Solution 1
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
📚 Related Questions
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.
Why do electromagnetic waves not require a medium to travel?
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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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.
What is a position versus time graph?
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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Answer:
Explanation:
Given:
F =20 N
D = 60 m
________
W - ?
W = F·D = 20·60 = 1 200 J
.
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)
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
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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at a solid wall rebounds at 11 m/s. What fraction of the initial kinetic energy is transformed into thermal energy?
The fraction of the initial kinetic energy is transformed into thermal energy is 3/4.
What fraction of the initial kinetic energy is transformed into thermal energy?
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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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.
Answer:................
Explanation:.............
The magnitude of acceleration of the crate be 7.14 m/s².
What is acceleration?
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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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.
Answer:
Explanation:
T = 25 s
25 = 2*pi*sqrt(L/9.8)
L = 155.14 m
The period and frequency of the pendulum are equal to 2 sec and 0.5 Hz.
What is a simple pendulum?
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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