Answer:In other words, with w = 130, W = 129.5, what is x?
You find this by plugging in the values for w, W and R and solving for x.
Note: x is the distance from the center. You were asked for the distance from the surface (the altitude) so there's one more calculation to do when you find x.
Explanation:
Explain length and time dilation and give an example of when each is observed.
Answer:
Length contraction
A moving object traveling at a velocity approaching the speed of light will appear to be shorter or to have undergone contraction.
The proportion by which the object is observed to have contracted is given by Lorentz transformation as follows;
[tex]L = L_{0}\cdot \sqrt{1 -\dfrac{v^{2}}{c^{2}}}= \dfrac{L_{0}}{\gamma }[/tex]
Time dilation
As the relative speed of motion of an object approaches the speed of light, the clock in the frame in motion will be observed to be moving slowly or dilated in a proportion given by Lorentz transformation as follows;
[tex]T = \dfrac{T_{0}}{\sqrt{1 -\dfrac{v^{2}}{c^{2}}}}[/tex]
Explanation:
Example of length contraction example
Two square boxes of side length L which are travelling at a velocity of 0.9 × c, are going to arranged in a single box of side side length L according to length contraction Lorentz transformation, to stationary observer we have
[tex]2 \times L\cdot \sqrt{1 -\dfrac{(0.9 \cdot c)^{2}}{c^{2}}}= 0.8 \cdot L[/tex]
To the stationary observer, the 2 boxes of length L will fit side by side in the single box of length L, while to those on the space ship carrying the boxes, the size of the single box is [tex]L\cdot \sqrt{1 -\dfrac{(0.9 \cdot c)^{2}}{c^{2}}}= 0.4 \cdot L[/tex], which will not contain half of one box
Example of of time dilation example
Twin A of two twins, twin A and B went on a space journey at the speed of 0.87·c for 5 years, the number of years past for twin B when they meet again will be [tex]T = \dfrac{5}{\sqrt{1 -\dfrac{(0.87\cdot c)^{2}}{c^{2}}}} = 10.14 \ years[/tex]
A vat of nitrogen at its boiling point (-196 degrees C) absorbs 384000 J of heat. How much mass of nitrogen burns off? (Unit = kg)
Answer:
1.92 kg of nitrogen.
Explanation:
The following data were obtained from the question:
Heat absorbed (Q) = 384000 J
Note: Heat of vaporisation (ΔHv) of nitrogen = 5600 J/mol
Next, we shall determine the number of mole of nitrogen that absorbed 384000 J.
This is illustrated below:
Q = mol·ΔHv
384000 = mole of N2 x 5600
Divide both side by 5600
Mole of N2 = 384000/5600
Mole of N2 = 68.57 moles
Next, we shall convert 68.57 moles of nitrogen, N2 to grams.
This can be obtained as follow:
Molar mass of N2 = 2 x 14 = 28 g/mol.
Mole of N2 = 68.57 moles.
Mass of N2 =..?
Mole = mass /molar mass
68.57 = mass of N2 /28
Cross multiply
Mass of N2 = 68.57 x 28
Mass of N2 = 1919.96 g
Finally, we shall convert 1919.96 g to kilograms.
This can be achieved as shown below:
1000g = 1 kg
Therefore,
1919.96 g = 1919.96/1000 = 1.92 kg.
Therefore, 1.92 kg of nitrogen were burned off.
Answer:
Explanation:
i cheat on Acellus cause I dont care about school. If i did I would be going to public school... Im never gonna use this info in my life so I dont bother learning it.
an elastic cord 61 cm long when a weight of 75N hangs from it, but 85cm when a weight of 210N hangs from it. what is the spring constant of the cord
Answer:
560 N/m
Explanation:
F = kx
75 N = k (0.61 m − L)
210 N = k (0.85 m − L)
Divide the equations:
2.8 = (0.85 − L) / (0.61 − L)
2.8 (0.61 − L) = 0.85 − L
1.708 − 2.8L = 0.85 − L
0.858 = 1.8L
L = 0.477
Plug into either equation and find k.
75 = k (0.61 − 0.477)
k = 562.5
Rounded to two significant figures, k = 560 N/m.
please help me with this question
Car at rest:
velocity= 0m/s
Acceleration:
0.2m/s²
Since total time:
3 min = 180s
Formula of acceleration:
acceleration = [final velocity - initial velocity] ÷ [total time]
Velocity at end:
0.2m/s² = [final velocity - 0m/s] ÷ [180s]
0.2m/s² × 180s = [final velocity]
[final velocity] = 36m/s
Distance travelled:
Velocity = displacement(distance) ÷ time
36m/s = displacement(distance) ÷ 180s
displacement(distance) = 36m/s × 180s
displacement(distance) = 6480m
Hey I'm sorry but i do not understand why the answer on your worksheet for distance travelled is 3240m... its half of what my answer is...
explain why energy is important to us?
