Final answer:
To lift a 100 kg friend 30 meters high with a 200 N exertion force, one could use a pulley system or a lever with a mechanical advantage of five. The pulley system would require a 150-meter long rope, while the lever would need a 5:1 length ratio between your side and your friend's side.
Step-by-step explanation:
To lift your friend who has a mass of 100 kg, 30 meters off the ground, you would need to design a machine that could apply a force greater than the gravitational force acting on your friend. The gravitational force (weight) can be calculated as Weight (W) = mass (m) × gravity (g), which is 100 kg × 9.8 m/s2 = 980 N. Since you can exert a force of 200 N with your arms, you would need a force multiplier, such as a pulley system or lever system, to lift your friend.
One option is to use a pulley system with a mechanical advantage (MA) of five, meaning you would need five pulleys. This would divide the force necessary to lift your friend by five, requiring you to only exert a force of 196 N, which is slightly less than your maximum capacity. To lift your friend 30 meters using this system would require a length of rope 150 meters long (5 × 30 meters) to pull through the pulleys.
Another option is to use a lever with a long enough arm to achieve the same mechanical advantage. If you use a lever, the length on your side must be five times longer than your friend's side, meaning that for every meter your friend is lifted, you would need to travel five meters.
The energy required for lifting your friend will be determined by the formula Energy (E) = Weight × height (h), which is 980 N × 30 m = 29400 J. This calculation assumes no friction or other losses.