Forces and Newton’s Laws: Physics 0625 (Cambridge O Level / IGCSE)

A skater is moving across smooth ice at a constant velocity in a straight line. At one instant, a friend pushes her forward with a horizontal force of $65\text{ N}$, while air resistance acts on her with a horizontal force of $65\text{ N}$ in the opposite direction. What is the resultant force on the skater at this instant, and what happens to her velocity as a result?

A cyclist rides her bicycle along a flat, straight road.

(a) State the name of two different resistive forces that act on the cyclist and bicycle as she rides along, and briefly state what causes each one. [2]

(b) The cyclist's brakes work by pressing rubber brake blocks against the wheel rims. Describe, in terms of friction, the effect this contact has on the motion of the wheel, and describe one other effect this friction has on the brake blocks and wheel rims themselves. [2]

(c) While cycling, the cyclist pedals so that the forward driving force from the wheels is exactly balanced by the total resistive force acting on her. State what this tells you about her speed, and explain your answer by referring to the resultant force and Newton's first law. [2]

(d) The cyclist then pedals harder so that the forward driving force increases to $230\text{ N}$, while the total resistive force stays at $205\text{ N}$. Calculate the resultant force now acting on the cyclist and bicycle, and state the effect this has on her speed. [2]

A student investigates how a spring stretches under different loads. She clamps the spring vertically with its top end fixed, and fixes a metre rule vertically alongside the spring so that she can read off its length.

(a) State two other pieces of apparatus the student needs for this experiment (in addition to the spring, clamp stand and metre rule), and describe how she uses the metre rule to obtain an accurate length reading for each load. [3]

(b) The table below shows her results.

Calculate the extension of the spring for each of the loads $1.0\text{ N}$, $2.0\text{ N}$, $3.0\text{ N}$ and $4.0\text{ N}$. [2]

(c) The student plots a graph of extension (vertical axis) against load (horizontal axis) using these results. Describe the shape of this graph, and state what this shape shows about the relationship between the load and the extension over this range of loads. [2]

A go-kart and its driver have a combined mass of $180\text{ kg}$. The go-kart's engine provides a forward driving force of $640\text{ N}$. As the go-kart moves along a straight, flat track, a total resistive force (from friction and air resistance) of $100\text{ N}$ acts against its motion.

(a) Calculate the resultant force acting on the go-kart. [2]

(b) Calculate the acceleration of the go-kart produced by this resultant force. [2]

(c) State the direction of this acceleration, and explain how you can tell this from the resultant force. [2]

(d) The driver then releases the accelerator so that the engine no longer provides any driving force, although the resistive force of $100\text{ N}$ still acts on the go-kart. State and explain what now happens to the go-kart's speed. [2]

A spring is tested in a laboratory. The table shows the load applied to the spring and the resulting extension.

(a) Use the results for loads from $0$ to $8.0\text{ N}$, where the extension is directly proportional to the load, to calculate the spring constant, $k$, of the spring in $\text{N/cm}$. [2]

(b) State which load in the table is beyond the limit of proportionality for this spring, and explain your answer by referring to the pattern in the data. [2]

(c) A second, different spring has a spring constant of $k = 4.0\text{ N/cm}$. Calculate the extension produced when a load of $9.0\text{ N}$ is hung from this spring. [2]

(d) A small ball is whirled around at a constant speed in a horizontal circle on the end of a string, the string providing the force needed to keep the ball moving on this circular path. The ball is then replaced with a second ball of greater mass, which is whirled at the same speed around a circle of the same radius. State and explain what must happen to the force provided by the string on the second ball, compared with the first. [2]

A crate rests on a smooth (frictionless) workshop floor. Three ropes pull on it horizontally, all along the same straight line. One rope pulls the crate to the right with a force of $20\text{ N}$. The other two ropes pull the crate to the left, with forces of $8\text{ N}$ and $5\text{ N}$. What is the resultant force acting on the crate, and in which direction does it act?

A worker in a workshop sands a wooden plank by pushing a sanding block back and forth across its surface.

(a) State the effect that friction has on the motion of the sanding block as it is pushed across the plank, and state the direction friction acts in, relative to the block's motion. [2]

(b) State one other effect that this friction has, referring to energy. [2]

(c) The worker then drags a wooden crate of mass $25\text{ kg}$ across the workshop floor at a slow, constant velocity, by applying a horizontal pushing force of $85\text{ N}$. State the size of the friction force acting on the crate, and explain your answer using the resultant force and Newton's first law. [2]

(d) The worker pushes harder, so the pushing force increases to $110\text{ N}$ while the friction force stays at $85\text{ N}$. Calculate the resultant force now acting on the crate. [1]

(e) Calculate the acceleration of the crate produced by this resultant force. [1]

A technician tests two different springs, P and Q, by hanging various loads from each and measuring the extension produced. Both springs obey Hooke's law over the full range of loads shown. The results are given in the table below.

For each spring, a graph of load, $F$ (vertical axis), against extension, $x$ (horizontal axis), gives a straight line through the origin, and the gradient of this line is equal to the spring constant.

(a) Using two points from the table for spring P, calculate the gradient of its load-extension line, and hence state its spring constant $k_P$, in N/cm. [2]

(b) Using two points from the table for spring Q, calculate the gradient of its load-extension line, and hence state its spring constant $k_Q$, in N/cm. [2]

(c) State which spring, P or Q, is stiffer, and explain how the spring constants found in (a) and (b) show this. [2]

(d) Assuming spring P continues to obey Hooke's law beyond a load of $8.0\text{ N}$, calculate the extension it would produce for a load of $11.0\text{ N}$. [2]

A force acting on an object can change its speed, its direction of motion, or its shape (or some combination of these). Which of the following examples shows a force changing an object's shape only, without changing its speed or its direction of motion?

A ball of mass $0.20\text{ kg}$ is attached to one end of a string and whirled around in a horizontal circle of radius $0.80\text{ m}$ at a constant speed of $4.0\text{ m/s}$. The tension in the string provides the resultant force that keeps the ball moving along this circular path.

(a) State the direction of the resultant force acting on the ball at any instant, relative to the ball's velocity at that instant. [1]

(b) Explain, in terms of the resultant force described in (a), why the ball's speed stays constant even though a resultant force is continuously acting on it. [2]

(c) The string is then shortened so that the ball moves at the same constant speed of $4.0\text{ m/s}$, but now on a circle of smaller radius. State and explain what happens to the size of the force needed to keep the ball moving on this smaller circle, compared with the original circle. [2]

(d) While the ball is moving on the circular path, the string suddenly breaks. Describe the subsequent motion of the ball immediately after the string breaks, and explain your answer in terms of the forces now acting on it (ignore gravity and air resistance). [2]