A student uses a bottle opener to find that a force of 15 N must be exerted to lift a cap 1.4mm. The opener has a velocity ratio of 16 and efficiency of 90%
(a) What is the mechanical advantage of the opener?
(b) What force is applied to the bottle cap?
(c) How far does the handle of the opener move?
The velocity ratio is 16, so the distance that the hand moves the bottle opener is
0.0015 m x 16 = .0.024 m. The energy expended lifting the cap is
E = (0.024 m)(15 N) = 0.36 J
(a) The mechanical advantage is the ratio of the force applied to the cap to the force applied to the opener. That equals 0.9 x 16 = 14.4
(b) The force applied to the cap is 0.9 * 16 * 15 N = 2160 N
(c) Multiply the velocity ratio (16) by the distance that the cap moves.
in part (b) you have considered force applied to be load shouldn't it be the effort put in to open the bottle.
Hence making it 15/0.9*16
No, the force applied to the bottle cap gets reduced by the efficiency factor, 0.9. However I did the multiplication incorrectly. It should be 216 N
To answer these questions, we need to understand the concepts of mechanical advantage, force, and work. The mechanical advantage (MA) of a machine is the ratio of the output force to the input force.
(a) To find the mechanical advantage of the opener, we can use the formula MA = Velocity ratio / efficiency. Given that the velocity ratio is 16 and the efficiency is 90%, we have:
MA = 16 / 0.90
= 17.78 (rounded to two decimal places)
Therefore, the mechanical advantage of the opener is approximately 17.78.
(b) To find the force applied to the bottle cap, we can use the formula Force = MA × Input force. Given that the input force is 15 N and the mechanical advantage is 17.78, we have:
Force = 17.78 × 15
≈ 266.70 N
Therefore, the force applied to the bottle cap is approximately 266.70 N.
(c) To find how far the handle of the opener moves, we can use the formula Work = Force × Distance. The work done on the bottle cap is equal to the force applied multiplied by the distance the cap is lifted. Rearranging the formula, we have:
Distance = Work / Force
Given that the force is 15 N and the distance the cap is lifted is 1.4 mm, we first need to convert the distance to meters:
1.4 mm = 1.4 × 10⁻³ m
Then, we can calculate the distance:
Distance = (15 N) × (1.4 × 10⁻³ m) / (266.70 N)
≈ 0.0000787 m
Therefore, the handle of the opener moves approximately 0.0000787 meters.