Forces and their effects：練習問題

A student hangs a mass on a spring and measures the extension. If the spring constant of the spring is \(25\text{ N/m}\) and a force of \(5.0\text{ N}\) is applied, what is the extension of the spring, assuming the limit of proportionality is not exceeded?

A spring has a natural length of \(15.0\text{ cm}\). When a force of \(6.0\text{ N}\) is applied, the length of the spring becomes \(18.0\text{ cm}\). Calculate the force required to stretch the spring to a total length of \(21.5\text{ cm}\), assuming the limit of proportionality is not exceeded.

Use the velocity-time graph below to calculate the total distance travelled by the object over the \(19\text{-second}\) period shown.

A spring has a spring constant \(k\) of \(50\text{ N/m}\). What is the force required to produce an extension of \(0.1\text{ m}\), assuming the limit of proportionality is not exceeded?

An astronaut has a mass of \(70\text{ kg}\). The gravitational field strength on the Moon is approximately \(1.6\text{ N/kg}\). Calculate the weight of the astronaut on the Moon.

State whether velocity and time are scalar or vector quantities.

A courier drives a delivery van \(12\text{ km}\) North along a straight road, then realizes they missed a stop and drives \(15\text{ km}\) South along the same road. Calculate the total distance traveled and the magnitude of the final displacement from the starting point.

A box of mass \(15\text{ kg}\) is pushed across a horizontal floor with a constant force of \(60\text{ N}\). If the box accelerates at a rate of \(2.4\text{ m/s}^2\), calculate the magnitude of the frictional force acting against the motion.

A student uses a spring to investigate the relationship between force and extension. The spring has an original length of 15.0 cm.

(a) The student hangs a weight of 4.0 N on the spring. The new length of the spring becomes 19.0 cm. Calculate the extension of the spring.

(b) Calculate the spring constant \(k\) of this spring using the formula \(F = k \times e\). Give your answer in N/cm.

(c) Weight is a force acting on an object due to gravity. State the equation used to calculate the weight of an object if its mass and the gravitational field strength are known.

A wooden crate with a mass of \(25\text{ kg}\) is being pushed across a horizontal floor. The person pushing the crate exerts a forward force of \(85\text{ N}\). There is a constant frictional force of \(20\text{ N}\) acting against the motion.

(a) Determine the resultant force acting on the crate.
(b) Calculate the acceleration of the crate.