Answer:
a. 1.80 %
b. 0.60 %
c. 1.20 %
d. 0.60 %
e. 0.60 %
Explanation:
In order to calculate percent uncertainties in each case, we forst need to calculate the average value:
Average Diameter = (16.4 mm + 16.8 mm + 16.9 mm + 16.6 mm +16.8 mm)/5
Average Diameter = 16.7 mm
Now, the formula for percent uncertainty is:
% Uncertainty = (Uncertainty/Average) * 100 %
where,
Uncertainty = |Value - Average|
For Each Case:
a. 16.4 mm:
Uncertainty = |16.4 mm - 16.7 mm| = 0.3 mm
Therefore,
% Uncertainty = (0.3 mm/16.7 mm) * 100%
% Uncertainty = 1.80 %
b. 16.8 mm:
Uncertainty = |16.8 mm - 16.7 mm| = 0.1 mm
Therefore,
% Uncertainty = (0.1 mm/16.7 mm) * 100%
% Uncertainty = 0.60 %
c. 16.4 mm:
Uncertainty = |16.9 mm - 16.7 mm| = 0.2 mm
Therefore,
% Uncertainty = (0.2 mm/16.7 mm) * 100%
% Uncertainty = 1.20 %
d. 16.6 mm:
Uncertainty = |16.6 mm - 16.7 mm| = 0.1 mm
Therefore,
% Uncertainty = (0.1 mm/16.7 mm) * 100%
% Uncertainty = 0.60 %
e. 16.8 mm:
Uncertainty = |16.8 mm - 16.7 mm| = 0.3 mm
Therefore,
% Uncertainty = (0.1 mm/16.7 mm) * 100%
% Uncertainty = 0.60 %
The deck of a bridge is suspended 235 feet above a river. If a pebble falls off the side of the bridge, the height, in feet, of the pebble above the water surface after t seconds is given by y = 235 − 16t^2.
Required:
a. Find the average velocity (in ft/s) of the pebble for the time period beginning when t = 2 and lasting the following amount of time.
1. 0.1 sec:________
2. 0.05 sec:_______
3. 0.01 sec:_______
b. Estimate the instantaneous velocity (in ft/s) of the pebble after 3 seconds. ft/s.
Answer:
(a) 1, average velocity = -65.6 m/s
2, average velocity = -64.8 m/s
3, average velocity = -64.16 m/s
(b) The instantaneous velocity is -96 m/s
Explanation:
(a)
Average velocity is given by;
[tex]y(t_2,t_1) = \frac{y(t_2) - y(t_1)}{t_2-t_1}[/tex]
(1)
[tex]y(2.1,2) = \frac{(235-16*2.1^2) - (235-16*2^2)}{2.1-2}\\\\ y(2.1,2) = -65.6 \ m/s[/tex]
(2)
[tex]y(2.05,2) = \frac{(235-16*2.05^2) - (235-16*2^2)}{2.05-2}\\\\ y(2.05,2) = -64.8 \ m/s[/tex]
(3)
[tex]y(2.01,2) = \frac{(235-16*2.01^2) - (235-16*2^2)}{2.01-2}\\\\ y(2.01,2) = -64.16 \ m/s[/tex]
b. y = 235 - 16t²
The instantaneous velocity is given by;
v = dy /dt
dy / dt = -32t
when t = 3 s
v = -32(3)
v = -96 m/s
(a)The average velocity for the 0.1 sec,0.05 sec,0.01 sec will be -65.6 m/s, -64.8 m/s and -64.16 m/s respectively.
What is the average velocity?The total displacement traveled by an object divided by the total time taken is the average velocity.
