Example 6
A proton is fired from far away toward the nucleus of an iron atom,
which we can model as a sphere containing 26 protons.
The diameter of the nucleus is 9.0 x 10-15 m.
What initial speed does the proton need to just reach the surface of
the nucleus?
*Assume the nucleus remains at rest.
In a hard disk drive, a constant torque of 14 N⋅m is applied to the magnetic disk when the drive starts recording data. The magnetic disk has a mass of 0.2 kg and radius 2m. Determine the magnitude of the angular acceleration of the disk? [please solve if you know]
The angular acceleration of the magnetic disk is determined as 35 rad/s².
Conservation of angular momentum
The angular acceleration of the disk is determined from the principle of conservation of angular momentum.
τ = Iα
where;
τ is torqueI moment of inertia of the diskα is angular acceleration of the diskI = ¹/₂MR²
I = ¹/₂ x 0.2 x 2²
I = 0.4 kgm²
α = τ/I
α = (14)/(0.4)
α = 35 rad/s²
Thus, the angular acceleration of the disk is determined as 35 rad/s².
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A boat crossing a 153.0 m wide river is directed so that it will cross the river as quickly as possible. The boat has a speed of 5.10 m/s in still water and the river flows uniformly at 3.70 m/s. Calculate the total distance the boat will travel to reach the opposite shore.
We have the relation
[tex]\vec v_{B \mid E} = \vec v_{B \mid R} + \vec v_{R \mid E}[/tex]
where [tex]v_{A \mid B}[/tex] denotes the velocity of a body A relative to another body B; here I use B for boat, E for Earth, and R for river.
We're given speeds
[tex]v_{B \mid R} = 5.10 \dfrac{\rm m}{\rm s}[/tex]
[tex]v_{R \mid E} = 3.70 \dfrac{\rm m}{\rm s}[/tex]
Let's assume the river flows South-to-North, so that
[tex]\vec v_{R \mid E} = v_{R \mid E} \, \vec\jmath[/tex]
and let [tex]-90^\circ < \theta < 90^\circ[/tex] be the angle made by the boat relative to East (i.e. -90° corresponds to due South, 0° to due East, and +90° to due North), so that
[tex]\vec v_{B \mid R} = v_{B \mid R} \left(\cos(\theta) \,\vec\imath + \sin(\theta) \, \vec\jmath\right)[/tex]
Then the velocity of the boat relative to the Earth is
[tex]\vec v_{B\mid E} = v_{B \mid R} \cos(\theta) \, \vec\imath + \left(v_{B \mid R} \sin(\theta) + v_{R \mid E}\right) \,\vec\jmath[/tex]
The crossing is 153.0 m wide, so that for some time [tex]t[/tex] we have
[tex]153.0\,\mathrm m = v_{B\mid R} \cos(\theta) t \implies t = \dfrac{153.0\,\rm m}{\left(5.10\frac{\rm m}{\rm s}\right) \cos(\theta)} = 30.0 \sec(\theta) \, \mathrm s[/tex]
which is minimized when [tex]\theta=0^\circ[/tex] so the crossing takes the minimum 30.0 s when the boat is pointing due East.
It follows that
[tex]\vec v_{B \mid E} = v_{B \mid R} \,\vec\imath + \vec v_{R \mid E} \,\vec\jmath \\\\ \implies v_{B \mid E} = \sqrt{\left(5.10\dfrac{\rm m}{\rm s}\right)^2 + \left(3.70\dfrac{\rm m}{\rm s}\right)^2} \approx 6.30 \dfrac{\rm m}{\rm s}[/tex]
The boat's position [tex]\vec x[/tex] at time [tex]t[/tex] is
[tex]\vec x = \vec v_{B\mid E} t[/tex]
so that after 30.0 s, the boat's final position on the other side of the river is
[tex]\vec x(30.0\,\mathrm s) = (153\,\mathrm m) \,\vec\imath + (111\,\mathrm m)\,\vec\jmath[/tex]
and the boat would have traveled a total distance of
[tex]\|\vec x(30.0\,\mathrm s)\| = \sqrt{(153\,\mathrm m)^2 + (111\,\mathrm m)^2} \approx \boxed{189\,\mathrm m}[/tex]
An object moves 20 m east in 30 s and then returns to its starting point taking an additional 50 s. If west is chosen as the positive direction, what is the sign associated with the average velocity of the object
The sign associated with the average velocity of the object is negative.
