ASVAB Mechanical Comprehension Practice Test 143738 Results

Your Results Global Average
Questions 5 5
Correct 0 2.89
Score 0% 58%

Review

1 If the green box weighs 60 lbs. and is 3 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 6 ft.?
62% Answer Correctly
30 lbs.
15 lbs.
120 lbs.
360 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 = \( \frac{R_ad_a}{d_b} \) = \( \frac{60 lbs. \times 3 ft.}{6 ft.} \) = \( \frac{180 ft⋅lb}{6 ft.} \) = 30 lbs.

2 If the force applied at the blue arrow over 6 ft. moves the green box 3.0 ft., what is the mechanical advantage of this lever?
55% Answer Correctly
6
1
2
2.2
Solution

Mechanical advantage (MA) can be calculated knowing only the distance the effort (blue arrow) moves and the distance the resistance (green box) moves. The equation is:

MA = \( \frac{E_d}{R_d} \)

where Ed is the effort distance and Rd is the resistance distance. For this problem, the equation becomes:

MA = \( \frac{6 ft.}{3.0 ft.} \) = 2

You might be wondering how having an effort distance of 2 times the resistance distance is an advantage. Remember the principle of moments. For a lever in equilibrium the effort torque equals the resistance torque. Because torque is force x distance, if the effort distance is 2 times the resistance distance, the effort force must be \( \frac{1}{2} \) the resistance force. You're trading moving 2 times the distance for only having to use \( \frac{1}{2} \) the force.

3 The green box weighs 15 lbs. and a 20 lbs. weight is placed 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?
57% Answer Correctly
0 ft.
1.67 ft.
6.67 ft.
2.22 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 = \( \frac{R_bd_b}{R_a} \) = \( \frac{20 lbs. \times 5 ft.}{15 lbs.} \) = \( \frac{100 ft⋅lb}{15 lbs.} \) = 6.67 ft.

4

Which of the following is the formula for torque?

61% Answer Correctly

τ = r/F

τ = F/r

τ = F/r2

τ = rF
Solution

Torque measures force applied during rotation: τ = rF.  Torque (τ, the Greek letter tau) = the radius of the lever arm (r) multiplied by the force (F) applied. Radius is measured from the center of rotation or fulcrum to the point at which the perpendicular force is being applied. The resulting unit for torque is newton-meter (N-m) or foot-pound (ft-lb).

5 If the radius of the axle is 7 and the radius of the wheel is 8, what is the mechanical advantage of this wheel and axle configuration?
52% Answer Correctly
-1
0.88
1.14
7
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 8 and the output radius (where the resistance is being applied) is 7 for a mechanical advantage of \( \frac{8}{7} \) = 1.14