Forces and their interactions, work done and elasticity：練習問題

An object has a mass of \(5 \text{ kg}\). Calculate its weight on Earth, where the gravitational field strength is approximately \(9.8 \text{ N/kg}\).

A force of \( 12 \text{ N} \) is applied to a spring, causing it to stretch by \( 0.04 \text{ m} \). Calculate the spring constant \( k \) of the spring, assuming it is within the limit of proportionality.

A spring has a spring constant of \(50\, \text{N/m}\). It is stretched by \(0.1\, \text{m}\). Calculate the elastic potential energy stored in the spring, provided the limit of proportionality is not exceeded.

Which statement correctly describes the relationship between the weight and mass of an object?

Which of the following factors would increase the braking distance of a car but have no effect on the thinking distance?

Explain the difference between distance and displacement in terms of scalar and vector quantities.

A velocity-time graph shows an object accelerating from \(0 \text{ m/s}\) to \(12 \text{ m/s}\) in a time of \(4 \text{ s}\). Calculate the acceleration of the object and state the correct units.

A spring stores \( 4 \text{ J} \) of elastic potential energy when it is extended by \( 0.4 \text{ m} \). Calculate the spring constant, \( k \), of the spring.

A car is travelling along a straight road at a constant speed.

(a) Use Newton's First Law to explain the relationship between the driving force and the resistive forces acting on the car.
(b) The car later accelerates. Describe how the resultant force must change to cause this acceleration.

A van with a mass of \( 2000 \text{ kg} \) accelerates from rest to a speed of \( 30 \text{ m/s} \) in \( 15 \text{ seconds} \).

(a) Calculate the acceleration of the van.
(b) Calculate the resultant force required to produce this acceleration using Newton's Second Law \( F = ma \).
(c) Explain why the actual driving force provided by the engine must be greater than the resultant force calculated in part (b).