HESI Physics Practice Test

To find the magnitude of the resulting force between the two objects, use Coulomb’s Law:

Q1 = the charge on the point-like object one (unit of measure is Coulomb, C)
Q2 = the charge on the point-like object two (unit of measure is Coulomb,C )
r = the distance between the two objects (unit of measure is meter, m)
k = the proportionality constant (unit of measure is N.m²c²)

Step 1: Convert μC to C (1 μC = 1 x 10^-6 C)

+0.5 μC = 5 x 10^-6 C

– 0.4 μC = 4 x 10^-6 C

Step 2: Insert the values into the equation

Q1 = 5 x 10^-6 C

Q2 = 4 x 10^-6 C

r = 2

We know that average speed is the distance an object travels divided by the time the object travels. However, this question asks for the distance.

Step 1: Rearrange the average speed equation (s = d/t) to solve for distance.

s = d/t

s * t = (d/t) * t

st = d

d = st

The distance traveled is the average speed of the motorcycle multiplied by the time the motorcycle traveled.

Step 2: Convert time from minutes to seconds.

Time must be expressed in seconds. So, we need to convert the time the motorcycle travels from minutes to seconds before computing the distance.

2 min * (60 s / 1 min) = 120 s

2 minutes is 120 seconds.

Step 3: Calculate the distance traveled.

To calculate the distance traveled by the motorcycle, we multiply its average speed (59 m/s) by the new value for time (120 s).

d = s * t

d = 59 m/s * 120 s

d = 7,080 m

The motorcycle travels 7,080 m.

We know the average velocity is half the sum of the initial and final velocities. However, this question asks us for the initial velocity.

Step 1: Rearrange the average velocity formula to solve for the initial velocity.

We can solve for the initial velocity by multiplying the average velocity by two and then subtracting the final velocity from the result.

v_av  = (v_f  + v_i) / 2

v_av * 2 = [(v_f  + v_i) / 2] * 2

(v_av  * 2) – v_f = v_f+ v_i – v_f

v_i = (vav * 2) – v_f

Step 2: Calculate the magnitude of the initial velocity of the motorcycle.

Substitute the following values into our new initial velocity formula: average velocity (vav = 76 m/s), and final velocity (v_f  = 26 m/s):

v_i = (v_av * 2) – v_f

v_i = (76 m/s * 2) – 26 m/s

v_i = 152 m/s – 26 m/s

vi = 126 m/s

The initial velocity is 126 m/s. 

Use the equation for angular displacement (Θ) to solve this equation.

Θ = S / r

Where:

S = 678 m

r = 145 m

Solve for the angular displacement:

Θ = 678 m / 145 m

Θ = 4.7

Step 1: Calculate the net force.

To determine the mass of the object, we must first determine the net force acting on it.

According to the question, there are two forces:

Force acting to the right, F_right = 432 N

Force acting to the left, F_left = 120 N

The forces are acting in opposite directions. The magnitude of the net force can be calculated as:

F_net = F_right + (-F_left)

F_net = 432 N – 120 N

F_net = 312 N

Step 2: Calculate the acceleration using Newton’s second law of motion.

Now that the net force (312 N) is determined, we can use Newton’s second law of motion to determine the mass of the box:

F = ma

Where F=force, k = the constant of proportionality, and a=acceleration

First, we convert the formula to solve for mass:

F = ma

(F/a) = (ma/a)

m = (F/a)

Substituting the values for net force (312 N) and the acceleration (62 m/s²) of the object:

m = (F/a)

m = (312 N / 62 m/s²)

m = 5.033 kg

The mass of the object is 5.03 kg.

Kinetic Energy is the energy an object possesses because of its velocity. Any object that is in motion is using kinetic energy: a child running, a thrown ball, someone skiing down a hill, or a book falling off of a shelf. This is why the equation takes into account the object’s mass and the rate at which they are traveling (their velocity).

KE = ½ x mv²

KE = Kinetic energy (expressed in Joules – J)

m = mass (expressed in kilograms)

v² = velocity (expressed in meters per second squared)

To find the velocity we must isolate it:

2 x KE = 2 x ½ x mv²

2 x KE = mv²

2 x KE / m = mv² / m

2 x KE / m = v²

m = 70 kg

KE = 1500 J

v² = 2 x 1500 J / 70 kg = 42.85 m²/s²

We then take the square root of this and v = 6.54 m/s

*Don’t forget that the velocity is squared*

Use the equation

frequency = speed / wavelength

(derived from the equation speed = frequency  × wavelength)

Then plugging in the related values:

frequency = 67 m/s / 7.2 m
frequency = 9.31 Hz.