Average velocity is given by;
[tex]\rm y(t_2,t_1)=\frac{y(t_2)-y(t_1)}{t_2-t_1} \\\\[/tex]
The average velocity for case 1;
[tex]\rm y(2.1,2)=\frac{(235-16\times 2\times 1^2)-(235-16 \times 2^2)}{2.1-2} \\\\ \rm y(2.1,2)=\-65.6 \ m/sec[/tex]
The average velocity for case 2;
[tex]\rm y(2.015,2)=\frac{(235-16\times 2.05^2)-(235-16 \times 2^2)}{2.05-2} \\\\ \rm y(2.1,2)=\-64.8 \ m/sec[/tex]
The average velocity for case 3;
[tex]\rm y(2.01,2)=\frac{(235-16\times 2.01^2)-(235-16 \times 2^2)}{2.01-2} \\\\ \rm y(2.1,2)=\-64.16 \ m/sec[/tex]
Hence the average velocity for the 0.1 sec,0.05 sec,0.01 sec will be -65.6 m/s, -64.8 m/s and -64.16 m/s respectively.
(b) The instantaneous velocity will be -96 m/s.
The given equation in the problem is;
[tex]\rm y = 235 - 16t^2[/tex]
The instantaneous velocity is given as;
[tex]v = \frac{dy}{dt} \\\\ \frac{dy}{dt} = -32t\\\\ t = 3 s\\\\ v = -32\times 3\\\\ v = -96 m/s[/tex]
Hence the instantaneous velocity will be -96 m/s.
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Why si unit develop all over the world?
Answer:
SI unit is used in most places around the world, so our use of it allows scientists from disparate regions to use a single standard in communicating scientific data without vocabulary confusion.
Explanation:
hope it helps
Si unit is used almost all around the world, so our use of it allows
Scientist from disparate regions to use a single standered in communicating scientific data without vocabulary confusion
[tex]\huge{\gray{\sf Question:} }[/tex]
A body describes simple harmonic motion with an amplitude of 5 cm and a period of 0.2 s. Find the acceleration and velocity of the body when the displacement is (a) 5 cm, (b) 3 cm and (c) 0 cm.
Answer:
ANSWER
A = 5 cm = 0.05 m
T = 0.2 s
ω=2π/T=2π/0.2=10πrad/s
plz give brainlist
hope this helped
Answer:
[tex]here \: amplitude = 5cm (convert \: to \: si \: unit) = .05m \\ t = .2sec \\ omega = \frac{2\pi}{t} \\ = \frac{2\pi}{.2 } = 10\pi \frac{rad}{s} \\ we \: want \: find \: a \: and \: v \\ we \: know \: that \: a = - {omega}^{2} x \\ v = omega \sqrt{ {r}^{2} - {x}^{2} } \\(1)x = .05m \\ a = - {10\pi}^{2} \times .05 = - 5 {\pi}^{2} \frac{m}{ {s}^{2} } \\ v = 10\pi \sqrt{ {.05}^{2} - {.05}^{2} } = 0 \\ 2)x = 3cm = .03m \\ a = {(10\pi)}^{2} \times .03 = - 3 {\pi}^{2} \frac{m}{ {s}^{2} } \\ v = 10\pi \sqrt{ {.05}^{2} - {.03}^{2} } = 10\pi \times .04 = .4\pi \frac{m}{s} \\ 3)x = 0 \\ a = - {(10\pi)}^{2} \times 0 = 0 \\ v = 10\pi \times \sqrt{ {.05}^{2} - {0}^{2} } = - 10\pi \times .05 = .5\pi \frac{m}{s} \\ thank \: you[/tex]
The acceleration of a piston is given by : rw^2 cos(wt-pi/4) find amplitude.
Given :
The acceleration of a piston is given by :
[tex]a=r\omega^2cos\ (\omega t-\dfrac{\pi}{4})[/tex]
To Find :
The amplitude of the acceleration of piston .
Solution :
Now , acceleration is :
[tex]a=r\omega^2cos\ (\omega t-\dfrac{\pi}{4})[/tex]
Now , amplitude is maximum of any function .
So , maximum value of [tex]cos\ \theta[/tex] is equal to 1 .
Therefore , amplitude of the acceleration of piston is :
[tex]A=r\omega^2[/tex]
Hence , this is the required solution .
