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**Answer:**

**The initial angular velocity of the bus wheel:**

**ω₀ ≈ 15.6 rad / s**

**Explanation:**

Given:

V₀ = 8.22 m/s - **Starting speed of the bus**

V= 0 m/s - **Final speed of the bus (the bus has stopped)**

ω = 0 rad/c - **Final angular velocity of the bus wheel**

t = 13.3 s - **Bus deceleration time**

R = 0.530 m - **Bus wheel radius**

____________________

ω₀ - ? - **The initial angular speed of the wheels.**

1)** Bus linear acceleration module:**

a = ( V₀ - V) / t = (8.22 - 0) / 13.3 ≈ 0.62 m/s²

2) **Bus angular accelerations module:**

ε = a / R = 0.62 / 0.530 ≈ 1.17 rad / s²

3) **The initial angular velocity of the bus wheel:**

ω₀ = ε·t = 1.17·13.3 ≈ **15.6 rad / s**

Question

A sound pulse emitted underwater reflects off a school of fish and is detected at the same place 0.10 s later. How far away are the fish? (Assume the water temperature is 20 degrees C.)

Solution 1

I'll assume that the **properties** of the water are that sound waves in fresh water move at a speed of 1497 m/s at a temperature of 25 °C. If the speed is 0.01s, you must divide it by 100 to get 14.97; but, since it travels there and back in 0.01s, you must split it in half i.e 7.485m.

**Without a medium, what kind of wave can travel?**

**Electromagnetic** waves

In contrast to mechanical waves, electromagnetic waves can travel without a medium. This implies that electromagnetic waves can pass not only through solid objects like air and rock but also through empty space.

Answer and **justification** Since electromagnetic waves are not conveyed by the vibration of particles, they do not need a medium to travel. Electric and magnetic fields, which can exist anywhere, oscillate, creating waves. Waves can therefore exist in solids, liquids, gases, or empty space.

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Question

Which of the position versus time graphs below matches the following description: a speed versus time graph has a horizontal line at 5 m/s from zero to five seconds?

Solution 1

The **position versus time graph** that matches the description: a **speed** versus time graph has a horizontal line at 5 m/s from zero to five seconds is Graph A; The correct option is A.

A **position versus time graph **is a graph that plots the position of an object against the time it takes for the object to move from one point to another.

The slope of a position versus time graph represents the **speed** or velocity of the object.

The slope of a position time graph = distance or position/time

A speed versus time graph is a graph that plots the speed of an object against the time it takes for the object to move to that speed.

The slope of a position versus time graph represents the **acceleration** of the object.

Considering the given **speed versus time graphs**:

Graph A: the speed versus time graph has a horizontal line at 5 m/s from zero to five seconds.

Graph B: the speed versus time graph shows variation is speed over time

Graph C: the speed versus time graph shows a constant increase in speed over time

Graph D; the speed versus time graph shows a constant decrease in speed over time

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Question

6. Mikey can kick the ball to Sage with a force of 20 N, making it travel 60m. Give the work done on the ball.

Solution 1

**Answer:**

**Explanation:**

Given:

F =20 N

D = 60 m

________

W - ?

W = F·D = 20·60 = 1 200 J

Question

.

A 2155 kg demolition ball swings at the end of a 17.5m cable on the arc of a vertical

circle. At the lowest point of the swing, the ball is moving at 8.6m/s. Determine the

tension in the cable at the lowest point. (Hint: T-mg =mv^2/r)

Solution 1

**Answer:**

**Thread tension:**

**T =** F + P = 9 108 + 21 120 ≈ **30 230 N**

**Explanation:**

Given:

m = 2155 kg

R = 17.5 m

V = 8.6 m/s

g = 9.8 m/s²

_______________

T - ?

**Modulus of centripetal force (force is directed towards the center of the circular arc):**

[tex]F = \frac{m\cdot V^2}{R} = \frac{2155\cdot 8.6^2}{17.5} = 9108 N[/tex]

**Ball weight (directed vertically down):**

*W = m·g = 2155·9.8 ≈ 21 120 N*

**Let's use the hint. Thread tension:**

**T =** F + W = 9 108 + 21 120 ≈ **30 230 N**

Solution 2

The **tension** in the cable at the lowest point of the swing is [tex]30248.196 N[/tex].

To determine the **tension **in the cable at the lowest point of the** swing**, we can use the hint provided:

[tex]T-mg=\frac{mv^{2}}{r}[/tex]

where T represents** tension**,

m is the mass of the **demolition ball** (2155 kg),

g is the **acceleration** due to gravity (approximately 9.8 m/s^2),

v is the **velocity** of the ball (8.6 m/s), and

r is the** radius** of the circular path (17.5 m).