The net force acting on the box is simply the sum of all forces acting on the box. Since the two forces are opposing each other, one force is considered positive and the other is considered negative.

The net force is represented by the following equation:

F_net = F_left + (-F_right )

Step 1: Calculate the net force.

According to the question,

Force to the left, F_left = 146.5 N 

Force to the right, F_right = 90.6 N

F_left ＞F_right , and therefore the net force on the box will be towards the left. We plug in the given values to calculate the magnitude of the force:

F_net = F_left + (-F_right )

F_net = 146.5 N + (-90.6 N)

F_net= 55.9 N

The net force acting on the box is 55.9 N to the left.

n this question, we use the formula for the centripetal force:

F = centripetal force
m = mass
V = velocity
r = radius of the circular path

STEP 1. Convert the velocity from km/h to m/s:

STEP 2. Fill in the values:

F = 5601.85 N

Since both the cyclist and her bicycle are traveling at 4 m/s, we need to account for the combined mass, which is 66.8 kg. She is riding southward, so the answer needs to include the direction (south) as well.

p = momentum (measured in kg⋅m/s)
m = mass (measured in kg)
v = velocity (measure in m/s)

Thus, the momentum, p, is:
p = 66.8 kg x 4 m/s
p = 267.2 kg m/s south

Potential Energy is the energy that is stored in some way. For example chemical bonds store energy. The energy due to their position in a gravitational field, i.e. are very high off the ground, is gravitational potential energy.

The formula for gravitational potential energy is

PE = mgh

PE = potential energy (measured in Joules – J)

m = mass (measure in kilograms – kg)

g = gravitational acceleration (- 9.8 m/s²)

h = height of the object (measured in meters – m)

To find mass we must isolate it by dividing both sides by gh.

PE / gh = mgh / gh

PE / gh = m

The PE of the basket is 58.6 J

The gravitational constant for Earth is 9.81 m/s²

The height of the table is 1.25m

Mass = 58.6 / (9.81 m/s² x 1.25m) = 4.778 kg which is about 4.78 kg

Acceleration is the change of velocity over a period of time. Acceleration is represented mathematically by the following equation, where a = acceleration (expressed in m/s²), v_f = final velocity (expressed in m/s²), v_i = initial velocity (expressed in m/s²), and Δt = change in time (expressed in s).

a = (v_f – v_i ) / Δt

Step 1: Convert time from minutes to seconds.

We need to express the given values for initial velocity  (v_i  = 45 m/s), its final velocity (v_f  = 117 m/s), and the new value of the time interval (Δt = 720 s)* into the acceleration formula:

a = (v_f – v_i ) / Δt

a = (117 m/s – 45 m/s ) / Δt

a = 72 m/s / 720 s

a = 0.1 m/s²

The car is accelerating at 0.1 m/s².

*The 720 seconds come from converting the given time of 12 minutes into seconds. Since there are 60 seconds in a minute, you multiply 12 minutes by 60 seconds per minute:

$12\text{ minutes}\times 60\text{ seconds/minute}=720\text{ seconds}$

The equation for momentum is p = mv. Since the mass of an object remains the same, only its velocity is changed. Thus, the formula for change in momentum is written as Δp = mΔv. The symbol Δ is called “delta” and is used to represent a change in the magnitude (number). In this case, we are using it to represent the change in velocity.

Δp = mΔv

Δp = (5 kg) (2 m/s – 1.5 m/s)

Δp = (5 kg)(0.5 m/s)

Δp = 2.5 kg m/s

Step 1: Rearrange the weight equation to solve for mass.

W = mg

(W/g) = (mg/g)

m = W/g

Step 2: Plug in our values for the weight (1300 N) and gravity (9.8 m/s²) to solve for mass:

m = (W/g)

m = (1300 N / 9.8 m/s²)

m = 132.65 kg

The mass of the refrigerator is 132.65 kg.

Since the object falls freely, it moves only under the force of gravity. Therefore, its acceleration is equal to the acceleration due to gravity. The height of the balloon is the same as the vertical distance d_y that the object falls. The mathematical formula to calculate distance given uniform acceleration is given as follows:

d_y = (½)gt² + v_i t 

where d_y = vertical distance, g = acceleration due to gravity, t = time, and v_i = initial velocity.

Step 1: Determine the height of the balloon by calculating the vertical distance traveled by the object.

