ASVAB Mechanical Comprehension Simple Machines Practice Test 857315 Results

Your Results Global Average
Questions 5 5
Correct 0 3.00
Score 0% 60%

Review

1 How much resistance could a 100 lb. effort force lift using a block and tackle pulley that has 8 ropes supporting the resistance?
82% Answer Correctly
880 lbs.
266 lbs.
800 lbs.
802 lbs.
Solution

The mechanical advantage (MA) of a block and tackle pulley is equal to the number of times the effort force changes direction. An easy way to count how many times the effort force changes direction is to count the number of ropes that support the resistance which, in this problem, is 8. With a MA of 8, a 100 lbs. effort force could lift 100 lbs. x 8 = 800 lbs. resistance.

2 If a 60 lbs. weight is placed 9 ft. from the fulcrum at the blue arrow and the green box is 4 ft. from the fulcrum, how much would the green box have to weigh to balance the lever?
61% Answer Correctly
0 lbs.
270 lbs.
135 lbs.
33.75 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:

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

Ra = \( \frac{R_bd_b}{d_a} \) = \( \frac{60 lbs. \times 9 ft.}{4 ft.} \) = \( \frac{540 ft⋅lb}{4 ft.} \) = 135 lbs.

3 If the green box weighs 75 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
32.14 lbs.
525 lbs.
64.29 lbs.
0 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 = \( \frac{R_ad_a}{d_b} \) = \( \frac{75 lbs. \times 6 ft.}{7 ft.} \) = \( \frac{450 ft⋅lb}{7 ft.} \) = 64.29 lbs.

4 What is the power output of a 6 hp engine that's 90% efficient?
40% Answer Correctly
2970 \( \frac{ft⋅lb}{s} \)
990 \( \frac{ft⋅lb}{s} \)
15 \( \frac{ft⋅lb}{s} \)
11880 \( \frac{ft⋅lb}{s} \)
Solution
\( Efficiency = \frac{Power_{out}}{Power_{in}} \times 100 \)
Solving for power out: \( P_{o} = \frac{E \times P_{i}}{100} \)
Knowing that 1 hp = 550 \( \frac{ft⋅lb}{s} \), Pi becomes 6 hp x 550 \( \frac{ft⋅lb}{s} \) = 3300 \( \frac{ft⋅lb}{s} \)
\( P_{o} = \frac{E \times P_{i}}{100} = \frac{90 \times 3300 \frac{ft⋅lb}{s}}{100} \) \( = \frac{297000 \frac{ft⋅lb}{s}}{100} \) = 2970 \( \frac{ft⋅lb}{s} \)
5 If the green box weighs 55 lbs. and 10 lbs. of force is applied 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?
55% Answer Correctly
5.09 ft.
2.55 ft.
1.27 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:

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

da = \( \frac{R_bd_b}{R_a} \) = \( \frac{10 lbs. \times 7 ft.}{55 lbs.} \) = \( \frac{70 ft⋅lb}{55 lbs.} \) = 1.27 ft.