A plastic "boat" with a square cross section floats in a liquid. One by one, you place masses inside the boat and measure how far the boat extends below the surface. Your data are as follows:
Draw an appropriate graph of the data and, from the slope and intercept of the best-fit line, determine the mass of the boat and the density of the liquid.
Therefore, the length of bottle above the water is
The expression for Buoyancy force acting on a submerged object in a liquid is,
Here, is density of the fluid, is displaced volume of the liquid due to object, and is acceleration due to gravity.
Convert the radius of the soda bottle from centimeter to meter.
Convert the volume of soda from mile-liters to liters.
Using Archimedes' Principle, the floating force equals to the weight of the liquid displaced. A half full soda can is floating because it displaces at least half can volume of water plus a bit more to support the can's own weight.
The volume of the soda can is,
Here, / is the length of the soda can.
If we change the volume to . One liter is , the volume of soda can is , so we have calculated the length of the can from the above equation:
As the soda can is half full with water, it is immersed half-length / to support the half full of water and plus a bit more as a result of the weight of the can itself.
Here, the mass density of water and is the gravitational acceleration. Solve the equation for .
The length of the can above water is
Disk brakes, such as those in your car, operate by using pressurized oil to push outward on a piston. The piston, in turn, presses brake pads against a spinning rotor or wheel, as seen in . Consider a industrial grinding wheel, in diameter, spinning at . The brake pads are actuated by diameter pistons, and they contact the wheel an average distance from the axis. If the coefficient of kinetic friction between the brake pad and the wheel is , what oil pressure is needed to stop the wheel in ?
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