy to the matter upon which the work is being done.