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)

Study Guide - Practice Questions

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