# Calculus

A 20 meter long steel cable has density 2 kg per meter. It is hanging straight down. There is a 100 kg bucket of concrete attached to the bottom. How much work is required to lift the bucket 10 meters by lifting the cable ten meters? Gravitational force equals 9.8 in this problem. I tried to do the integration, separately for the top half and bottom half of the rope, but it didn't work.

1. 0
2. 0
3. 5
1. hanging mass = 100 + 2 x

F = g(100+2x)

do dW = F dx from x = 0 to x = 20

W = g (100 x + x^2) at 20 - at 0
= g (2000 + 400)
= g (2400) = 23520 Joules

then from x = 0 to x = 10
g (1000 + 100) = 1100 g = 10780 Joules

subtract I get 12740 Joules

1. 0
2. 0
posted by Damon
2. Why do you subtract the 2 integrals?

1. 0
2. 0
posted by Andre

## Similar Questions

1. ### Calculus

A factory is located on one bank of a straight river that is 2000 m wide. On the opposite bank but 4500 m downstream is a power station from which the factory draws its electricity. Assume that it costs \$3 per meter to lay an
2. ### Physics

A 100.0 meter long transmission cable is suspended between two towers. If the mass density is 2.00 kg/m and the tension in the cable is , what is the speed in m/s of waves on the cable?
3. ### physics

What hanging mass will stretch a 1.6 meter long, 0.66cm diameter steel wire by 1.4cm.? Need answer in kg. ( this is all that is in the question , no other hints given).
4. ### physics

Help: A 2 meter long, uniform bar with a mass of 46 kg is suspended from a pin so it can rotate freely. It is supported by a cable half a meter from the end. Find the tension force in the cable and the magnitude and direction of
5. ### calculus

A cable runs along the wall from C to P at a cost of \$3 per meter, and straight from P to M at a cost of \$5 per meter. If M is 16 meters from the nearest point A on the wall where P lies, and A is 50 mters from C, find the
6. ### physics

A silver bar 0.125 meter long is subjected to a temperature change from 200 C to 100 C. What will be the length of the bar after the temp change? A:0.124764 meter B:0.00023635 meter C: 0.00002363 meter D:0.0000189 meter
7. ### math

a parabolic bridge over a road is 4 meter tall 4 meter wide and 5 meter long determain the maximum height of a 2 meter truck can drive under the bridge
8. ### Physics

a 10m long steel cable is lifting a 30 ton crate upward off a ship. If the cable streches by .5cm under these conditions, determine the radius of the steel cable. Young's modulus of steel :2x10raised to 9 Pa
9. ### physics

A hollow steel buoy in thee form of a sphere of radius 0.5m is fixed by a wire to the base of a river. If the mass of the buoy is 20kg, calculate the tension in the cable. (Take density of water=1000 kilograms per cubic meter).
10. ### math

The diameter of a hydrogen atom is about 5×10^-11 meter. Suppose 8.4×10^8 hydrogen atoms were arranged side by side in a straight line. Multiply these numbers to find the length of this line of atoms. What is the length in

More Similar Questions