ASVAB Mechanical Comprehension Practice Test 367013 Results

	Your Results	Global Average
Questions	5	5
Correct	0	3.05
Score	0%	61%

Review

The steering wheel of a car is an example of which type of simple machine?

89% Answer Correctly

	fixed pulley
	first-class lever
	wheel and axle
	block and tackle

Solution

A wheel and axle uses two different diameter wheels mounted to a connecting axle. Force is applied to the larger wheel and large movements of this wheel result in small movements in the smaller wheel. Because a larger movement distance is being translated to a smaller distance, force is increased with a mechanical advantage equal to the ratio of the diameters of the wheels. An example of a wheel and axle is the steering wheel of a car.

2 What is the power output of a 5 hp engine that's 50% efficient?

40% Answer Correctly

	4125 \( \frac{ft⋅lb}{s} \)
	250 \( \frac{ft⋅lb}{s} \)
	0 \( \frac{ft⋅lb}{s} \)
	1375 \( \frac{ft⋅lb}{s} \)

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 \( \frac{ft⋅lb}{s} \), P_i becomes 5 hp x 550 \( \frac{ft⋅lb}{s} \) = 2750 \( \frac{ft⋅lb}{s} \)
\( P_{o} = \frac{E \times P_{i}}{100} = \frac{50 \times 2750 \frac{ft⋅lb}{s}}{100} \) \( = \frac{137500 \frac{ft⋅lb}{s}}{100} \) = 1375 \( \frac{ft⋅lb}{s} \)

3 If the green box weighs 50 lbs. and 65 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

	3.9 ft.
	1.95 ft.
	0.98 ft.
	15.6 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 = \( \frac{R_bd_b}{R_a} \) = \( \frac{65 lbs. \times 3 ft.}{50 lbs.} \) = \( \frac{195 ft⋅lb}{50 lbs.} \) = 3.9 ft.

4 If A = 9 ft., B = 3 ft., C = 8 ft., the green box weighs 35 lbs. and the blue box weighs 50 lbs., what does the orange box have to weigh for this lever to balance?

44% Answer Correctly

	20.63 lbs.
	6.88 lbs.
	0 lbs.
	41.25 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:

f_Ad_A = f_Bd_B + f_Cd_C

For this problem, this equation becomes:

35 lbs. x 9 ft. = 50 lbs. x 3 ft. + f_C x 8 ft.

315 ft. lbs. = 150 ft. lbs. + f_C x 8 ft.

f_C = \( \frac{315 ft. lbs. - 150 ft. lbs.}{8 ft.} \) = \( \frac{165 ft. lbs.}{8 ft.} \) = 20.63 lbs.

5 If the green arrow in this diagram represents 360 ft⋅lb of work, how far will the box move if it weighs 180 pounds?

73% Answer Correctly

	90 ft.
	1 ft.
	2 ft.
	45 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 360 ft⋅lb and the resistance force is 180 lbs. and we need to calculate the resistance distance:

W_in = F_resistance x d_resistance
360 ft⋅lb = 180 lbs. x d_resistance
d_resistance = \( \frac{360ft⋅lb}{180 lbs.} \) = 2 ft.