Answer:
we need it to work and without it we dont have strength to do anything
Answer:
energy is important to all living organisms. energy for producers comes from the sun, and energy for consumers comes from other living organisms. the abundance of energy available for organisms impacts the population.
(I) A hiker determines the length of a lake by listening for the echo of her shout reflected by a cliff at the far end of the lake. She hears the echo 2.5 s after shouting. Estimate the length of the lake.
Answer:
425 m
Explanation:
From the question,
v = 2x/t.................... Equation 1
Where v = speed of sound in air, x = Length of the lake, t = time.
make x the subject of the equation
x = vt/2............... Equation 2
Given: t = 2.5 s
Constant: v = 340 m/s.
Substitute these values into equation 2
x = 340(2.5)/2
x = 425 m.
Hence the length of the lake is 425 m
A firework is initially at rest explodes into 2 pieces one of which weighing 2.0 kg flies to the right at15 m/s the other piece flies to tje left at 20m/s wjat is tge mass of firework before explosion??
Answer:
3.5 kg
Explanation:
use the equation; (m1v1i) + (m2v2i) = (m1v1f) + (m2v2f)
= m1(0) - m1v1f = m2v2f - m2(0)
= (-2.0)(15)/-20
= 1.5 kg
then add the other piece (2.0kg)
1.5 + 2.0 = 3.5 kg
The mass of firework before explosion is 3.50kg.
mass flying to right m1 = 2kg
v1 = 15 m/s
mass flying to left m2 = ?
v2 = - 20m/s
initial velocity u = 0
by conservation of linear momentum
m1v1+ m2v2 = (m1+m2 ) u
2x 15- m2x 20 = 0
m2 = 1.50kg
therefore mass of firework before explosion
m1+m2
2+ 1.50
= 3.50kg
What is mass?Mass is the amount of matter in a physical body. It also measures the body's inertia, the resistance to acceleration when a net force is applied. The mass of an object also determines its gravitational force on other objects. The basic SI unit of mass is the kilogram.
Body mass is always constant. One way to calculate mass:
mass = volume × density. Weight is a measure of the gravitational force acting on a mass. The SI unit of mass is the "kilogram".
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A ball is projected at an angle of elevation of 60 ° with an initial velocity of 120m/s.calculate
1) The time taken to get to the maximum height
ii) the time of flight
Explanation:
It is given that,
The angle of projection is 60 degrees
Initial velocity of the ball is 120 m/s
We need to find the time taken to get to the maximum height and the time of flight.
Time taken to reach the maximum height is given by :
[tex]T=\dfrac{u^2\sin^2\theta}{2g}[/tex]
g is acceleration due to gravity
[tex]T=\dfrac{(120)^2\times \sin^2(60)}{2\times 10}\\\\T=540\ s[/tex]
(ii) Time of flight,
[tex]t=\dfrac{2u\sin\theta}{g}[/tex]
So,
[tex]t=\dfrac{2\times 120\times \sin(60)}{10}\\\\t=20.78\ s[/tex]
Hence, this is the required solution.
Sally is concerned about the X-ray images her dentist plans to take of her teeth. She has read that X-rays can cause tissue effects, such as skin reddening and hair loss. Which statement would best inform Sally of the level of risk
Answer:
B. The dentist uses X-ray radiography, which takes too short a time to cause those problems.
Explanation:
The statement B would best inform Sally of the level of risk. The dentist uses X-ray radiography, which takes too short a time to cause those problems and risk.
What is X-ray imaging?X-ray imaging provides images of human internal organs. The photos depict your body parts in various colors of black and white.
Because various tissues absorb varying quantities of radiation, this is the case. Because calcium absorbs the most x-rays, bones appear white.
When X-ray radiation passes into our bodies, it damages molecular structures and may cause injury.
Human cells are damaged by extremely high doses of radiation, as indicated by skin burns, hair loss, and an increased risk of cancer.
Sally is concerned about the X-ray images her dentist plans to take of her teeth. She has read that X-rays can cause tissue effects, such as skin reddening and hair loss.
