Forces

A trolley has a mass of $6.0\,\text{kg}$ and moves with a velocity of $2.5\,\text{m/s}$ east. State which of these two quantities is a vector.

A scale drawing uses $1.0\,\text{cm}$ to represent $4.0\,\text{N}$. Describe the arrow that represents a force of $20\,\text{N}$ acting vertically downwards.

A cyclist's speedometer reads $11\,\text{m/s}$ while the cyclist travels south-west. Give the cyclist's speed and velocity, and explain why these are different quantities even though their magnitudes match.

State whether friction and gravitational force are contact or non-contact forces.

A magnet attracts an iron pin across a small gap. Describe the force interaction between the magnet and the pin.

A parachutist is falling through the air while attached to an open parachute by cords. Name one non-contact force and two different contact forces acting in this situation, giving the object on which each named force acts.

A $7.5\,\text{kg}$ bag is in a region where $g=9.8\,\text{N/kg}$. Calculate the bag's weight.

A sample has mass $2.4\,\text{kg}$. Its weight is $23.5\,\text{N}$ at location A and $3.8\,\text{N}$ at location B. Calculate the gravitational field strength at each location.

An explorer has mass $68\,\text{kg}$. A newtonmeter would show $666\,\text{N}$ for the explorer on planet P and $177\,\text{N}$ on moon Q. Determine $g$ at P and Q, then explain what happens to the explorer's mass during the journey.

Two horizontal forces act on a crate: $16\,\text{N}$ east and $9\,\text{N}$ west. Calculate the resultant force.

A model boat is pulled forwards by $42\,\text{N}$. Water resistance is $27\,\text{N}$ and air resistance is $6\,\text{N}$, both backwards. Determine the resultant force on the boat.

Forces on a rail cart are $85\,\text{N}$ east, $34\,\text{N}$ west and $19\,\text{N}$ west. Calculate the resultant, then state the additional single force needed to make the forces balanced.

A horizontal force of $35\,\text{N}$ moves a box $4.0\,\text{m}$ horizontally. Calculate the work done by the force.

A winch lifts a load vertically through $6.5\,\text{m}$ using a constant upward force of $480\,\text{N}$. Calculate the work done and identify the energy store that increases.

A powered trolley moves $12\,\text{m}$ along a level floor. Its motor provides a forward force of $180\,\text{N}$ while friction is $140\,\text{N}$. Calculate the work done by the motor, the energy transferred thermally by friction and the remaining energy transferred to the trolley's kinetic energy store.

A spring's length changes from $0.18\,\text{m}$ to $0.23\,\text{m}$. Calculate its extension.

Within its linear region, a spring extends by $0.075\,\text{m}$ when a force of $18\,\text{N}$ is applied. Calculate the spring constant and predict the extension produced by $12\,\text{N}$.

A spring of constant $240\,\text{N/m}$ is stretched by $0.18\,\text{m}$ without exceeding its limit of proportionality. Calculate the applied force and the elastic potential energy stored. State what observation after unloading would show that the spring had instead been inelastically deformed.

A force of $28\,\text{N}$ acts perpendicular to a handle $0.35\,\text{m}$ from its pivot. Calculate the moment.

A seesaw is balanced. A child of weight $360\,\text{N}$ sits $1.5\,\text{m}$ to the left of the pivot. Calculate how far to the right of the pivot a child of weight $450\,\text{N}$ must sit.

A uniform $4.0\,\text{m}$ beam of weight $220\,\text{N}$ is supported at its left end and at a point $3.2\,\text{m}$ from the left end. A $300\,\text{N}$ load is placed at the right end. Calculate the upward force from the support at $3.2\,\text{m}$.

A gas pushes normally on a hatch with force $240\,\text{N}$. The hatch area is $0.080\,\text{m}^2$. Calculate the pressure.

A liquid exerts a normal force of $54\,\text{N}$ on a sensor of area $30\,\text{cm}^2$. Calculate the pressure on the sensor.

A sealed chamber produces the same normal force of $1260\,\text{N}$ on either of two removable panels. Panel X measures $0.30\,\text{m}$ by $0.20\,\text{m}$ and panel Y measures $0.45\,\text{m}$ by $0.35\,\text{m}$. Calculate the pressure on each panel and determine which panel experiences the lower pressure.

Oil has density $820\,\text{kg/m}^3$. Calculate the pressure due to a $1.5\,\text{m}$ column of the oil when $g=9.8\,\text{N/kg}$.

Two pressure sensors are $0.40\,\text{m}$ and $2.10\,\text{m}$ below the surface of a liquid of density $960\,\text{kg/m}^3$. Calculate the pressure difference when $g=9.8\,\text{N/kg}$.

