Q: A small molecule has a diameter of $$0.1\ \mathrm{nm}. If $$the average speed of the molecule is $$320\ \mathrm{m/s}$$ and the mean free path is $$0.05\ \mathrm{\mu m}$$, estimate the value of the diffusion coefficient $$D$$ for the molecule.

$$D = \dfrac{1}{3} \lambda v = \dfrac{1}{3} \times 0.05 \times 10$$^{-6}$$\ \mathrm{m} \times 320\ \mathrm{m/s} = 5.3 \times 10$$^{-6}$$\ \mathrm{m^2$/s}$$

Q: A rocket sled decelerates horizontally at $$90\ \mathrm{m/s^2$}$$ for $$5\ \mathrm{s}. $$What is the total distance traveled during this time?

$$d = \dfrac{1}{2} a t^2$ = \dfrac{1}{2} \times 90 \times 25 = 1125\ \mathrm{m}$$

Q: An object consists of two pieces. The mass of one piece is $$6.47\ \mathrm{kg}$$, the volume of the second piece (aluminum) is $$4.44 \times 10$$^{-4}$$\ \mathrm{m^3$}. If $$the density of aluminum is $$2.70 \times 10^3$\ \mathrm{kg/m^3$}$$, what is the total mass of the object?

$$m_{total} = 6.47 + (2.70 \times 10^3$ \times 4.44 \times 10$$^{-4}$$) = 6.47 + 1.20 = 7.67\ \mathrm{kg}$$

Q: A heavy rock is dropped from rest at the top of a cliff and falls $$100\ \mathrm{m}$$ before hitting the ground. How long does it take to fall to the ground?

$$t = \sqrt{\dfrac{2h}{g}} = \sqrt{\dfrac{2 \times 100}{9.8}} \approx 4.52\ \mathrm{s}$$

Q: A Boeing 737 with a mass of $$51,000\ \mathrm{kg}$$ sits at rest at the start of a runway. The pilot turns the pair of jet engines to full throttle, and the thrust accelerates the plane down the runway. After traveling $$940\ \mathrm{m}$$, the plane reaches its takeoff speed of $$70\ \mathrm{m/s}$$ and leaves the ground. What is the thrust of each engine?

$$F = m a = m \dfrac{v^2$}{2d} = 51,000 \times \dfrac{70^2$}{2 \times 940} \approx 142,553\ \mathrm{N}$$

Q: A 12 kg dog running across a smooth floor at $$4.0\ \mathrm{m/s}$$ tries to stop but ends up sliding. If the dog slides $$180\ \mathrm{cm}$$ before stopping, what is the kinetic friction between her paws and the floor?

$$\mu_k = \dfrac{v^2$}{2 g d} = \dfrac{4.0^2$}{2 \times 9.8 \times 1.8} \approx 0.25$$

Q: A 75 kg skydiver with a $$20\ \mathrm{m^2$}$$ open parachute falls after jumping from a plane. What is the terminal velocity if the drag coefficient $$C_d is$$ $$0.7$$ and air density $$\rho is$$ $$1.2\ \mathrm{kg/m^3$}$$?

$$v_t = \sqrt{\dfrac{2 m g}{C_d \rho A}} = \sqrt{\dfrac{2 \times 75 \times 9.8}{0.7 \times 1.2 \times 20}} \approx 12.7\ \mathrm{m/s}$$

Question 1

A small molecule has a diameter of $$0.1\ \mathrm{nm}. If $$the average speed of the molecule is $$320\ \mathrm{m/s}$$ and the mean free path is $$0.05\ \mathrm{\mu m}$$, estimate the value of the diffusion coefficient $$D$$ for the molecule.

Accepted Answer

$$D = \dfrac{1}{3} \lambda v = \dfrac{1}{3} 	imes 0.05 	imes 10$$^{-6}$$\ \mathrm{m} 	imes 320\ \mathrm{m/s} = 5.3 	imes 10$$^{-6}$$\ \mathrm{m^2$/s}$$

Question 2

The average speed of molecules in a gas is inversely proportional to the square root of their mass. If the mass of a helium atom is $$4\ \mathrm{u}$$ and the mass of a nitrogen molecule is $$28\ \mathrm{u}$$, what is the ratio of their average speeds?

Accepted Answer

$$\dfrac{v_{He}}{v_{N_2$}} = \sqrt{\dfrac{m_{N_2$}}{m_{He}}} = \sqrt{\dfrac{28}{4}} = \sqrt{7} \approx 2.65$$

Question 3

A rocket sled decelerates horizontally at $$90\ \mathrm{m/s^2$}$$ for $$5\ \mathrm{s}. $$What is the total distance traveled during this time?

Accepted Answer

$$d = \dfrac{1}{2} a t^2$ = \dfrac{1}{2} 	imes 90 	imes 25 = 1125\ \mathrm{m}$$

Question 4

A student pours $$100.0\ \mathrm{mL} of $$graduated cylinder and places it on a scale, recording a reading of $$140.0\ \mathrm{g}. $$What is the density of the liquid in SI units?

Accepted Answer

$$\rho = \dfrac{m}{V} = \dfrac{140.0\ \mathrm{g}}{100.0\ \mathrm{mL}} = 1.4\ \mathrm{g/mL} = 1400\ \mathrm{kg/m^3$}$$

Question 5

An object consists of two pieces. The mass of one piece is $$6.47\ \mathrm{kg}$$, the volume of the second piece (aluminum) is $$4.44 	imes 10$$^{-4}$$\ \mathrm{m^3$}. If $$the density of aluminum is $$2.70 	imes 10^3$\ \mathrm{kg/m^3$}$$, what is the total mass of the object?

