# Density Practice Problems

An oil pump maintains a volume flow rate v through a pipeline of diameter d when the pressure difference is Δp. A mechanic replaced the pipeline with a different one. Both pipelines are of the same length. What pressure difference (Δp_{ new} ) is needed to maintain the same volume flow rate v if the diameter of the new pipeline is half that of the old one?

The steel cable of a wrecker can support a maximum tension of T without breaking. The cable diameter is 3 cm, and the breaking stress is 5 ×** **10^{8} Pa. Find the value of T.

You apply two tangential forces of magnitude 3 × 10^{5} N on the opposite faces of a cubic aluminum box. The dimensions of the box are 6 cm × 6 cm × 6 cm. What is i) the shear strain of the box, and ii) the displacement x (in microns)

Suppose a 1 m^{3} cube of ice is transported without melting from Mount Everest to a location at sea level. The atmospheric pressures at the peak of Mount Everest and at sea level are 0.31 atm and 1 atm, respectively. Determine the change in the volume of ice (ΔV). Take the compressibility k of ice as 5.00 × 10^{-10} Pa^{-1}.

When the car engine starts, the lubricating oil heats up and the pressure decreases by a value of 10^{7} Pa. The initial volume of oil is 5000 cm^{3} and its bulk modulus is 5 x 10^{9} Pa. What is the change in the volume (ΔV) and compressibility (k) of oil?

Two cylinders, A and B, identical in shape but made of different materials, are totally immersed in oil. Cylinder A is made of nickel, while cylinder B is made of brass. The two cylinders are subject to the same pressure change. Determine the ratio of the volume change of cylinder A to that of cylinder B ( ΔV_{A}/ΔV_{B}). The bulk modulus of nickel and brass are 1.70 × 10^{11} Pa and 6.00 × 10^{10} Pa respectively.

During a rescue mission, a firefighter uses an 11 mm diameter cable to lift a 70 kg person. The cable is made of polyester and has an initial length of 50 m. The length of the cable increases by 0.35 m under the weight of the person. Find Young's modulus (Y) of polyester.

A 9.6 mm ring finger tendon shows a tensile strain of 6% when a force of 400 N is applied perpendicular to its surface. Assume that the tendon can be modeled as a cylinder and has Young's modulus of 1.2 × 10^{9} Pa. What is the diameter (d) of the tendon?

A science class wants to study percentage error in measured quantities using a silver cube. They purchase silver worth $100 at a cost of $19.94 per ounce. 1.000 ounce is equal to 28.35 g. The silver is to be molded into a cube that is used to determine the density of silver. What is the theoretical length of the cube?

A cylinder made of unknown material has a diameter of 8.0 cm and a height of 10 cm. An engineer wishes to house an axle at the center of the cylinder. Therefore, they drill a hole of diameter 4.0 cm at the center of the cylinder. The engineer measures the weight of the hollowed cylinder to be 25.0 N. Determine the density of the unknown material.

A male worker can safely lift 250 N at the workplace. A disk is made of copper, and it has a thickness of 1.0 cm and a diameter of 58.0 cm. Will a single male worker safely lift the disk alone? (hint: what is the weight of the disk?)

A maintenance team is analyzing the percentage of a pipe's area that is blocked by pipe scaling. The team measures the pressure at a place before the region characterized by the intense scaling and finds it to be 2.60 × 10^{5} Pa. The pressure at the narrowed area is 2.05 *×* 10^{5} Pa. The team uses flow rate and determines that the fluid flows at 4.0 m/s in the region before the scaling. If the fluid flowing in the pipe has a specific gravity of 0.8976, calculate the percentage of the pipe's area that is occupied by scales.

A city water company pipes water from a raised area using pipes of different diameters. At a point near the source, water flows at a speed of 5 m/s and the pressure is measured to be 4.60 × 10^{4} Pa. At a point 8.0 m below the first point, the company uses a pipe 1.5 times the diameter used at the point near the source. Determine the pressure at this lower point.

A circular concrete tank with a hollow top is connected to a dam in a hydroelectric power plant. The height of the water in the tank is 60.0 m. A pipe of diameter 2.54 cm is connected at the base of the tank. Determine the speed of water as it leaves through the pipe and the volume flowing from the pipe per second.

Room temperature is defined as 25°C. The speed of sound at room temperature is 346 m/s. An engineer is using a sound wave with a frequency of 1000 Hz to tune the sound level in a piece of equipment. i) Determine the wavelength and time for one oscillation in milliseconds. ii) Determine the new wavelength if the frequency is quadrupled.

At t = 0, two waves are traveling toward each other with a speed of 0.4 cm/s on a tight wire as shown below. If each square measures 0.5 cm, what is the most likely shape of the wire at t = 5.0 s.