What is correct regarding an ideal isotropic antenna? a. An ideal isotropic antenna is a highly efficient antenna used extensively in today’s communication systems b. An ideal isotropic antenna is a specialized antenna used to direct EM signal energy towards a specific direction c. An ideal isotropic antenna is a theoretical antenna that does not exist in practice, but is useful in explaining power density and unguided EM signal attenuation d. None of the above are correct statements
Answer:
C An ideal isotropic antenna is a theoretical antenna that does not exist in practice, but is useful in explaining power density and unguided EM signal attenuation
Explanation:
Because practically speaking there is no ideal isotropic antenna it is only imaginary radiating in all directions and use as an arbitrary point for antenna gain
.A cart rolling down an incline for 5.0 seconds has an acceleration of 1.6 m/s2. If the cart has a beginning speed of 2.0 m/s, and its final velocity of 10 m/s, what was the car's displacement?
Use the formula,
[tex]\Delta x=v_it+\dfrac12at^2[/tex]
where [tex]\Delta x[/tex] is the cart's displacement (from the origin), [tex]v_i[/tex] is its initial speed, [tex]a[/tex] is its acceleration, and [tex]t[/tex] is time.
[tex]\Delta x=\left(2.0\dfrac{\rm m}{\rm s}\right)(5.0\,\mathrm s)+\dfrac12\left(1.6\dfrac{\rm m}{\mathrm s^2}\right)(5.0\,\mathrm s)^2[/tex]
[tex]\implies\boxed{\Delta x=30\,\mathrm m}[/tex]
Alternatively, since acceleration is constant, we have
[tex]\dfrac{v_f+v_i}2=\dfrac{\Delta x}t[/tex]
That is, we have these two equivalent expressions for average velocity, where [tex]v_f[/tex] is the cart's final velocity. Solve for [tex]\Delta x[/tex]:
[tex]\dfrac{10\frac{\rm m}{\rm s}+2.0\frac{\rm m}{\rm s}}2=\dfrac{\Delta x}{5.0\,\mathrm s}[/tex]
[tex]\implies\boxed{\Delta x=30\,\mathrm m}[/tex]
A car traveling due east at 20 m/s reverses its direction over a period of 10 seconds so that it is now traveling due west at 20 m/s. What is the direction of the car's average acceleration over this period?a- The car's average acceleration points due west.b- The car's average acceleration is zero.c- The car's average acceleration points due east.d- The direction of the car's average acceleration cannot be determined from the given information.
Answer:
The car's average acceleration points due west.
Explanation:
Resolving the acceleration will give a resultant due west
Can air make shadows
Answer:no
Explanation:the way to see air is by steaming something sometimes you might not see the air but you can see the shadow
A car accelerates at a rate of 5ft/s/s for a time of 9 seconds. How far does the car go?
The car will move in a speed of 45 meter per second
Answer: The car will move in a speed of 45 meter per second
Explanation:
Light travels at 3 × 108 m/s, and it takes about 8 min for light from the sun to travel to Earth. Based on this, the order of magnitude of the distance from the sun to Earth is g
Answer:
The order of magnitude of the distance from the sun to Earth is 10⁸ km.
Explanation:
The order of magnitude of the distance from the sun to Earth can be calculated as follows:
[tex] c = \frac{x}{t} [/tex]
Where:
c: is the speed of light = 3x10⁸ m/s
t: is the time = 8 min
Hence, the distance is:
[tex] x = c*t = 3 \cdot 10^{8} m/s*8 min*\frac{60 s}{1 min} = 1.44 \cdot 10^{11} m = 1.44 \cdot 10^{8} km [/tex]
Therefore, the order of magnitude of the distance from the sun to Earth is 10⁸ km.
I hope it helps you!
Determine the slope of this graph from zero seconds to five seconds.
