Jan Dangerfield, Stuart Haring and, Julian Gilbey Solutions for Exercise 2: EXERCISE 5A

A car of mass $2000 \mathrm{kg}$ pulls a caravan of mass $1200 \mathrm{kg}$ along a straight horizontal road. The resistance on the car is $20 \mathrm{N}$ and the resistance on the caravan is $80 \mathrm{N}.$ The maximum possible driving force from the car's engine is $1900 \mathrm{N}.$ The tow-bar will break if the tension exceeds $680 \mathrm{N}.$

Find the maximum possible driving force before the tow-bar breaks.

A car of mass $2000 \mathrm{kg}$ pulls a caravan of mass $1200 \mathrm{kg}$ along a straight horizontal road. The resistance on the car is $20 \mathrm{N}$ and the resistance on the caravan is $80 \mathrm{N}.$ The maximum possible driving force from the car's engine is $1900 \mathrm{N}.$ The tow-bar will break if the tension exceeds $680 \mathrm{N}.$ Find the maximum possible acceleration.

A $15 \mathrm{kg}$ mass hangs in equilibrium on a heavy chain. The chain is modeled as ten $1 \mathrm{kg}$ masses joined by short rods of negligible mass. Including the connection at each end of the chain, this makes $11$ short rods. Work out the tension in each of the $11$ short rods. Take $g=10 \mathrm{m} {\mathrm{s}}^{-2}$.

A horizontal bar of mass $1 \mathrm{kg}$ hangs from a pair of parallel vertical rods, of negligible mass, attached to either end of the bar. A third vertical rod is connected to the middle of the bar and a $4 \mathrm{kg}$ mass hangs from this, below the rod. Work out the tension in each of the rods.

A train consists of an engine and five carriages. The engine has mass $100000 \mathrm{kg}$ and each carriage has mass $20000 \mathrm{kg}.$ The engine produces a driving force of $350000 \mathrm{N}.$ The resistance force on the engine is $10000 \mathrm{N}$ and the resistance on each carriage is $2000 \mathrm{N}.$ The train moves in a straight line on a horizontal track. Find the tension in the coupling between the third carriage and the fourth carriage. Take $g=10 \mathrm{m} {\mathrm{s}}^{-2}$.
 

A car pulls a caravan up a hill. The slope of the hill makes an angle $\theta$ with the horizontal, where $\mathrm{sin\theta }=\frac{1}{20}.$ The car has mass $1900 \mathrm{kg}$ and the caravan has mass $600 \mathrm{kg}.$ The driving force from the engine of the car is $1200 \mathrm{N}.$ The resistance on the car is $20 \mathrm{N}$ and that on the caravan is $80 \mathrm{N}.$ Find the force in the tow-bar and state whether it is a tension force or a thrust force. Take $g=10 \mathrm{m} {\mathrm{s}}^{-2}$.
 

A car tows a caravan down a hill. The slope of the hill makes an angle $\mathrm{\theta }$ with the horizontal, where $\mathrm{sin\theta }=\frac{1}{20}.$ The car has mass $1900 \mathrm{kg}$ and the caravan has mass $600 \mathrm{kg}.$ The car is braking, so the driving force from the engine of the car is negative. This braking force is $250 \mathrm{N}$ (a driving force of $-250 \mathrm{N}$). The resistance on the car is $20 \mathrm{N}$ and that on the caravan is $80 \mathrm{N}.$ Find the force in the tow-bar and state whether it is a tension force or a thrust force. Take $g=10 \mathrm{m} {\mathrm{s}}^{-2}$.

A car tows a caravan down a hill. The slope of the hill makes an angle $\mathrm{\theta }$ with the horizontal, where $\mathrm{sin\theta }=0.05.$ The force from the car's engine is a braking force (a negative driving force). The car has mass $1800 \mathrm{kg}$ and the caravan has mass $600 \mathrm{kg}.$ The resistance on the car is $20 \mathrm{N}$ and that on the caravan is $80 \mathrm{N}.$ The force in the tow-bar is a thrust of $50 \mathrm{N}.$ Show that the force from the car's engine is $-420 \mathrm{N}.$ Take $g=10 \mathrm{m} {\mathrm{s}}^{-2}$.