MAT 21B Lecture Notes - Lecture 14: Specific Weight
MAT 21B – Lecture 14 – Physics Application of the Definite Integral on Work
• Work, W is the force, F exerted on an object times the distance, d such that W =
F * d. The weight of an object acts as the force in situations like these.
• There are two types of problems associated with work
o 1) The work, dW, done on an object, B by the position dependent force,
when the coordinate of B changes by dx is The
differential, dx represents a tiny distance.
o 2) The work, dW, done lifting an object of weight, dm, and height, h(x) is
The differential, dm represents a tiny force.
• Example: Calculate the work done in lifting a 100 feet chain that weighs 200 lb.
The linear weight density of the chain is
Then, the weight, m(x)
of the remaining chain after x feet has been pulled up is (100 – x) *
. The
work done pulling up the chain C is
To convert this value into calories:
.
• Example 2: How many calories does it take to build a pyramid of height 2 feet
with a base of 3 feet? The density of the brick is
.
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Mat 21b lecture 14 physics application of the definite integral on work: work, w is the force, f exerted on an object times the distance, d such that w = The differential, dm represents a tiny force: 2) the work, dw, done lifting an object of weight, dm, and height, h(x) is (cid:2869)(cid:2868)(cid:2868) =(cid:884)(cid:3039)(cid:3029). The linear weight density of the chain is =(cid:2870)(cid:2868)(cid:2868) (cid:3039)(cid:3029) of the remaining chain after x feet has been pulled up is (100 x) * (cid:884)(cid:3039)(cid:3029). The work done pulling up the chain c is (cid:1849)= (cid:1856)(cid:1849)= (cid:1865)(cid:4666)(cid:1876)(cid:4667)(cid:1856)(cid:1876)= (cid:884)(cid:4666)(cid:883)(cid:882)(cid:882) (cid:2869)(cid:2868)(cid:2868)(cid:2868) (cid:2869)(cid:2868)(cid:2868)(cid:2868) (cid:4666)(cid:883)(cid:882)(cid:882) (cid:1876)(cid:4667)(cid:1856)(cid:1876) (cid:1876)(cid:4667)(cid:1856)(cid:1876)=(cid:884) . The density of the brick is (cid:887) (cid:3039)(cid:3029)2: example 2: how many calories does it take to build a pyramid of height 2 feet. The height, h(y) for one slab is y feet and the width of one slab, (cid:1875)(cid:4666)(cid:1877)(cid:4667)=(cid:885) (cid:2871)(cid:2870)(cid:1877).