Average velocity of the object
The average velocity of the object is calculated as follows;
Average velocity = (v1 + v2)/2
v1 = -20/30 = -0.667 m/s
v2 = 20/50 = 0.4 m/s
Average velocity = (-0.667 + 0.4)/2
Average velocity = -0.134 m/s
Thus, the sign associated with the average velocity of the object is negative.
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A 0.3Kg mass of liquid is heated from 20°C to 53°C. The specific heat capacity of the
liquid is 22001/Kg C. How much energy is transferred to the liquid?
The total energy is transferred to the liquid is = 217809.9 J
Given:-It is given in the question that—
weight of the liquid= 0.3kg
specific heat capacity=22001/kg C
temperature changes between 20°C to 53°C
Solution:-we can easily solve this problem by using the formula of the calorimetry principle.
The formula is —
Q= m×s×t [Q=total energy is transferred, m= mass of the substance, s= specific heat, t= final temperature - initial temperature]
by putting the value on what is given in this question —
Q= 0.3×22001×(53-20)
= 217809.9 J
So energy transferred to the liquid is=217809.9 J
If the net force acting on a moving object CAUSES NO CHANGE IN ITS VELOCITY, what happens to the object's momentum?
A. It decreases.
B. It remains equal to the force.
C. It increases.
D. It stays the same.
If the net force acting on a moving object causes no change in its velocity, the object's momentum will stay the same.
What is momentum?Momentum of a body in motion refers to the tendency of a body to maintain its inertial motion.
The momentum is the product of its mass and velocity.
This suggests that if the net force acting on a moving object causes no change in its velocity, the momentum of the object will remain the same.
Therefore, if the net force acting on a moving object causes no change in its velocity, the object's momentum will stay the same.
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A car is moving along a straight line op is shown below it moves from O to P in 8sec and return to p to q in 6sec. What is the average velocity and the speed of the car
Answer:
The answer would be A
Explanation:
A uniform cylindrical rod is 0.63m long and it has cross sectional area of 0.1m. calculate the depth of immersion
The depth of immersion of the uniform cylindrical rod is 0.63m.
What is Depth of immersion?This is defined as the distance in which a body reaches when it is submerged.
Depth of immersion = Volume/Cross-sectional area
Volume = Cross-sectional area × length
= 0.1m² × 0.63m = 0.063m³
Depth of immersion = 0.063m³ / 0.1m²
= 0.63m
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A 12-kilogram mass has a kinetic energy of 150 joules. The speed of the object is
A.25.0 B.12.5 c.3.55 D.5.00
Answer:
OPTION D 5 m/s
Explanation:
0.5 × 12 × v² = 150
sqrt(150/6) = v
v = 5 m/s
Is the universe endless?
The universe may indeed have an end one day according but it is yet to be shown in science.
Is the universe endless?While there is certainly no way a person will live long enough to know if the universe will end or not, nevertheless certain scientific calculations are helpful.
From astronomical calculations, the universe is anticipated to have existed for about 13.8 million years. Thus, the universe may indeed have an end one day according but it is yet to be shown in science.
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Please answer if you know :)
Answer1. :(20/25)*200/*25 2. Increase the radius or apply the force perpendicular to the wrench
Explanation:torque =force*distance*sine of the angle between applied force and axis of wrench
Given the information in the velocity vs. time graph, what is the displacement of the object after 1 second?
Answer:
V / T is the slope of the graph
S = V / T so the slope of the graph will be the displacement at that point
Even tho the above assumes uniform quantities, the instantaneous displacement at any time is the slope of the graph at that point in case one has a graph that is not a straight line.
Which describes an image that a concave mirror can make?
The image is always virtual.
The image can be either virtual or real.
The image is never upside down.
The image can only be the same size as the object.
Answer:
B. The image can either be virtual or real.
Explanation:
Concave mirrors can either produce real or virtual images. The image is upright given that it is virtual or real given that it is in front of the mirror. The images produced by the concave mirrors can also be reduced (in height), enlarged (in terms of size) or having same size as that of the object.
I hope this helps you understand about the images formed by concave mirrors.
Have a nice studies.
C. A rocket moves from the velocity
2000ms ¹ to 6000 ms¹ after
moving as far as 80km. Calculate
the time taken by the rocket.