Explanation:
(m2-m1)/t
25-0/5
25/5
5m/s
The position of a particle is given by the function x = \left(2t^3 - 6t^2 + 12\right) m, where t is in s. Question:At what time is the acceleration zero? (with working out)
Answer:
t = 1secExplanation:
Given the position of a particle expressed by the equation x = (2t^3 - 6t^2 + 12)m, where t is in seconds, the acceleration function can be gotten by taking the second derivative of the function with respect to t as shown;
a = d/dt(dx/dt)
First let us get dx/dt
dx/dt = 3(2)t³⁻¹-2(6)t²⁻¹+0
dx/dt = 6t²-12t
a = d/dt(dx/dt)
a = d/dx(6t²-12t)
a = 2(6)t²⁻¹-12t¹⁻¹
a = 12t - 12t⁰
a = 12t-12
If the acceleration is zero, then;
12t-12 = 0
add 12 to both sides
12t-12+12 = 0+12
12t = 12
t = 12/12
t = 1sec
Hence the time when acceleration is zero is 1sec
3. According to the Guinness Book of Records the heaviest baby ever born weighed 29 lbs 4 oz. (29.25 lbs).
What was the baby's mass in kg? (Historical Note: The birth occurred in Effingham IL in 1939 and due to
respiratory problems the baby died two hours later. The heaviest babies to survive weighed 22.5 lbs and were born
in 1955 and 1982.)
Answer: 13.2678 kg
Explanation: Well, 13.2678 kg is 29.25 in mass and kg.
An isolated system contains two objects with charges q1q1 and q2q2. If the charge on object 1 is doubled, what is the charge on object 2? g
Answer:
The new charge on the second object is q₂ - q₁
Explanation:
Given;
charge on the first object, q₁
charge on the second object, q₂
Since there is no external force on isolated system, the total charge in the system is given by;
Q = q₁ + q₂
q₂ = Q - q₁
When the charge on object 1 is doubled, q₁' = 2q₁
let q₂' be the new charge on object 2
q₂' = Q - q₁'
q₂' = (q₁ + q₂) - 2q₁
q₂' = q₁ + q₂ - 2q₁
q₂' = q₂ - q₁
Therefore, the new charge on the second object is q₂ - q₁
The charge on object 2 will be "q₂ - q₁".
Charge on object:The charge's quantity on such an item represents the degree of imbalance between its electrons as well as protons.
Just to calculate the overall charge of a positively (+) charged item, divide the total no. of valence electrons by the overall number of protons.
According to the question,
Object 1's charge = q₁
Object 2's charge = q₂
Let,
New charge of object 2 be "q₂'".
The total charge in the system will be:
Q = q₁ + q₂
or,
q₂ = Q - q₁
hence,
The charge on object 2 be:
→ q₂' = Q - q₁'
By substituting the values,
= (q₁ + q₂) - 2q₁
= q₁ + q₂ - 2q₁
= q₂ - q₁
Thus the answer above is appropriate.
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Why is the endocrine system important in psychology
the endocrine system releases hormones, and hormones impact the systems that cause changes in our behavior, including changes in what we might call biological motivations.
How do scientists use the evidence they gather?
Answer:
When conducting research, scientists use the scientific method to collect measurable, empirical evidence in an experiment related to a hypothesis (often in the form of an if/then statement), the results aiming to support or contradict a theory.
What's the name of the theory that explains things better than newton's laws ?
An object is moving in a negative direction with a negative acceleration, for example an object dropped out a window. What does it mean that both velocity and acceleration are negative?
Answer:
yes bc they are falling :]
Explanation:
Question 1
When you stand on a floor the electrons surround your shoes and the floor. What is the force that prevents you from falling through a floor?
a) atomic direction
b) potential energy
c) atomic speed
d) electrical repulsion
Answer:
d) electrical repulsion
Explanation:
When you stand on a floor, the two different bodies i.e your shoes and the floor on which you stand, are in a very close contact, the electrons that surround your shoes and that of the floor exert a repulsive force on each other, also known as Coulomb's force of repulsion or electrical repulsive force.
This electrical repulsive force prevents you from falling through the floor.
Explain the difference between the justice system laws and scientific laws
A man standing on the top of a hill and sees a flagpole he knows is 45 feet high. The angle of depression to the bottom of the pole is 12 degrees, and the angle of elevation to the top of the pole is 16 degrees. Find his distance from the pole
Answer:
160.44 feetExplanation:
check the attachment for the diagram of the set up for proper clarification.
