1). A spring has a natural length of 30 cm. If a 23 -N force is required to keep
ID: 2844826 • Letter: 1
Question
1). A spring has a natural length of 30 cm. If a 23-N force is required to keep it stretched to a length of 38 cm, how much work W is required to stretch it from 30 cm to 34 cm? (Round your answer to two decimal places.)
2)A tank is full of water. Find the work required to pump the water out of the spout. (Use 9.8 m/s2 for g. Use 1000 kg/m3 as the density of water. Assume r = 6 m and h = 2 m.)
3) A bucket that weighs 6 lb and a rope of negligible weight are used to draw water from a well that is 80 ft deep. The bucket is filled with 40 lb of water and is pulled up at a rate of 1.5 ft/s, but water leaks out of a hole in the bucket at a rate of 0.15 lb/s. Find the work done in pulling the bucket to the top of the well.
Show how to approximate the required work by a Riemann sum. (Enter xi* as xi.)
( )?x
Express the work as an integral.
Evaluate the integral.
( )ft-lb
4) Find the derivative of the function. Simplify where possible.
A spring has a natural length of 30 cm. If a 23-N force is required to keep it stretched to a length of 38 cm, how much work W is required to stretch it from 30 cm to 34 cm? (Round your answer to two decimal places.) A tank is full of water. Find the work required to pump the water out of the spout. (Use 9.8 m/s2 for g. Use 1000 kg/m3 as the density of water. Assume r = 6 m and h = 2 m.) A bucket that weighs 6 lb and a rope of negligible weight are used to draw water from a well that is 80 ft deep. The bucket is filled with 40 lb of water and is pulled up at a rate of 1.5 ft/s, but water leaks out of a hole in the bucket at a rate of 0.15 lb/s. Find the work done in pulling the bucket to the top of the well. Show how to approximate the required work by a Riemann sum. (Enter xi* as xi.) Express the work as an integral. Evaluate the integral. Find the derivative of the function. Simplify where possible. y = 7arctan(x - sqrt(1 + x^2))Explanation / Answer
Ok, here's how you do it:
First, you know that:
W=(kx^2)/2
Where
W = Work
k = spring constant
x = change of length of the spring.
So first we must find k:
k=F/x
where F is force, then
k=26N/(26cm-20cm)=433.3 N/m
now we can calculate the work made by the spring:
W= (kx^2)/2 = ((433.3N/m)(30cm-20cm)^2)/2 = 2.17 J
So it is required 2.17 J of work in order to stretch the spring from 20cm to 30cm.
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2). F = m a...thus the weight of the water is [ 9.8 x 1000 ] per cubic meter
work = force x distance = [ 9.8 x10^3 ] { ? ( 12y - y
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