Please help me with these problems! I don't know why, but I can't get them!
2. When a particle is located a distance x meters from the origin, a force of cos (pix/3)newtons acts on it. How much work is done in moving the particle from x=1 to x=2? Interpret your answer by considering the work done from x=1 to x=1.5 and from x=1.5 to x=2.
5. A force of 10 lb is required to hold a spring stretched 4 in. beyond its natural length. How much work is done in stretching it form its natural length to 6 in. beyond its natural length?
7. Suppose that 2 J of work is needed to stretch a spring from its natural length of 30 cm to a length of 42 cm. a) How much work is needed to stretch it from 35 cm to 40 cm? b) How far beyond its natural length will a force of 30 N keep the spring stretched?
10. A chain lying on the ground is 10 m long and its mass is 80 kg. How much work is required to raise one end of the chain to a height of 6m?
12. A bucket that weights 4 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 trate of 2 ft/s, but water leaks out of a hole in the bucket at a rate of .2 lb/s. Find the work done in pulling the bucket to the top of the well.
15. An aquarium 2 m long, 1 m wide, and 1 m deep is full of water. Find the work needed to pump half of the water out of the aquarium. (Use the fact that density of water is 1000 kg/cubic meter.)
24. A vertical plate is submerged in water and has the shape of a right triangle (4 ft across, 3 ft down, and 1 ft below the surface of the water). Explain how to approximate the hydrostatic force against one sid of e the palte by a Riemann sum. Then epress the force as an integral and evaluate it.
28. A large tank is designed with ends in the shape of the region between the curves y=(x-squared)/2 and y=12, measured in feet. Find the hydrostatic force on one end of the tank if it is filled to a depth of 8 ft with gasoline. (Assume the gasoline's density is 42 lb/cubic feet.)
33. The mass mi is located on the point pi. Find the moments Mx and My and the center of mass of the system.
m1=6, m2= 5, m3=10;
P1(1,5), P2(3,-2), P3(-2,-1)
36. Sketch the region bounded by the curves, and visually estimate the location of the centroid. Then find the exact coordinates of the centroid.
3x+2y=6, y=0, x=0
(With this one, I just need help with finding the exact coordinates of the centroid.)
21. a)Newtonâs Law of Gravitation states that two bodies with masses m1 and m2 attract each other with a force
F=G(m1m2/r2)
where r is the distance between the bodies and G is the gravitational constant. IF one of the bodies is fixed, find the work needed to move the other from r=a to r=b.
b) Compute the work required to launch a 1000-kg satellite vertically to an orbit 1000 km high. You may assume that Earthâs mass if 5.98X1024 kg and is concentrated at its center. Take the radius of Earth to be 6.37X106 m and G=6.67X10-11 Nm2/kg2.
Even if you can only answer one, it is GREATLY APPRECIATED!
THANKS!