In the figure, a spring of spring constant 3.10 x 10ª N/m is between a rigid beam and the output piston of a hydraulic lever. An empty container with negligible mass sits on the input piston. The input piston has area A¡, and the output piston has area 21.0A;. Initially the spring is at its rest length. How many kilograms of sand must be (slowly) poured into the container to compress the spring by 5.60 cm? Beam Container Spring,

A tank has the shape of an inverted circular cone with height 7 m and base radius 3 m. It filled w water. Set up the integral form, don't evaluate it, for the work required to empty the tank by pumping all of the water to the top of a tank. (The density of water is 1000 kg/m³ and the acceleration due to gravity is 9.8 m/s²). 9800 7 S 9800 9800 49 9 - 49 * (7 — x)² dx 9 (7-2)²dx 49 (7 — x)² dx 7 9 [²3/10 S 49 -(7 — x)³ dx 7 9 √2/2 49 -(7 — x)² dx

A woman of m = 58 kg stands on the ice. The contact area between her skate and the ice is A = 0.0047 m2. a. Express the force that the person exerts on the ice, F, in terms of m and g. You do not need to include the force of the column of air above her.

garbage worker tears the arm off a droid. he throws it down a garbage chute and it lands in trash filled with nasty smelly liquids. the overall density is 840kg/m^3. if the arm has a desnity of 5460kg/m^3 and is a cylinder with the volume of 0.0330m^3 what is the buyoncy force in newtons acting on the arm?

Assume that a raindrop has a volume of 0.05 cm^3 and you need an Avogadro's number of raindrops to fill up the cubic water tank. What is the length of the edge of the tank?

You put a marble on a balance and find it has a mass of 1.2 grams.  It is an irregular shape, so you need to do displacement to find its volume. You put it in a graduated cylinder with a starting volume of 30.0 mL of water. After you add the marble, the water rises to 31.5 mL.  What is the density? Group of answer choices 0.038 g/mL 1.3 g/mL 0.80 g/mL 1.8 g/mL

Answer for a) is 1.06 x 10^6 J The answer for b) is 4.43 x 10^6 J

The aorta carries blood away from the heart and eventually branches into a large number of capillaries that distribute the blood to various body organs. If for an average person, the aorta has a radius of 1.2 cm and blood travels through it at a speed of 45 cm/s and the capillaries have an average radius of 5.0 x 104 cm and blood travels through them at a speed of 0.005 cm/s, determine the approximate number of capillaries in the human body. capillaries Vinuing Sound Work Bovert to I Rocponco