Physics Study Guide for the HESI Exam

General Information

The Physics section of the HESI exam is considered experimental and is not required for many students. If you are required to complete the Physics section of the test, it is likely because your program requires you to have knowledge of radiology or other imaging. Key concepts to keep in mind when studying for this section are as follows:

Laws of Physics

Newton’s

There are three laws of motion:

Newton’s first law: An object will remain at rest or at constant velocity unless an external force is applied.

Newton’s second law: Force = mass \(\cdot\) acceleration

\[F = ma\]

Newton’s third law: If object \(1\) exerts a force on object \(2\), then object \(2\) simultaneously exerts an equal and opposite force on object \(1\).

\[F_A = F_B\]

Ohm’s

Current \(I\) is directly proportional to voltage (\(V\)) and inversely proportional to resistance (\(R\)).

\[I =\frac{V}{R}\]

Coulomb’s

The magnitude of the electrostatic force (\(F\)) between two point charges (\(q_1\) and \(q_2\)) is directly proportional to the product of the magnitude of the charges and inversely proportional to the square of the distance (\(r\)) between them.

\[F = \frac{k{q_1}q_2}{r^2}\]

where \(k\) is Coulomb’s constant of proportionality

\[k = \frac{1}{4πε_0}\]

and

\(ε_0\) is the permittivity of free space.

Wave Classification

In waves, energy is transferred by vibrations. There are two types of waves: longitudinal and transverse.

In longitudinal waves, the vibrations are in the same direction as the direction of travel. Sound waves and seismic \(P\) waves created during earthquakes are examples of longitudinal waves.

In transverse waves, the vibrations are at \(90\) degrees (right angles) to the direction of travel. Light waves, radio waves, and other electromagnetic waves are examples of transverse waves.

The three main parameters used to describe a wave are wavelength, amplitude, and frequency.

• The wavelength is the distance between a point on one wave and the same point on the next wave, i.e., the distance between two successive peaks or two successive troughs.

• The amplitude is the maximum height of the wave from its undisturbed position.

• The frequency is the number of waves per second and is measured in \(s^{–1}\) or Hertz (\(Hz\)).

Kinetic Energy vs. Potential Energy

Kinetic energy is the energy of an object due to its motion. The kinetic energy (\(KE\)) of an object of mass (\(m\)) traveling at velocity (\(v\)) is expressed as follows:,

\[KE = \frac{1}{2}mv^2\]

Potential energy (\(PE\)) is the energy of an object due to its position within a field. For example, the gravitational potential energy (\(GPE\)) of an object is defined as follows:

\[PE = mgh\]

where \(g\) is the gravitational field strength and \(h\) is the height of an object.

Another kind of potential energy is elastic potential energy (\(EPE\)). This is the energy stored in an object that is stretched or compressed, such as a spring.

\[EPE = \frac{1}{2}kx^2\]

where \(k\) is the spring constant and \(x\) is the length of stretch or compression relative to the resting position.

The total energy of a system (\(U\)) is constant and is equal to the sum of the kinetic and potential energy.

\[U = KE + PE\]

As the kinetic energy increases, the potential energy must decrease by the same amount to keep \(U\) constant. For example, when a ball is dropped, its \(PE\) is converted to \(KE\).

Currents and Voltage

Current is the flow of charge and, in an electric circuit, the electric current is carried by negatively charged electrons, which move around the circuit. Current is normally measured in amperes (\(A\)).

Voltage is the difference in electrical energy (potential difference) between two points in a circuit. Voltage is measured in volts and can be determined by rearranging Ohm’s law.

For example, for a circuit with \(I = 25 mA (0.025 A)\) and \(R = 200 kΩ (200,000 Ω)\), determine the value of V using the following equation:

\(V = IR = 0.025 \times 200,000 = 5000 V\) or \(5 kV\).

