This worksheet is based on events in the mathematical thriller A Question of Will. Get
it now at:
www.MathNovel.com OverloadedBombTruckWorkedSolution
Question1
First up – how much does a pint of milk weigh? Well, a British pint is about 568 mL, while a United States pint is about 473 mL. Since these are all estimates, let’s split the difference and say a pint is about half a litre and ignore the weight of the plastic container which should be quite light. (1 mark) We should also check the density of milk – about 1.03 kg / L. This is close enough to 1 that we can just assume milk is 1 kg / litre. (1 mark) So a single container will weigh about 0.5 kg. There are 10 containers in a crate – so each crate weighs about 5 kg. Then there are 400 crates in the truck – so the total grocery load is about 2000 kg, or 2 tonnes. (1 mark) Question2
Based on the assumption of Hooke’s law, the weight of the load in the back of the truck should be about 5 times greater than the grocery load – since 20 cm / 4 cm = 5. (1 mark) So the estimated bomb load in the truck is about 5 × 2 tonnes = 10 tonnes. (1 mark) Question3
This third truck has a smaller amount of spring compression, so the expected load in the back should be less: Truck load = spring compression distance / grocery spring compression distance × grocery weight Third truck load = 12 / 4 (1 mark) × 2 tonnes Third truck load = 6 tonnes (1 mark) Question4
The load per truck is 10 tonnes. At 1.25 kg per bottle, that works out to: Number of bottles = number of trucks × truck load weight / weight per bottle Number of bottles = 5 × 10000 / 1.25 Number of bottles = 40000 bottles (1 mark) At a black market price of $20 per bottle: Total black market value = number of bottles × price per bottle Total black market value = 40000 × $20 Total black market value = $800000 (1 mark) All content copyright Michael Milford. See www.MathNovel.com for more information.