ASVAB Mechanical Comprehension Practice Test 597665 Results

	Your Results	Global Average
Questions	5	5
Correct	0	3.26
Score	0%	65%

Review

1 If the green arrow in this diagram represents 550 ft⋅lb of work, how far will the box move if it weighs 110 pounds?

72% Answer Correctly

	2 ft.
	22 ft.
	20 ft.
	5 ft.

Solution

The Law of Work states that the work put into a machine is equal to the work received from the machine under ideal conditions. In equation form, that's:

W_in = W_out
F_effort x d_effort = F_resistance x d_resistance

In this problem, the effort work is 550 ft⋅lb and the resistance force is 110 lbs. and we need to calculate the resistance distance:

W_in = F_resistance x d_resistance
550 ft⋅lb = 110 lbs. x d_resistance
d_resistance = \( \frac{550ft⋅lb}{110 lbs.} \) = 5 ft.

2 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

	0.72
	0.8
	2.8
	0.88

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.

Two gears are connected and the smaller gear drives the larger gear. The speed of rotation will __________ and the torque will __________.

61% Answer Correctly

	increase, increase
	decrease, increase
	decrease, decrease
	increase, decrease

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.

4 If input effort is 200 ft⋅lb, what output effort will be produced by a machine with a mechanical advantage of 6?

79% Answer Correctly

	0ft⋅lb
	300ft⋅lb
	600ft⋅lb
	1200 ft⋅lb

Solution

Mechanical advantage is the ratio of output force to input force and tells us by how many times a machine multiplies input effort. So, a machine with a mechanical advantage of 6 will multiply an input effort of 200 ft⋅lb by 6 to produce an output effort of 1200 ft⋅lb.

5 If the green box weighs 30 lbs. and 30 lbs. of force is applied 5 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

	15 ft.
	5 ft.
	20 ft.
	0 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 = \( \frac{R_bd_b}{R_a} \) = \( \frac{30 lbs. \times 5 ft.}{30 lbs.} \) = \( \frac{150 ft⋅lb}{30 lbs.} \) = 5 ft.