ASVAB Mechanical Comprehension Practice Test 397019 Results

	Your Results	Global Average
Questions	5	5
Correct	0	3.47
Score	0%	69%

Review

Which of the following surfaces would have the lowest coefficient of friction?

85% Answer Correctly

	concrete
	ice
	leather
	tile

Solution

Coefficient of friction (μ) represents how much two materials resist sliding across each other. Smooth surfaces like ice have low coefficients of friction while rough surfaces like concrete have high μ.

An inclined plane increases ___________ to reduce ____________.

58% Answer Correctly

	force, power
	force, distance
	distance, force
	distance, power

Solution

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.

3 60 lbs. of effort is used by a machine to lift a 300 lbs. box. What is the mechanical advantage of the machine?

84% Answer Correctly

	1
	2
	5
	-1

Solution

Mechanical advantage is resistance force divided by effort force:

MA = \( \frac{F_r}{F_e} \) = \( \frac{300 lbs.}{60 lbs.} \) = 5

4 If the green box is 5 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

	0.8
	-2.2
	2.4
	0.4

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 = \( \frac{E_a}{R_a} \) = \( \frac{4 ft.}{5 ft.} \) = 0.8

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.

5 If the green box weighs 65 lbs. and 45 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

	0 ft.
	6.23 ft.
	2.08 ft.
	8.31 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 = \( \frac{R_bd_b}{R_a} \) = \( \frac{45 lbs. \times 3 ft.}{65 lbs.} \) = \( \frac{135 ft⋅lb}{65 lbs.} \) = 2.08 ft.