(20s)
Answer:
20s
Explanation:
t=d/(V2-V1)
t= 80000m/(6000-2000)
t= 20s
Type the correct answer in the box.use numerals instead of words. if necessary, use / for the fraction bar. δabc is a right triangle in which ∠b is a right angle, ab = 1, ac = 2, and bc = . cos c × sin a =
From the diagram The value of cos C × sin A = [tex]\frac{3}{4}[/tex]
Determine the numerical value of cos C × sin AFirst step : determine the values of cos C and sin A
cos C = adjacent / hypotenuse
= a / b
= [tex]\sqrt{3} / 2[/tex]
= √3/2
sin A = sin 60⁰
= √3/2
Therefore the numerical value of cos C * sin A = [tex]\frac{3}{4}[/tex]
In conclusion From the diagram The value of cos C × sin A = [tex]\frac{3}{4}[/tex]
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Calculate the total distance travelled by the motorcyclist over 0-60
Estimate how long a 2500 W electric kettle would take to boil away 1.5 Kg of water . The specific latent heat of vaporization of water is 4000000 J / Kg .
The time it would take a 2500 W electric kettle to boil away 1.5 Kg of water is 2400 seconds
How to calculate the timeUse the formula:
Power × time = mass × specific heat
Given mass = 1. 5kg
Specific latent heat of vaporization = 4000000 J/ Kg
Power = 2500 W
Substitute the values into the formula
Power × time = mass × specific heat
2500 × time = 1. 5 × 4000000
Make 'time' the subject
time = 1. 5 × 4000000 ÷ 2500 = 6000000 ÷ 2500 = 2400 seconds
Therefore, the time it would take a 2500 W electric kettle to boil away 1.5 Kg of water is 2400 seconds.
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A 1-kg block is lifted vertically 1 m at constant speed by a boy. The work done by the boy is about:
Answer:
[tex]9.8\; {\rm J}[/tex], assuming that the gravitational field strength is [tex]g = 9.8\; {\rm N \cdot kg^{-1}}[/tex].
Explanation:
Notice that both the speed and the direction of motion of this block are constant. In other words, the velocity of this block is constant.
By Newton's Second Law, the net force on this block would be [tex]0[/tex]. External forces on this block should be balanced. Thus, the magnitude of the (downward) weight of this block should be equal to the magnitude of the (upward) force that the boy applies on this block.
Let [tex]m[/tex] denote the mass of this block. It is given that [tex]m = 1\; {\rm kg}[/tex]. The weight of this block would be:
[tex]\begin{aligned}\text{weight} &= m\, g \\ &= 1\; {\rm kg} \times 9.8\; {\rm N \cdot kg^{-1}} \\ &= 9.8\; {\rm N}\end{aligned}[/tex].
Hence, the force that the boy applies on this block would be upward with a magnitude of [tex]F = 9.8\; {\rm N}[/tex].
The mechanical work that a force did is equal to the product of:
the magnitude of the force, and the displacement of the object in the direction of the force.The displacement of this block (upward by [tex]s = 1\; {\rm m}[/tex]) is in the same direction as the (upward) force that this boy had applied. Thus, the work that this boy had done would be the product of:
the magnitude of the force that this boy exerted, [tex]F = 9.8\; {\rm N}[/tex], andthe displacement of this block in the direction, [tex]s = 1\; {\rm m}[/tex].[tex]\begin{aligned}\text{work} &= F\, s \\ &= 9.8\; {\rm N} \times 1\; {\rm m} \\ &= 9.8\; {\rm J}\end{aligned}[/tex].
Which two options would INCREASE the electric force between two charged particles?
A. Increase the distance between the particles. B. Decrease the charge of one of the particles. C. Decrease the charge of both particles
D. Decrease the distance between the particles
E. Increase the charge of one of the particles.
The electric force between two charged particles can be increased by decreasing the distance between the two particles.
How to increase electric force between two charged particles.The technique of decreasing the separation distance between objects increases the force of attraction or repulsion between the objects. while
increasing the separation distance between objects decreases the force of attraction or repulsion between the objects.
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The chart lists the masses and velocities of four objects.
A 3-column table with 4 rows titled Motion of 4 Objects. The first column labeled Object has entries W, X, Y, Z. The second column labeled Mass (kilograms) has entries 58, 34, 89, 60. The third column labeled Velocity (meters per second) has entries 1, 2, 0.5, 2.
Which object requires the greatest change in momentum in order to stop its motion?
W
X
Y
Z
The object which requires the greatest change in momentum in order to stop its motion is object Z.