A fully submerged cuboid is $0.30\,\text{m}$ high and has horizontal top and bottom areas of $0.012\,\text{m}^2$. It is in water of density $1000\,\text{kg/m}^3$, where $g=9.8\,\text{N/kg}$. Calculate the pressure difference between its bottom and top, use this to calculate the upthrust, and predict its initial motion if its weight is $30\,\text{N}$.

State what microscopic event produces atmospheric pressure on a window.

Explain why a barometer records a lower atmospheric pressure at the top of a tall mountain than at sea level.

At high altitude, the pressure inside a sealed case is $101\,\text{kPa}$ and the atmospheric pressure outside is $75\,\text{kPa}$. A flat lid has area $0.012\,\text{m}^2$. Calculate the resultant force on the lid and state its direction.

A walker travels $14\,\text{m}$ north and then $5\,\text{m}$ south. Determine the distance and displacement.

A robot moves $6.0\,\text{m}$ east and then $8.0\,\text{m}$ north. Calculate its distance and the magnitude and direction of its displacement.

A survey drone flies $600\,\text{m}$ east, $250\,\text{m}$ west and then $120\,\text{m}$ north. Calculate the total distance and the magnitude and direction of its displacement from launch.

A toy car travels $24\,\text{m}$ in $6.0\,\text{s}$ at constant speed. Calculate its speed.

A runner covers $300\,\text{m}$ in $48\,\text{s}$, rests for $12\,\text{s}$ and then covers another $200\,\text{m}$ in $32\,\text{s}$. Calculate the average speed for the whole interval.

A delivery drone travels $1.8\,\text{km}$ to a site in $2\,\text{min}\ 20\,\text{s}$. It waits for $30\,\text{s}$, then returns along the same route at a constant $15\,\text{m/s}$. Calculate its average speed for the complete trip from departure to return.

A train moves north at a speed of $18\,\text{m/s}$. State its velocity.

A cart moves $50\,\text{m}$ east and then $20\,\text{m}$ west in a total time of $10\,\text{s}$. Calculate its average velocity.

A rescue vehicle travels $90\,\text{m}$ east and then $120\,\text{m}$ north in $30\,\text{s}$. Calculate the magnitude and direction of its average velocity, and compare this with its average speed.

A runner travels $156\,\text{m}$ in $48\,\text{s}$ at constant speed. Calculate the gradient of the distance–time graph.

A distance–time graph is a straight line from $(0\,\text{s},0\,\text{m})$ to $(24\,\text{s},120\,\text{m})$. It is then horizontal for $8\,\text{s}$. State what happens during the horizontal section and calculate the speed during the first section.

A robot moves along a straight track. Its distance from the start is $0\,\text{m}$ at $0\,\text{s}$, $54\,\text{m}$ at $12\,\text{s}$, $150\,\text{m}$ at $28\,\text{s}$ and $150\,\text{m}$ at $40\,\text{s}$. The graph joins these points with straight lines. Calculate the speed in each time interval and the average speed over all $40\,\text{s}$.

A scooter increases its velocity from $3.0\,\text{m s}^{-1}$ to $15.0\,\text{m s}^{-1}$ in $8.0\,\text{s}$. Calculate its average acceleration.

A velocity–time graph rises uniformly from $0$ to $12\,\text{m s}^{-1}$ in $4.0\,\text{s}$, stays horizontal for $6.0\,\text{s}$, then falls uniformly to $0$ in $3.0\,\text{s}$. Determine the acceleration in each section.

A train accelerates uniformly from $8.0\,\text{m s}^{-1}$ to $20.0\,\text{m s}^{-1}$ while travelling $168\,\text{m}$. Calculate its acceleration and the time taken.

A boat moves at constant velocity. Its propeller provides a forward force of $680\,\text{N}$. Determine the total resistive force.

A van travels in a straight line at a steady $18\,\text{m s}^{-1}$. The engine force is $920\,\text{N}$. Explain the motion in terms of the forces and state the resultant force.

A lift moves upward. The motor force is $6200\,\text{N}$ upward, its weight is $5800\,\text{N}$ and friction is $400\,\text{N}$ downward. Describe its motion. The motor force then falls to $5000\,\text{N}$ while the lift is still moving upward. Calculate the new resultant force and describe the change in motion.

A resultant force accelerates a $12\,\text{kg}$ object at $1.5\,\text{m s}^{-2}$. Calculate the resultant force.

A student uses a wheeled cart, a pulley and slotted masses to investigate how force affects acceleration while total mass stays constant. Describe how the student should change the force, measure the acceleration and improve the reliability of the results. State the expected relationship.

A $1250\,\text{kg}$ car increases its velocity from $8.0\,\text{m s}^{-1}$ to $26.0\,\text{m s}^{-1}$ in $9.0\,\text{s}$. The resistive forces total $700\,\text{N}$. Calculate the acceleration, the resultant force and the engine force.

A hammer exerts a downward force on a nail. State the corresponding Newton's Third Law force.