From the diagram, the man's distance from the pole is labelled AB.
To get AB =, we need to get side CB first which is equal to ED i.e ED = CB.
From ΔCDE, opposite side = 45 feet and the adjacent is ED.
USing TOA, according to trig function SOH, CAH, TOA;
tan 16° = opp/adj = BD/ED
tan 16° = 45/ED
ED = 45/tan 16°
ED = 156.93 feet
Since ED = CB, hence CB = 156.93 feet
From ΔABC, adj = CB and hypotenuse = AB. According to CAH;
cos 12° = adj/hyp = CB/AB
cos 12° = 156.93/AB
AB = 156.93/cos 12°
AB = 160.44 feet
Hence the man's distance from the pole is 160.44 feet
26.0 g of copper pellets are removed from a 300∘C oven and immediately dropped into 120 mL of water at 21.0 ∘C in an insulated cup.What will the new water temperature be?
Answer:
The new water temperature is 26.4 °C
Explanation:
Given;
mass of copper, [tex]M_{cu}[/tex] = 26 g = 0.026 kg
temperature of copper, t = 300 °C
volume of water, V = 120 mL = 0.12 L
temperature of water, t = 21 °C
density of water, ρ = 1 kg/L
mass of water = density x volume
mass of water = (1 kg/L) x 0.12 L = 0.12 kg
heat lost by copper = heat gained by water
Both copper and water reach final temperature, T
Heat gained by water, [tex]Q_w[/tex] = [tex]m_w[/tex]cΔθ = [tex]m_w C(T - t)[/tex]
[tex]Q_w = m_w C(T - t)\\\\Q_w = 0.12*4200(T-21)\\\\Q_w = 504(T-21)[/tex]
Heat lost by copper is given by;
[tex]Q_{cu} = m_{cu}C(300-T)\\\\Q_{cu} = 0.026*385(300-T)\\\\Q_{cu} = 10.01(300 - T)[/tex]
[tex]Q_{cu} = Q_w[/tex]
504(T- 21) = 10.01(300 - T)
504 T - 10584 = 3003 - 10.01 T
504 T + 10.01 T= 3003 + 10584
514.01 T = 13587
T = (13587) / 514.01
T = 26.4 °C
Therefore, the new water temperature is 26.4 °C
The new water temperature using the given parameters is;
26.49°C
We are given;
Mass of copper; m_cu = 26 g = 0.026 kg
Temperature; T_cu = 300 °C
Volume of water; V = 120 mL = 0.12 L
Temperature of water, T_w = 21 °C
Density of water; ρ = 1 kg/L
Let us find the mass of water from the formula;
m_w = ρ × V
m_w = 1 × 0.12
m_w = 0.12 kg
Now, from the principle of conservation of energy, we can say that the total heat lost by a hot body is equal to the total heat gained by a cold body.
The hot body here is copper while the cold body is water. Thus;
Heat lost by copper = Heat gained by water
Formula for heat lost by copper is;
Q_cu = m_cu * c_cu * (T_f - T_cu)
Formula for heat gained by water is;
Q_w = m_w * c_w * (T_f - T_w)
Where;
T_f is final temperature reached by copper and water
c_cu is specific heat capacity of copper = 385 J/kg.°C
c_w is specific heat capacity of water = 4200 J/kg.°C
Thus;
Q_cu = 0.026 × 385 × (300 - T_f)
Q_cu = 3030 - 10.01T_f
similarly;
Q_w = 0.12 × 4200 × (T_f - 21)
Q_w = 504T_f - 10584
Thus;
3030 - 10.01T_f = 504T_f - 10584
3030 + 10584 = 504T_f + 10.01T_f
13614 = 514.01T_f
T_f = 13614/514.01
T_f = 26.49°C
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Give three examples of unbalanced forces in your everyday life. HELP FAST PLZ
Answer:
1. Kicking a soccer ball
2. Playing tug of war
3. Bouncing a Ball
Explanation:
The mass of a high speed train is 4.5×105 kg, and it is traveling forward at a velocity of 8.3×101 m/s. Given that momentum equals mass times velocity, determine the values of m and n when the momentum of the train (in kg⋅m/s) is written in scientific notation.