Motion

Acceleration

Acceleration is the rate of change of velocity of an object and is measured in \(ms^{–2}\).

\[a =\frac{change\,in\,velocity}{time} = \frac{∆v}{t}\]

If a car increases its speed from \(10 ms^{–1}\) to \(20 ms^{–1}\) in 20 s, its acceleration will be:

\[\frac{20-10}{20}=\frac{10}{20}= 0.5 ms^{-2}\]

Mass

An object’s acceleration can also be determined using Newton’s second law if the mass of the object and the force acting on the object are known.

The momentum (\(p\)) of an object is given by the product of its mass and velocity and is measured in kg \(ms^{–1}\) or \(Ns\).

\[p = mv\]

For example, a bus weighing 10 metric tons (10,000 kg) and traveling at a speed of \(25 \;ms^{–1}\) will have a momentum of \(10,000 \times 25 = 250,000 \;Ns\).

Linear and Rotational Motion

Linear motion is when an object moves in a straight line, whereas rotational motion involves an object rotating around a fixed point or spinning on an axis, like the Earth rotating around the Sun.

Linear velocity (\(v\)) is given by the distance (\(d\)) travelled in a given time (\(t\)):

\[v =\frac{d}{t}\]

Rotational velocity (\(ω\)) is given by the rotational displacement (\(θ\)) in a given time:

\[ω=\frac{θ}{t}\]

The rotational displacement is an angle, so the units are degrees or radians. One complete revolution corresponds to an angular displacement of \(360\) degrees or \(2\pi\) radians.

Optics

The wavelength (\(λ\)) of a transverse wave traveling at a constant velocity is related to its frequency (\(f\)) by,

\[λ= \frac{v}{f}\]

The speed of light is \(3 \cdot 10^8 ms^{–1}\), so a light wave with a frequency of \(300\; MHz\) will have a wavelength of \(3 \cdot 10^8/300 \cdot 10^6 = 1m\).

For an object placed in front of a concave mirror, the relationship between the image distance \((d_i)\), the object distance \((d_o)\) and the focal length (\(f\)) is expressed as follows:

\[\frac{1}{f} = \frac{1}{d_o} +\frac{1}{d_i}\]

The magnification (\(M\)) is defined as,

\[M = \frac{h_i}{h_o} = -\frac{d_i}{d_o}\]

where \(h_i\) is the image height and \(h_o\) is the object height.

e.g. Find the image height of a \(5\)-cm-high object, placed \(10\) cm away from a concave mirror with a focal length of \(20\) cm.

We know \(d_i = 10 cm\) and \(f = 20\) cm, so the first equation can be used to find \(d_o\)

\[\frac{1}{20} = \frac{1}{d_o} +\frac{1}{10} ⟶ \frac{1}{d_o} =\frac{1}{20}-\frac{1}{10} ⟶ \frac{1}{d_o} =-0.05⟶ d_o = -20 cm\]

We also know \(h_o\) = \(5\) cm, so the second equation can now be used to find the image height:

\[\frac{h_i}{5} = -\frac{10}{-20} ⟶ h_i = 5 \cdot 0.5 = 2.5 cm\]

Static Electricity

Static electricity is caused by the uneven distribution of charges across the surface of an object. Imagine a balloon being rubbed against someone’s head and stuck to a wall―when the two objects are in contact, negatively charged electrons are transferred from the hair to the balloon. The hair becomes positively charged because it has lost electrons, while the balloon becomes negatively charged because it has gained electrons. Like charges repel, causing the positively charged hair strands to stand on end. Opposite charges attract, so the negatively charged balloon will be attracted to positively charged particles in the wall, causing it to stick.

Gravitation

The force of gravity (\(Fg\)) is the attractive force that is felt between all objects. The gravitational force felt by two objects is directly proportional to the product of their masses (\(m1\) and \(m2\)) and inversely proportional to the square of the distance (\(r\)) between them, i.e., the more massive the objects and the closer together they are, the stronger the gravitational force produced.

\[F_g = G\frac{m_1m_2}{r^2}\]

where \(G\) is the gravitational constant \(6.673x10^{-11} Nm^2kg^{-2}\).