Force and Newton’s laws：練習問題

A puck is sliding across a perfectly smooth, frictionless ice surface with a constant velocity of $$5.0\text{ m s}^{-1}$$ towards the east. Which of the following statements correctly describes the net force acting on the puck?

Two blocks, \(M_1\) of mass \(4.0 \text{ kg}\) and \(M_2\) of mass \(2.0 \text{ kg}\), are placed side-by-side on a rough horizontal surface. A constant horizontal pushing force \(P = 42 \text{ N}\) is applied to \(M_1\), pushing both blocks. The coefficient of kinetic friction between the blocks and the surface is uniform, \(\mu_k = 0.20\). Assume the blocks move together.

What is the magnitude of the force exerted by block \(M_1\) on block \(M_2\)? (Take the acceleration due to gravity \(g = 10 \text{ m s}^{-2}\).)

A block of mass \(m = 4.0 \text{ kg}\) is placed on a rough plane inclined at \(30^\circ\) to the horizontal. The coefficient of static friction between the block and the plane is \(0.40\). A horizontal force \(P\) is applied to the block, pushing it towards the incline as shown in the diagram. Determine the maximum magnitude of \(P\) for which the block remains at rest.
(Take the acceleration due to gravity \(g = 9.8 \text{ m s}^{-2}\))

An object has a mass of $$10\text{ kg}$$ on Earth. If the acceleration due to gravity on Earth is $$9.8\text{ m s}^{-2}$$, what is the weight of the object on Earth?

Two forces, \( F_1 = 30 \text{ N} \) and \( F_2 = 40 \text{ N} \), act on a particle of mass \( 5 \text{ kg} \) at the same time. If the two forces are perpendicular to each other, calculate the magnitude of the acceleration of the particle.

A constant net force is applied to an object with a mass of \( 4.0 \text{ kg} \), causing it to accelerate at \( 2.5 \text{ m s}^{-2} \). Calculate the magnitude of this net force.

A spacecraft of mass \( m \) is traveling in deep space where gravitational effects are negligible. If the engines exert a constant thrust \( F \) for a time interval \( \Delta t \), use Newton’s Second Law to derive an expression for the change in velocity \( \Delta v \) of the spacecraft.

Two blocks, A (mass \(m\)) and B (mass \(2m\)), are placed in contact on a frictionless horizontal surface. A constant horizontal force \(F\) is applied to block A, pushing the two blocks together. Determine the magnitude of the force block A exerts on block B in terms of \(F\), and state the Newton's Law used to relate the forces between the two blocks.

A luggage of mass \( 15 \text{ kg} \) is being pulled along a horizontal floor at a constant velocity by a horizontal force of \( 45 \text{ N} \).

(a) Calculate the weight of the luggage. (Take \( g = 9.81 \text{ m s}^{-2} \))

(b) What is the net force acting on the luggage? Explain your answer with reference to Newton’s First Law.

(c) Determine the magnitude of the friction force acting on the luggage.

(d) If the pulling force is increased to \( 75 \text{ N} \) and the friction force remains unchanged, calculate the new acceleration of the luggage.

A heavy box of mass \( 15 \text{ kg} \) is pulled across a flat, rough horizontal surface by a student using a light string. The string makes an angle of \( 20^\circ \) above the horizontal. The coefficient of kinetic friction between the box and the surface is \( 0.35 \). (Take \( g = 9.8 \text{ m s}^{-2} \)) (Imagine a diagram: the box is on the floor, and a force \( T \) is applied diagonally upwards at a \( 20^\circ \) angle to the ground.)

(a) Draw a free-body diagram for the box, showing all forces acting on it. (1 point)

(b) Show that the normal force \( R \) exerted by the floor on the box is \( R = 147 - T \sin 20^\circ \). (1 point)

(c) Determine the tension \( T \) in the string if the box moves at a constant velocity. (1 point)

(d) If the student increases the pulling force to \( T = 75 \text{ N} \), calculate the magnitude of the acceleration of the box. (2 points)