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Speed of Toast

 
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songul



Joined: 23 Jun 2007
Posts: 2

PostPosted: Sat Jun 23, 2007 8:25 pm    Post subject: Speed of Toast Reply with quote

I have been working on a problem recently. The problem is how fast does a slice of bread need to be thrown against a wall to generate enough heat to toast the bread?
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hepcj
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Joined: 23 Jun 2007
Posts: 125

PostPosted: Sat Jun 23, 2007 8:29 pm    Post subject: Re: Speed of Toast Reply with quote

Assuming the bread is moving at a constant velocity, v, it has momentum p= mv where m is the mass of the slice of bread. After hitting the wall, the bread comes to a halt, and so its momentum is zero. If the wall does not move backward after the collision, then the energy of motion has been converted into heat.
The heat energy required to toast the bread can be found by making some toast and taking a note of the time it takes to toast the bread and the power of the toaster. The energy required to toast the bread is E=VIt where t is the time required to toast the bread, V is the voltage of the toaster and I is the current. Alternatively, the toast might have a power rating P in Watts therefore E = P*t. (P around 1800 W for Dualit toaster).
This energy has to be the same as the kinetic energy of the bread, which is given by E = 0.5 mv^2.
Therefore, the velocity of the bread is:
v = sqrt((2*V*I*t)/m) or v = sqrt(2*P*t)/m)
Assuming the weight of the slice of bread is 0.03 kg, P = 1800 W * 90 sec = 16200 J.
v = sqrt(16200/0.03)
= (5.4 E+6 )^0.5
= 2324 m/s or over 2.3 km/s or 13,248 mph.

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