Answer:
The value of m = 3.735 and the value of n = 7.
Explanation:
The equation for the momentum of the train is,
P = mv
Here, m is the mass of the train and v is the speed of the train.
Substitute [tex]4.5 \times {10^5}{\rm{ kg}} , 8.3 \times {10^1}{\rm{ m/s}}[/tex] for m and v respectively in above equation.
[tex]\begin{array}{c}\\P = \left( {4.5 \times {{10}^5}{\rm{ kg}}} \right)\left( {8.3 \times {{10}^1}{\rm{ m/s}}} \right)\\\\ = 37.35 \times {10^6}{\rm{ kg}} \cdot {\rm{m/s}}\left( {\frac{{{{10}^1}{\rm{kg}} \cdot {\rm{m/s}}}}{{10\,{\rm{kg}} \cdot {\rm{m/s}}}}} \right)\\\\ = 3.735 \times {10^7}{\rm{ kg}} \cdot {\rm{m/s}}\\\end{array}[/tex]
According to the scientific notation, here the value of m is 3.735 and the value of n is 7 in the final answer of the momentum.
The value of m = 3.735 and the value of n = 7.
Given that the lines are parallel, what would be the value of angle "a" in the diagram found below?
Explanation:
Hey there!!
a = 40° { corresponding angles on a parallel lines are equal}.
As A and B are parallel, a and 40° are corresponding angles.
Hope it helps...
The value of angle "a" will be 40°
What is corresponding angle ?The angles which are on the same side of one of two lines cut by a transversal and are on the same side of the transversal is called corresponding angles.
since , angle a and angle B = 40° (given) are on the same relative position at the intersection where a straight line crosses two others and since both the lines are parallel to each other hence ,both the angles are said to be corresponding angles .This implies both the angles must be equal .
angle a = 40°
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The results of a dart game were precise but not accurate.The accepted value of the game was the center of the dartboard.Which correctly describes the results.
A. All of the darts hit the center of the board
B.Some of the darts hit the center of the board
C.The darts hit the same general area of the board
D.The darts hit very different areas of the board
Answer:
The darts hit the same general area of the board.
Answer: C. The darts hit the same general area of the board.
Explanation: The results of a dart game were precise but not accurate. The accepted value of the game was the center of the dartboard.
Which lists the elements in order from most conductive to least conductive?
potassium (K), selenium (Se), germanium (Ge)
germanium (Ge), potassium (K), selenium (Se)
selenium (Se), germanium (Ge), potassium (K)
potassium (K), germanium (Ge), selenium (Se)
Answer:
Answer: potassium (K) germanium (Ge) selenium (Se)
Explanation:
I just took the test, the farther to the right on the periodic table you go the less conductive it gets.
Answer:
Answer: potassium (K) germanium (Ge) selenium (Se)
Explanation:
The most conductive to least conductive is from left to right
A ball easily moves but not a bus when we push them. why?
Answer: The amount of matter is higher in a bus than a ball.
Explanation:
If a cheetah could maintain its top speed of 120 km/h for 20 minutes, how far would it run?
Scientists might use a diagram to model the water cycle. What are two
benefits of this model?
Answer:
B, and D
Explanation:
The two benefits of this model is it specify a process that is very complex. It can represent changes that occur very slowly. Thus option B and D is correct.
What is water cycle?The water cycle is defined as a cycle of events that involves precipitation as rain and snow, drainage in streams and rivers, and return to the atmosphere by evaporation and transpiration. Water moves through this cycle between the earth's oceans, atmosphere, and land.
It can also be defined as the route all water takes as it travels around Earth in various conditions.
There are basically six stages of water cycle.
EvaporationSublimationCondensationPrecipitationInfiltrationRunoffThus, the two benefits of this model is it specify a process that is very complex. It can represent changes that occur very slowly. Thus option B and D is correct.
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