Forces and their interactions：練習問題

In physics, quantities are categorized as either scalars or vectors. Which of the following is a vector quantity?

In physics, quantities are classified as either scalars or vectors. Which of the following groups contains only vector quantities?

A uniform beam of length \(2.0\text{ m}\) is pivoted at its midpoint. A load of \(50\text{ N}\) is placed \(0.4\text{ m}\) from the left end of the beam. A second load, \(W\), is placed at a distance of \(0.8\text{ m}\) from the pivot on the right side to keep the beam in equilibrium. Calculate the weight of \(W\).

A block of mass \(4.0\text{ kg}\) is pulled along a frictionless horizontal floor by a constant force of \(18\text{ N}\) acting to the right. Simultaneously, a second horizontal force of \(6.0\text{ N}\) acts on the block to the left. Calculate the acceleration of the block.

A car with a mass of \(1200\text{ kg}\) is traveling at a constant velocity of \(15\text{ m/s}\). The driver applies the brakes, providing a constant braking force that brings the car to a complete stop in \(4.0\text{ s}\). Calculate the magnitude of the average resultant force acting on the car during this time.

Calculate the weight of a \(75\text{ kg}\) astronaut on the Moon, where the gravitational field strength is \(1.6\text{ N/kg}\).

An object remains stationary on a horizontal surface when a horizontal force of \(15\text{ N}\) is applied. Explain the relationship between the applied force and the frictional force using vector terminology and identify the non-contact force acting on the object.

Calculate the total extension, in millimetres, of a system consisting of two identical springs connected in series when a \(6.0\text{ N}\) force is applied. Each spring has a spring constant \(k = 300\text{ N/m}\).

A student performs an experiment to investigate Hooke's Law using a metal spring.
(a) The original length of the spring is \(12.0\text{ cm}\). When a force of \(6.0\text{ N}\) is applied, the length becomes \(15.0\text{ cm}\). Calculate the spring constant \(k\) in \(\text{N/m}\).
(b) The student continues to add weights until the spring is permanently deformed. State the name of the point beyond which the spring no longer returns to its original shape.
(c) Explain the difference between scalar and vector quantities, and identify whether 'force' and 'extension' are scalars or vectors.

A small object with a mass of \(0.20\text{ kg}\) is released from rest in a tall cylinder filled with oil. A velocity-time graph of its motion would show the speed increasing at a decreasing rate until it becomes constant.

(a) Calculate the weight of the object. Take the gravitational field strength \(g = 9.8\text{ N/kg}\).
(b) At the instant the object is released, the upward drag force is zero. State the magnitude and direction of the resultant force acting on the object at this precise moment.
(c) As the object falls, it eventually reaches a constant speed known as terminal velocity. At this speed, the upward drag force is equal to the downward weight. Explain, using Newton’s First Law, why the velocity of the object remains constant at this point.
(d) If the object is replaced with a more streamlined version of the same mass, explain how the terminal velocity would be affected.