A book rests on a table. The Earth pulls the book downward. Identify the Newton's Third Law partner to this force and explain why it is not the table's upward force on the book.

A propeller pushes water backward with a force of $4.2\,\text{kN}$. The water resistance on the boat is $1.8\,\text{kN}$ backward and the boat's mass is $1200\,\text{kg}$. State the third-law force exerted by the water because of the propeller interaction, then calculate the boat's acceleration.

A driver's thinking distance is $12\,\text{m}$ and the braking distance is $28\,\text{m}$. Calculate the stopping distance.

A car travels at $15\,\text{m s}^{-1}$. The driver's reaction time is $0.64\,\text{s}$ and the braking distance is $19\,\text{m}$. Calculate the thinking distance and the stopping distance.

A delivery van has a reaction time of $0.75\,\text{s}$. At $20\,\text{m s}^{-1}$ its braking distance is $32\,\text{m}$; at $25\,\text{m s}^{-1}$ its braking distance is $50\,\text{m}$. Calculate the stopping distance at each speed and the increase in stopping distance.

State the typical range of human reaction times and give one factor that can increase a driver's reaction time.

A driver travels at $22\,\text{m s}^{-1}$ and reacts in $0.48\,\text{s}$. Calculate the thinking distance.

A student measures reaction time four times without a distraction and obtains $0.31$, $0.29$, $0.30$ and $0.89\,\text{s}$. With a distraction the results are $0.44$, $0.47$, $0.45$ and $0.46\,\text{s}$. Identify the anomalous result, calculate suitable mean times and evaluate the effect of the distraction.

Give one example of poor vehicle condition that increases braking distance and explain why it does so.

The average braking force on a car is $6200\,\text{N}$ on a dry road and $3100\,\text{N}$ on a wet road. The car has the same initial speed in both tests and stops in $18\,\text{m}$ on the dry road. Estimate the wet-road braking distance.

For one car in fixed conditions, measured braking distances are $6.2\,\text{m}$ at $10\,\text{m s}^{-1}$, $13.9\,\text{m}$ at $15\,\text{m s}^{-1}$ and $24.8\,\text{m}$ at $20\,\text{m s}^{-1}$. Show that the data are consistent with braking distance being proportional to speed squared, then estimate the distance at $25\,\text{m s}^{-1}$.

Describe the main energy transfer when friction in a vehicle's brakes brings the vehicle to rest.

A $1100\,\text{kg}$ car travels at $18\,\text{m s}^{-1}$. Its average braking force is $6600\,\text{N}$. Calculate its initial kinetic energy and the braking distance, assuming all of this energy is removed by the braking force.

A $1500\,\text{kg}$ car travelling at $22\,\text{m s}^{-1}$ is stopped by an average braking force of $8250\,\text{N}$. Calculate the braking distance and the magnitude of the deceleration. Explain one danger of increasing the braking force substantially.

A $0.18\,\text{kg}$ ball moves at $12\,\text{m s}^{-1}$. Calculate its momentum.

A $1350\,\text{kg}$ car travels west at $16\,\text{m s}^{-1}$. Calculate its momentum, including direction.

Vehicle A has mass $720\,\text{kg}$ and travels east at $18\,\text{m s}^{-1}$. Vehicle B has mass $1080\,\text{kg}$ and travels west at $11\,\text{m s}^{-1}$. Taking east as positive, calculate each momentum and determine which has the greater momentum magnitude and by how much.

A $2.0\,\text{kg}$ trolley moving at $3.0\,\text{m s}^{-1}$ collides with a stationary $1.0\,\text{kg}$ trolley. They stick together. Calculate their common velocity.

A $0.75\,\text{kg}$ trolley moving right at $6.4\,\text{m s}^{-1}$ catches a $1.25\,\text{kg}$ trolley moving right at $1.6\,\text{m s}^{-1}$. The trolleys lock together. Determine their final velocity.

A launcher of mass $3.8\,\text{kg}$ and a $0.20\,\text{kg}$ projectile are initially at rest. The projectile is fired horizontally at $32\,\text{m s}^{-1}$. Calculate the launcher's recoil velocity.

A $0.35\,\text{kg}$ ball moving at $8.0\,\text{m s}^{-1}$ is brought to rest in $0.10\,\text{s}$. Calculate the magnitude of the average force.

A $0.16\,\text{kg}$ ball travels toward a wall at $12\,\text{m s}^{-1}$ and rebounds at $8.0\,\text{m s}^{-1}$. Contact lasts $0.050\,\text{s}$. Calculate the magnitude and direction of the average force on the ball.

A $950\,\text{kg}$ vehicle travelling at $14\,\text{m s}^{-1}$ stops in a collision. A rigid structure would stop it in $0.080\,\text{s}$, while a crumple zone increases the stopping time to $0.32\,\text{s}$. Calculate the average force magnitude in each case and explain the safety benefit of the crumple zone.