Accepted Answer

$$m_{total} = 6.47 + (2.70 	imes 10^3$ 	imes 4.44 	imes 10$$^{-4}$$) = 6.47 + 1.20 = 7.67\ \mathrm{kg}$$

Question 6

Bob leaves home in Chicago at $$9:00 A.M. $$and drives east at $$60\ \mathrm{mph}. $$Susan, $$400$$ miles to the east in Pittsburgh, leaves at the same time and travels west at $$40\ \mathrm{mph}. $$When will they meet for lunch?

Accepted Answer

$$t = \dfrac{400}{60 + 40} = 4\ \mathrm{hours}$$

Question 7

A heavy rock is dropped from rest at the top of a cliff and falls $$100\ \mathrm{m}$$ before hitting the ground. How long does it take to fall to the ground?

Accepted Answer

$$t = \sqrt{\dfrac{2h}{g}} = \sqrt{\dfrac{2 	imes 100}{9.8}} \approx 4.52\ \mathrm{s}$$

Question 8

A Boeing 737 with a mass of $$51,000\ \mathrm{kg}$$ sits at rest at the start of a runway. The pilot turns the pair of jet engines to full throttle, and the thrust accelerates the plane down the runway. After traveling $$940\ \mathrm{m}$$, the plane reaches its takeoff speed of $$70\ \mathrm{m/s}$$ and leaves the ground. What is the thrust of each engine?

Accepted Answer

$$F = m a = m \dfrac{v^2$}{2d} = 51,000 	imes \dfrac{70^2$}{2 	imes 940} \approx 142,553\ \mathrm{N}$$

Question 9

A 12 kg dog running across a smooth floor at $$4.0\ \mathrm{m/s}$$ tries to stop but ends up sliding. If the dog slides $$180\ \mathrm{cm}$$ before stopping, what is the kinetic friction between her paws and the floor?

Accepted Answer

$$\mu_k = \dfrac{v^2$}{2 g d} = \dfrac{4.0^2$}{2 	imes 9.8 	imes 1.8} \approx 0.25$$

Question 10

A 75 kg skydiver with a $$20\ \mathrm{m^2$}$$ open parachute falls after jumping from a plane. What is the terminal velocity if the drag coefficient $$C_d is$$ $$0.7$$ and air density $$\rho is$$ $$1.2\ \mathrm{kg/m^3$}$$?

Accepted Answer

$$v_t = \sqrt{\dfrac{2 m g}{C_d ho A}} = \sqrt{\dfrac{2 	imes 75 	imes 9.8}{0.7 	imes 1.2 	imes 20}} \approx 12.7\ \mathrm{m/s}$$

Question 11

A penguin glides at $$4.8\ \mathrm{kg}$$ and is found to be decelerating at $$-0.07\ \mathrm{m/s^2$}$$ due to drag. If its drag coefficient is $$0.07$$, what is the penguin's drag force coefficient?

Accepted Answer

$$F_{drag} = m a = 4.8 	imes (-0.07) = -0.34\ \mathrm{N}$$

Question 12

A figure shows the acceleration graph for a particle with an initial velocity of $$10\ \mathrm{m/s}. $$What is the particle’s velocity at $$t = 8\ \mathrm{s} if $$the area under the curve is $$20\ \mathrm{m/s}$$?

Accepted Answer

$$v = v_0$ + \$$int_0$$^8 a(t) dt = 10 + 20 = 30\ \mathrm{m/s}$$

Question 13

A 12 kg box sits on a table. You press down on the box from above with a force of $$15\ \mathrm{N}. $$What is the tension in the rope if you lift the box vertically at constant speed?

Accepted Answer

$$T = mg = 12 	imes 9.8 = 117.6\ \mathrm{N}$$

Question 14

A 90-kg gymnast and a 240-pound football player are suspended from a rope. What is the weight in Newtons of the football player?

Accepted Answer

$$W = 240 	imes 4.448 = 1067.5\ \mathrm{N}$$

Question 15

A flea jumps by rapidly extending its hind legs. An angle of $$20^{\circ} is $$typical. The flea’s body reaches a takeoff speed of $$1.3\ \mathrm{m/s}$$ over a distance of $$1.0\ \mathrm{mm}. $$How long does the jump last?

Accepted Answer

$$t = \dfrac{d}{v} = \dfrac{0.001}{1.3} \approx 0.00077\ \mathrm{s}$$

Question 16

What is the magnitude of the gravitational force of the earth on the moon? (Earth mass $$M_E = 5.97 	imes 10$$^{24}$$\ \mathrm{kg}$$, Moon mass $$M_M = 7.35 	imes 10$$^{22}$$\ \mathrm{kg}$$, distance $$r = 3.84 	imes 10^8$\ \mathrm{m})$$

Accepted Answer

$$F = G \dfrac{M_E M_M}{r^2$} = 6.67 	imes 10$$^{-11}$$ \dfrac{5.97 	imes 10$$^{24}$$ 	imes 7.35 	imes 10$$^{22}$$}{(3.84 	imes 10^8$)^2$$} \approx 1.98 	imes $$10^{20}$$\ \mathrm{N}$

Question 17

If the moon were to stop revolving around the earth, what would be its acceleration toward the earth?

Accepted Answer

$$a = \dfrac{F}{M_M} = \dfrac{1.98 	imes 10$$^{20}$$}{7.35 	imes 10$$^{22}$$} \approx 0.0027\ \mathrm{m/s^2$}$$

Physics for Life Sciences: Key Concepts and Problem Types (Chapters 1–5)

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