Mechanical Comprehension and Physics Flashcards

A hydraulic lift is used to raise a 2,000 kg vehicle. The input piston has a surface area of 5 cm², and the output piston supporting the vehicle has a surface area of 500 cm². What is the minimum force that must be applied to the input piston to lift the vehicle? (Use g ≈ 10 m/s²)

Answer: 200 N

This problem is an application of Pascal's Principle, which states that pressure applied to an enclosed fluid is transmitted undiminished throughout the fluid. The pressure (P) is Force (F) per unit Area (A), so P = F/A. The pressure on the input piston (P_in) equals the pressure on the output piston (P_out). Therefore, F_in / A_in = F_out / A_out. First, calculate the force on the output piston (the weight of the vehicle): F_out = mass × g = 2,000 kg × 10 m/s² = 20,000 N. Now, solve for F_in: F_in = F_out × (A_in / A_out) = 20,000 N × (5 cm² / 500 cm²) = 20,000 N × (1 / 100) = 200 N.

Three gears are arranged in a line. Gear A has 10 teeth and drives Gear B, which has 20 teeth. Gear B then drives Gear C, which has 5 teeth. If Gear A rotates clockwise at 100 RPM, what is the rotational speed and direction of Gear C?

Answer: 200 RPM, clockwise

When one gear drives another, they rotate in opposite directions. So, if A is clockwise, B is counter-clockwise, and C is clockwise. For gear speeds, the relationship is (Speed A × Teeth A) = (Speed B × Teeth B). First, find Speed B: (100 RPM × 10) = (Speed B × 20), so Speed B = 50 RPM. Now, use Speed B to find Speed C: (Speed B × Teeth B) = (Speed C × Teeth C), so (50 RPM × 20) = (Speed C × 5). This gives 1000 = 5 × Speed C, so Speed C = 200 RPM. Therefore, Gear C rotates at 200 RPM in a clockwise direction.

A block is at rest on an inclined plane. Which of the following forces is responsible for preventing the block from sliding down the plane?

Answer: Static friction

Static friction is the force that opposes the initiation of motion between two surfaces in contact. In this scenario, the component of gravity parallel to the inclined plane is trying to pull the block down, but the force of static friction acts in the opposite direction (up the plane) to keep it stationary. The normal force acts perpendicular to the surface, and kinetic friction would only apply if the block were already sliding.

A sailor uses a single fixed pulley system to lift a 150 N load of supplies. Assuming the system is ideal (no friction), what is the minimum effort force the sailor must apply to lift the load?

Answer: 150 N

A single fixed pulley has a mechanical advantage of 1. This means it does not reduce the magnitude of the force required to lift the load. Its primary purpose is to change the direction of the applied force, making it more convenient to pull down rather than lift up. Therefore, the effort force required is equal to the load's weight, which is 150 N.

Which of the following physical principles best explains why a ship made of steel can float on water?

Answer: Archimedes' Principle

Archimedes' Principle states that the buoyant force on a submerged or floating object is equal to the weight of the fluid displaced by the object. A ship floats because its hull displaces a large volume of water. The weight of this displaced water creates an upward buoyant force that is equal to the total weight of the ship, allowing it to float, even though the steel it's made from is much denser than water.

An object is dropped from a great height. As it falls, its velocity increases until it reaches a constant speed, known as terminal velocity. At this point, which statement is true?

Answer: The force of air resistance equals the force of gravity.

Terminal velocity is reached when the net force on a falling object becomes zero, resulting in zero acceleration (constant velocity). The two main forces acting on the object are gravity (pulling it down) and air resistance (pushing it up). As the object's speed increases, air resistance increases. Terminal velocity occurs when the upward force of air resistance becomes equal in magnitude to the downward force of gravity. The net force is then zero, and the object stops accelerating.