ASVAB Mechanical Comprehension Simple Machines Practice Test 558270 Results

Your Results Global Average
Questions 5 5
Correct 0 3.15
Score 0% 63%

Review

1 If the green box weighs 15 lbs. and is 6 ft. from the fulcrum, how much force would need to be applied at the blue arrow to balance the lever if the arrow's distance from the fulcrum is 7 ft.?
62% Answer Correctly
51.43 lbs.
12.86 lbs.
25.71 lbs.
105 lbs.
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:

Rada = Rbdb

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

Rb = \( \frac{R_ad_a}{d_b} \) = \( \frac{15 lbs. \times 6 ft.}{7 ft.} \) = \( \frac{90 ft⋅lb}{7 ft.} \) = 12.86 lbs.

2 What is the mechanical advantage of this inclined plane if the length of the ramp is 28 ft. and the height of the green box is 4 ft.?
82% Answer Correctly
10
7
14
7.7
Solution

The mechanical advantage (MA) of an inclined plane is the effort distance divided by the resistance distance. In this case, the effort distance is the length of the ramp and the resistance distance is the height of the green box:

MA = \( \frac{d_e}{d_r} \) = \( \frac{28 ft.}{4 ft.} \) = 7

3 The green box weighs 35 lbs. and a 45 lbs. weight is placed 7 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?
57% Answer Correctly
9 ft.
27 ft.
2.25 ft.
3 ft.
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:

Rada = Rbdb

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

da = \( \frac{R_bd_b}{R_a} \) = \( \frac{45 lbs. \times 7 ft.}{35 lbs.} \) = \( \frac{315 ft⋅lb}{35 lbs.} \) = 9 ft.

4 If A = 11 ft., B = 2 ft., C = 7 ft., the green box weighs 25 lbs. and the blue box weighs 45 lbs., what does the orange box have to weigh for this lever to balance?
44% Answer Correctly
26.43 lbs.
275 lbs.
6.61 lbs.
0 lbs.
Solution
In order for this lever to balance, the torque acting on each side of the fulrum must be equal. So, the torque produced by A must equal the torque produced by B and C. Torque is weight x distance from the fulcrum which means that the following must be true for the lever to balance:

fAdA = fBdB + fCdC

For this problem, this equation becomes:

25 lbs. x 11 ft. = 45 lbs. x 2 ft. + fC x 7 ft.

275 ft. lbs. = 90 ft. lbs. + fC x 7 ft.

fC = \( \frac{275 ft. lbs. - 90 ft. lbs.}{7 ft.} \) = \( \frac{185 ft. lbs.}{7 ft.} \) = 26.43 lbs.

5 What is the efficiency of a machine has work input of 145 ft⋅lb and work output of 36 ft⋅lb?
68% Answer Correctly
4%
25%
0%
12%
Solution
Due to friction, a machine will never be able to utilize 100% of its work input. A certain percentage of that input will be lost in overcoming friction within the machine. Effeciency is a measure of how much of a machine's work input can be turned into useful work output and is calculated by dividing work output by work input and multiplying the result by 100:
\( Efficiency = \frac{Work_{out}}{Work_{in}} \times 100 \) \( = \frac{36 ft⋅lb}{145 ft⋅lb} \times 100 \) \( = 25% \) %