To calculate the vertical distance, substitute the initial velocity (v_i = 0 m/s, since the object is dropped), the acceleration (g = -9.8 m/s²), and the time (t = 80 s).

d_y = (½)gt²  + v_i t

v_i t cancels out because the initial velocity is 0.

d_y = (½)gt²

d_y = (½) (9.8 m/s²) * (80 s)2

d_y = 4.9 m/s² * 6400 s²

d_y = 31,360 m

The height of the balloon was 31,360 m when the object was dropped.

Answer: Like charges repel and opposites attract.

When two objects are charged with like (two positive or two negative) charges, they will repel one another.

When two objects are charged with opposite charges (one positive and one negative), they will be attracted to one another.

To calculate the force between two objects, use the equation for Newton’s Universal Law of Gravitation, which has the form:

F = Gm₁m₂/r²

Where G is the universal gravitational constant (6.67 x 10-11 N m² kg^-2), m₁ and m₂ are the masses of the two objects, and r is the distance between the objects.

Insert the values from the question, and solve for F.

F = (6.67 x 10^-11 N m² kg^-2)(3.6 kg)(3.5 kg)/(75 m)²

F = 1.5 x 10^-13 N

The formula for angular acceleration (α) is:
α = Δω/Δt

Where:
Δω is the change in angular velocity (expressed in revolutions per second – rev/s)
Δt is the change in time (expressed in seconds)
Δω = ω₂ – ω₁
Δt = t₂ – t₁

Convert units:
5.5 minutes = 330 seconds
5 minutes = 300 seconds

α = (240 rev/sec – 450 rev/s) / (330s – 300s)
α = – 210 rev/sec / 30s
α = – 7 rev/sec²

Since the speed was turned down, the sign is negative. However, we are not done. The answers are given in rev/min² so we need to convert rev/sec² to rev/min².

-7 rev/sec² * 60 sec/min = -420 rev/min

The magnification equation needs to be used, which has the following formula:

h_i / h_o = – d_i / d_o

Where:

h_i  is the image height

h_o is the object height

d_o is the object distance

d_i is the image distance.

Solve for image height:

h_i / h_o = – d_i / d_o

h_i / 6 cm = – 4.5 cm / 1.5 cm

h_i / 6 cm = – 3

h_i  = – 18 cm

The negative means the image is inverted.

To determine the circuit’s current, use the Ohm’s law equation:

V = I × R

V =  Voltage

I =  Current

R =  Resistance

Rearranging the equation to solve for I, we get:

I = V / R

Insert the values into the equation

I = 2.4 / 12

I = 0.2 A

To calculate this answer, use the following formula: n = c /v, where n is the index of refraction, c is the speed of light in a vacuum (3.00 x 10⁸ m/s), and v is the velocity of light in the medium.

n = c /v

n = (3.00 x 10⁸ m/s) / 2.0 x 10⁸ m/s

n = (3.00 x 10⁸ m/s) / 2.0 x 10⁸ m/s

n = 1.5

Acceleration is the change of velocity over a period of time. Acceleration is represented mathematically by the following equation, where a = acceleration (expressed in m/s²), v_f = final velocity (expressed in m/s² ), v_i = initial velocity (expressed in m/s² ), and Δt = change in time (expressed in s).

a = (v_f  – v_i ) / Δt

Where a = acceleration,  v_f = final velocity,  v_i = initial velocity, and Δt = change in time

Step 1: Manipulate the acceleration formula to isolate the variable for time.

The change in time can be determined from the acceleration formula as follows:

a = (v_f  – v_i ) / Δt

a*Δt = [(v_f  – v_i ) / Δt]  * Δt

aΔt/ a = (v_f  – v_i ) / a

Δt  = (v_f  – v_i ) / a

Step 2:  Check the sign of the acceleration.

Since the ball uniformly decelerates, the acceleration is negative.

Step 3: Calculate the change in time.

Substitute the initial velocity (v_i = 0.86 m/s), the acceleration ( a = -0.43 m/s2), and the final velocity (v_f = 0 m/s) into the new formula for time:

Δt  = (v_f  – v_i ) / a

Δt  = (0 m/s – 0.86 m/s ) / -0.43 m/s²

Δt  = – 0.86 m/s / -0.43 m/s²

Δt  = 2 s

It will take 2 s for the ball to come to rest.

Convex lenses are also called converging lenses because after light rays pass through them, they converge at a single point called the focal point. Convex lenses are used in magnifying glasses and cameras.