Let's solve Question 3 about the bottle opener lever. A bottle opener works as a lever system where we apply force at the handle to create a moment that opens the bottle cap. We're given that the minimum moment needed is 5 Newton meters, the distance from pivot to hand is 10 centimeters, and the distance from pivot to cap is 1 centimeter.
Now let's solve part A. We need to find the minimum force the hand must exert. Using the principle of moments, the moment created by the hand must equal the required moment of 5 Newton meters. Since moment equals force times distance, we have F hand times 0.1 meters equals 5 Newton meters. Solving for F hand, we get 5 divided by 0.1, which equals 50 Newtons.
Now for part B, we need to find the force exerted by the bottle opener on the cap. Using the same moment principle, the moment at the cap must equal the required 5 Newton meters. Since the distance from pivot to cap is 1 centimeter or 0.01 meters, we have F cap times 0.01 equals 5. Solving this gives us F cap equals 500 Newtons. Notice the force amplification - the opener multiplies the 50 Newton hand force by 10 times to produce 500 Newtons at the cap.
Now let's move to Question 4 about a ladder leaning against a wall. We have a uniform ladder in contact with a smooth wall at point A and rough ground at point B. Point A is 3.6 meters from the ground, point B is 1.2 meters from the wall, and the ladder weighs 54 Newtons. Since the wall is smooth, there's no friction there, but the ground is rough so friction exists at point B.
Let's solve parts A and B together. For part A, since the ladder is uniform, its center of gravity is at the midpoint. The perpendicular distance from the wall to the center of gravity is half the horizontal distance, which is 1.2 divided by 2 equals 0.6 meters. For part B, we use the principle of moments about point B. The clockwise moment from the weight is 54 times 0.6 equals 32.4 Newton meters. The anti-clockwise moment from the wall reaction is R A times 3.6. For equilibrium, these moments are equal, so R A equals 32.4 divided by 3.6, which gives us 9 Newtons.