What is momentum?Momentum of any object is the product of the velocity of the object and its mass.
p =mv
Given is the chart lists the masses and velocities of four objects.
Object Mass (kg) Velocity (m/s)
W 58 1
X 34 2
Y 89 0.5
Z 60 2
Calculate the momentum for all the objects.
Momentum for W, p = 58 x 1 = 58 kg.m/s
Momentum for X, p = 34 x 2= 68 kg.m/s
Momentum for Y, p = 89 x 0.5 = 44.5 kg.m/s
Momentum for Z, p = 60 x 2 = 120 kg.m/s
On comparing the data from calculated momentum, we have a conclusion that highest momentum is for object Z.
Therefore, the object which requires the greatest change in momentum in order to stop its motion is object Z.
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Answer:
z
Explanation:
:)
Diverse crops can become vulnerable to pests, disease, and climate change. Which part of this statement is false?
The statement 'diverse crops can become vulnerable to pests, disease, and climate change' is considered false regarding this last point (climate change).
What is adaptation?Adaptation is an evolutionary process where a species fits certain environmental conditions.
Plant species are intrinsically vulnerable to climate change because they are adapted to certain climate (temperature) conditions.
In conclusion, the statement 'diverse crops can become vulnerable to pests, disease, and climate change' is considered false regarding this last point (climate change).
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What can you infer about the changes in the environment over time at the mystery fossil dig site? Record your inferences in the spaces provided.
Describe the environment in Egypt before the mystery fossil organism emerged.
the fossil informed us about the climatic and geographical changes that occurs in the environment over time.
What the mystery fossil dig site informed us about environment?We can infer about the climate and geographical changes in the environment over time at the mystery fossil dig site because the fossil provides us information about the climatic condition as well as the geography of land when this fossil organism were alive.
So we can conclude that the fossil informed us about the climatic and geographical changes that occurs in the environment over time.
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Which graph best represents the relationship between the acceleration of an object falling freely near the surface of Earth and the time that it falls?
Figure 4 is the graph which best represents the relationship between the acceleration of an object falling freely near the surface of Earth and time taken.
What is a Graph?This is defined as a pictorial representation of data in an organized and defined manner.
The acceleration of an object falling freely near the surface of Earth is constant which is why option D was chosen.
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75m X A car moves with a uniform velocity 21 ms-1 from position P and a truck moves from rest with uniform acceleration 2 ms-2 from position Q in the same time in the same direction.
i) Determine the distance travelled in 20 seconds.
ii) How many times the private car will meet? Analyze mathematically.
Velocity after 20s for both
Car=21m/sTruck=2(20)=40m/s.Distance traveled for car
20(21)=420mDistance traveled by truck=
s=ut+1/2at²s=1/2(2)(20)²s=400m#b
Distance from Q
for car
420-75=345mFor truck
400mThe truck will meet the car after 75/21≈4s
Then for 6s the car keeps meeting because after 7 s Truck will archive 22m/s velocity
Total meet ups=6+1=7timesWhat happens to the light in a
concave lens?
a. the light diverges when it passes
through the lens.
b. the light diverges before it enters the
lens.
c. the light converges when it enters the
lens.
Answer:
a. the light diverges when it passes through the lens.
Explanation:
All the light rays after passing through the concave lens diverge and when produced backwards appear to meet at a point on the principal axis of the lens. This point is known as principal focus of a concave lens.
which wave carries the least energy?
Answer:
B
Explanation:
The answer is B, because the waves are farther apart then the others. And it also looks like radio waves, which carries the least energy.
Answer: The third one
Explanation: there isnt many waves in that one les waves = less energy and i took the quiz/test.
Q2
Radioactive waste from nuclear power stations is a man-made source of background
radiation.
(a) Give one other man-made source of background radiation
Answer:
the clock hand of watch which have radium-226 for luminance
Where do nebulae come from, in the opinion of science?
*
1 point
It was made from a giant rabbit's skin.
It formed from the same cloud of dust that our entire galaxy is made from
It formed from hydrogen, the first element created in the universe.
It formed debris that was left over after a nova or supernova
Answer:
It formed from the same cloud of dust that our entire galaxy is made from
Would young rocks be found near a volcano?
Answer:
maybe
Explanation:
young rocks may be found near volcanoes
Which best describes why gravity on earth has a stronger attraction with you than the sun has with you?.
Answer:
Earth has a smaller mass than the Sun, but it is much closer to you than the Sun, allowing for a stronger attraction.
Explanation:
Science :)