| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.16 |
| Score | 0% | 63% |
| 8.5 | |
| 10.5 | |
| 7.7 | |
| 7 |
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 = \( \frac{d_e}{d_r} \) = \( \frac{56 ft.}{8 ft.} \) = 7
If the handles of a wheelbarrow are 3 ft. from the wheel axle, what force must you exert to lift the handles if it's carrying a 270 lb. load concentrated at a point 0.5 ft. from the axle?
810 lbs |
|
90 lbs |
|
45 lbs |
|
0.83 lbs |
This problem describes a second-class lever and, for a second class lever, the effort force multiplied by the effort distance equals the resistance force multipied by the resistance distance: Fede = Frdr. Plugging in the variables from this problem yields:
Fe x 3 ft. = 270 lbs x 0.5 ft
Fe = 135 ft-lb. / 3 ft
Fe = 45 lbs
Two or more pulleys used together are called:
block and tackle |
|
gears |
|
wheel and axle |
|
third-class lever |
Two or more pulleys used together constitute a block and tackle which, unlike a fixed pulley, does impart mechanical advantage as a function of the number of pulleys that make up the arrangement. So, for example, a block and tackle with three pulleys would have a mechanical advantage of three.
| 43.75 lbs. | |
| 58.33 lbs. | |
| 350 lbs. | |
| 175 lbs. |
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 Ra, our missing value, and plugging in our variables yields:
Ra = \( \frac{R_bd_b}{d_a} \) = \( \frac{35 lbs. \times 5 ft.}{1 ft.} \) = \( \frac{175 ft⋅lb}{1 ft.} \) = 175 lbs.
Depending on where you apply effort and resistance, the wheel and axle can multiply:
speed or power |
|
force or speed |
|
force or distance |
|
power or distance |
If you apply the resistance to the axle and the effort to the wheel, the wheel and axle will multiply force and if you apply the resistance to the wheel and the effort to the axle, it will multiply speed.