Plugging in the given values, we have:

[tex]T-2155\times 9.81=\frac{2155\times 8.6^{2}}{17.5}[/tex]

[tex]T=30248.196 N[/tex]

Therefore, the **tension** in the cable at the lowest point of the** swing** is approximately [tex]30248.196 N[/tex].

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Question

Baseballs aren’t especially bouncy. A baseball fired at 20 m/s

at a solid wall rebounds at 11 m/s. What fraction of the initial kinetic energy is transformed into thermal energy?

at a solid wall rebounds at 11 m/s. What fraction of the initial kinetic energy is transformed into thermal energy?

Solution 1

The fraction of the **initial kinetic energy **is transformed into **thermal energy **is 3/4.

The fraction of the** initial kinetic energy** is transformed into **thermal energy **is calculated by applying the principle of conservation of energy as shown below.

Mathematically, this is given as;

ΔK.E = E

where;

- ΔK.E is the change in kinetic energy
- E is the thermal energy

E = K.Ef - K.Ei

where;

- K.Ef is the final kinetic energy
- K.Ei is the initial kinetic energy

E = (¹/₂mu² - ¹/₂mv²) / (¹/₂mu²)

where;

- m is the mass of the baseball
- v is the final velocity of the baseball
- u is the initial velocity of the baseball

E = (u² - v²) / (u²)

E = (20² - 10²) / (20²)

E = 0.75 = 3/4

Thus, the fraction of the **initial kinetic energy **is transformed into **thermal energy **is a function of the change in speed of the baseball.

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Question

Polaris is also called the North Star because Earth's North

Pole points toward it. As Earth rotates, other stars seem to

spin around Polaris in a counterclockwise direction. In one.

day, the stars will make one complete circle (360°) around

Polaris. Compare the positions of the constellations in the

two diagrams. Calculate how many hours have passed

between the first and second diagrams.

Pole points toward it. As Earth rotates, other stars seem to

spin around Polaris in a counterclockwise direction. In one.

day, the stars will make one complete circle (360°) around

Polaris. Compare the positions of the constellations in the

two diagrams. Calculate how many hours have passed

between the first and second diagrams.

Solution 1

**Answer:****.****.****.****.****.****.****.****.****.****.****.****.****.****.****.****.**

**Explanation:****.****.****.****.****.****.****.****.****.****.****.****.****.**

Question

what is the acceleration of a 38 kg crate being pushed horizontally by an 83 N force?

Solution 1

The magnitude of **acceleration **of the crate be **7.14 m/s².**

**Acceleration **is rate of change of velocity with time. Due to having both direction and magnitude, it is a vector quantity. Si unit of **acceleration **is meter/second² (m/s²).

**Mass **of the create be: m = 38kg.

**Force **applied on the create : F = 83N.

From Newton's** second law of motion**, we can write:

**force **= mass × acceleration

⇒ **acceleration **= force/mass = 38/83m/s² = 0.45 m/s².

Hence, **acceleration **of the create be 0.45 m/s².

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Question

Using the right hand rule, what do the three numbered vectors represent in the diagram below?

Solution 1

Using the right-hand rule, the correct answer is:

A) Magnetic field

B) Electric current

C) Force

The equation corresponding to this graphical representation is

F = IBL

where I is the current, B the magnetic field, L the length of the wire and F the magnetic force.

A) Magnetic field

B) Electric current

C) Force

The equation corresponding to this graphical representation is

F = IBL

where I is the current, B the magnetic field, L the length of the wire and F the magnetic force.

Question

You measure the period of a pendulum and get 25s. What is the length of the pendulum?

Solution 1

**Answer:**

**Explanation:**

T = 25 s

25 = 2*pi*sqrt(L/9.8)

L = 155.14 m

Question

A pendulum has a length of 1m. What is the period of this pendulum? What is the frequency of this pendulum?

Solution 1

The **period** and **frequency** of the **pendulum **are equal to 2 sec and 0.5 Hz.

A **simple pendulum **can be defined as a mechanical arrangement that possesses **periodic motion**. The simple pendulum is made of a bob having **mass** suspended by a thin **string** hung at its upper end of the length.

The** simple pendulum** moves freely back and forth in an **oscillatory motion** and the motion of the pendulum occurs in a vertical plane which is operated by the **gravitational force**.

The relationship between the **time period **and **length** of the pendulum is given by:

T = 2π√(L/g)

Where 'g' is the** acceleration **due to gravity and 'L' is the length of the pendulum.

T = 1/f where is the **frequency** of the pendulum.

Given, the **length** of a pendulum, L = 1 m

Then the **period** of the pendulum can be calculated as:

[tex]T = 2\times 3.14 \sqrt{\frac{1}{9.8} }[/tex]

T = 2 s

The **frequency** of the pendulum, f = 1/T = 1/2 = 0.5 Hz

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