Chapter 12

Find the mass density of a chunk of rock of mass \(215 \mathrm{~g}\) that displaces a volume of \(75.0 \mathrm{~cm}^{3}\) of water.

A packing crate \(2.50 \mathrm{~m} \times 0.80 \mathrm{~m} \times 0.45 \mathrm{~m}\) weighs \(1.41 \times 10^{5} \mathrm{~N}\). Find the stress (in kPa) exerted by the crate on the floor in each of its three possible positions.

A block of wood is \(55.9\) in. \(\times 71.1\) in. \(\times 25.4\) in. and weighs \(1810 \mathrm{lb}\). Find its weight density.

A packing crate \(2.50 \mathrm{~m} \times 20.0 \mathrm{~cm} \times 30.0 \mathrm{~cm}\) has a mass of \(975 \mathrm{~kg}\). Find the stress (in kPa) exerted by the crate on the floor in each of its three possible positions.

A force of \(36.0 \mathrm{~N}\) stretches a spring \(18.0 \mathrm{~cm} .\) Find the spring constant (in \(\mathrm{N} / \mathrm{m}\) ).

Find the volume (in \(\mathrm{m}^{3}\) ) of \(1350 \mathrm{~g}\) of nitrogen at \(0^{\circ} \mathrm{C}\) and 1 atm pressure.

A force of \(5.00 \mathrm{~N}\) is applied to a spring whose spring constant is \(0.250 \mathrm{~N} / \mathrm{cm}\). Find its change in length (in \(\mathrm{cm}\) ).

A block of gold \(9.00\) in. \(\times 8.00\) in. \(\times 6.00\) in. weighs \(302 \mathrm{lb}\). Find its weight density.

Each vertical steel column of an office building supports \(30, \overline{0} 00 \mathrm{lb}\) and is compressed \(0.00234\) in. Find the compression of each column if a weight of \(125,000 \mathrm{lb}\) is supported.

A piece of aluminum of mass \(6.24 \mathrm{~kg}\) displaces water that fills a container \(12.0 \mathrm{~cm} \times 12.0 \mathrm{~cm} \times 16.0 \mathrm{~cm} .\) Find its mass density.

Find the mass density of gasoline if \(106 \mathrm{~g}\) occupies \(155 \mathrm{~cm}^{3}\).

A \(12, \overline{0} 00-\mathrm{N}\) load is hanging from a steel cable that is \(10.0 \mathrm{~m}\) long and \(16.0 \mathrm{~mm}\) in diameter. Find the stress.

A rectangular cast-iron column \(25.0 \mathrm{~m} \times 25.0 \mathrm{~cm} \times 5.00 \mathrm{~m}\) supports a weight of \(6.80 \times 10^{6} \mathrm{~N}\). Find the stress in pascals on the column.

What was the original length of a spring with spring constant \(96.0 \mathrm{~N} / \mathrm{m}\) that is stretched to \(28.0 \mathrm{~cm}\) by a \(15.0-\mathrm{N}\) weight?

If \(20.4 \mathrm{in}^{3}\) of linseed oil weighs \(0.694 \mathrm{lb}\), what is its weight density?

A bar weighing \(26.0 \mathrm{~N}\) is supported horizontally on each end by two hanging springs, each \(15.0 \mathrm{~cm}\) long, with spring constants \(0.970 \mathrm{~N} / \mathrm{cm}\) and \(1.45 \mathrm{~N} / \mathrm{cm}\), respectively. The bar is \(6.00 \mathrm{~m}\) long and has a center of mass \(2.00 \mathrm{~m}\) from the spring with constant \(0.970 \mathrm{~N} / \mathrm{cm} .\) How far does each spring stretch?

If \(108 \mathrm{in}^{3}\) of ammonia gas weighs \(0.00301 \mathrm{lb}\), what is its weight density?

A firefighter weighs 725 N. She wears shoes that each cover an area of \(206 \mathrm{~cm}^{2}\). (a) What is the average stress she applies to the ground on which she is standing? (b) How does the stress change if she stands on only one foot?

Two identical wires are \(125 \mathrm{~cm}\) and \(375 \mathrm{~cm}\) long, respectively. The first wire is broken by a force of \(489 \mathrm{~N}\). What force is needed to break the other?

Granite has a mass density of \(2650 \mathrm{~kg} / \mathrm{m}^{3}\). Find its weight density in \(\mathrm{lb} / \mathrm{ft}^{3}\).

The cross-sectional area of a wire is \(2.50 \times 10^{-3} \mathrm{~cm}^{2}\) and its tensile strength is \(1.00 \times 10^{5} \mathrm{~N} / \mathrm{cm}^{2}\). What force will break the wire?

Find the mass density of a metal block \(18.0 \mathrm{~cm} \times 24.0 \mathrm{~cm} \times 8.00 \mathrm{~cm}\) with mass \(9.76 \mathrm{~kg}\)

A spring having a force constant of \(1.25 \mathrm{~N} / \mathrm{cm}\) is stretched through a distance of \(11.5 \mathrm{~cm} .\) How much work is required to stretch the spring?

Find the mass (in \(\mathrm{kg}\) ) of \(1.00 \mathrm{~m}^{3}\) of (a) water, (b) gasoline, (c) copper, (d) mercury, and (e) air at \(0^{\circ} \mathrm{C}\) and 1 atm pressure.

Copper has a mass density of \(8890 \mathrm{~kg} / \mathrm{m}^{3} .\) Find its mass density in \(\mathrm{g} / \mathrm{cm}^{3}\).

If racing alcohol has a mass density of \(790 \mathrm{~kg} / \mathrm{m}^{3}\), what mass will a 1250 -litre tank hold?

The specific gravity of material \(X\) is \(0.82\). Does it sink in or float on water?

The specific gravity of material \(Y\) is \(1.7\). Does it sink in or float on water?

The specific gravity of material \(Z\) is \(0.52\). Does it sink in or float on gasoline?

The specific gravity of material \(W\) is \(11.5 .\) Does it sink in or float on mercury?

Find the mass density of a 315 -g object that displaces \(0.275 \mathrm{~m}^{3}\) of water.

What is the mass density of a \(50 \overline{0}-\mathrm{g}\) block that displaces \(215 \mathrm{~cm}^{3}\) of water?