The statement B would best inform Sally about the level of risk. The dentist uses X-ray radiography, which takes too short a time to cause those problems and risk.
Hence, statement B would best inform Sally about the level of risk.
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Thurst exerted by an object of area20m² experiencing pressure 150 Nm‐² is ________
Answer:
3000 N
Explanation:
as we know that
pressure=force/area
so force=thurst
pressure=thurst/area
thyrst=pressure*area
pressure=150 Nm^-2
area=20m^2
so thurst=150*20=3000 N or 3*10^3 N
Which material allows light to pass through A. opaque materials only
B. transparent materials only C. translucent and opaque materials
D. transparent and translucent materials
Answer:
D. transparent and translucent materials
Explanation:
OPAQUE MATERIALS:
Opaque Materials are those materials that absorb all the light and do not allow the light to pass through them.
TRANSLUCENT MATERIALS:
Translucent materials are those materials, that absorb a portion of light, allowing the light to partially pass through them.
TRANSPARENT MATERIALS:
Transparent materials are those materials that do not absorb the light and allow the light to completely pass through them.
Therefore, the correct option is:
D. transparent and translucent materials
Allocate birr 5000 among the three workers in the ratio 1/3 :1/6 and 5/12.
Answer:
1666.7 ETB (birr)
833.3 ETB (birr)
2083.3 ETB (birr)
Explanation:
The first worker
5000*1/3=1666.7
The second worker
5000*1/6=833.3
The third worker
5000*5/12=2083.3
Hope this helps :) ❤❤❤
What is the magnitude of the electrostatic force that the two protons inside the nucleus of a helium atom exert on each other? ( A distance of approximately r = 2*10–15 m separates the two protons.)
Answer:
F = 57.6 N
Explanation:
An electrostatic force is either a force of attraction or repulsion between two charges. When the two charges are like charges, the force is that of repulsion. But when they are of opposite charges, then the force between them is an attractive force.
A proton has a charge of 1.6 × [tex]10^{-19}[/tex] C. The electrostatic force can be determined by;
F = [tex]\frac{kq_{1}q_{2} }{r^{2} }[/tex]
Where: k is a constant, [tex]q_{1}[/tex] is the first charge, [tex]q_{2}[/tex] is the second charge, and r is the distance between the charges.
But, [tex]q_{1}[/tex] = [tex]q_{2}[/tex] = 1.6 × [tex]10^{-19}[/tex] C, k = 9 × [tex]10^{9}[/tex] N[tex]m^{2}[/tex]/[tex]C^{2}[/tex], r = 2 × [tex]10^{-15}[/tex] m. Therefore;
F = [tex]\frac{9*10^{9}*1.6*10^{-19} *1.6*10^{-19} }{(2*10^{-15}) ^{2} }[/tex]
= [tex]\frac{2.304*10^{-28} }{4*10^{-30} }[/tex]
= 57.6 N
The electrostatic force between the protons is 57.6 N.
Neglecting air resistance, the distance s(t) in feet traveled by a freely falling object is given by the function s(t)=16t2, where t is time in seconds. The height of a certain tower is 840 feet. How long would it take an object to fall to the ground from the top of the building?
Answer:
t=7.25 sec
Explanation:
840=16t'2,
Which reverses the flow of current through
an electric motor?
Answer:
a commutator
Explanation:
In the school cafeteria, a trouble-making child blows a 12.0 g spitball through a 25.0 cm straw. The force (F) in Newtons, of his breath as a function of the distance along the straw (x) in meters, can be modeled as a linearly decreasing function for the first half of the straw, followed by a constant force through the rest of the straw. The force decreases by half along the first half of the straw. Assume there is negligible friction and the straw is held horizontally.
(a) Sketch a plot of the force of his breath as a function of position along the straw, labeling the force at x = 0 as F0.
(b) If the spitball begins from rest and leaves the straw with a speed of 16 m/s, how much work is done on the spitball?
(c) What is the maximum force F0, that acts on the spitball?
Answer:
A.) Find the attached file
B.) 1.536 J
C.) 123N
Explanation:
Given that the force (F) in Newtons, of his breath as a function of the distance along the straw (x) in meters, can be modeled as a linearly decreasing function for the first half of the straw,
Half of the straw = 12.5 cm
Let Force F = dependent variable
And distance x = independent variable
A.) Find the attached file for the graph.
Sinnce the force decreases by half along the first half of the straw. Assume there is negligible friction and the straw is held horizontally
B.) Given that the mass M = 12g = 12/1000 = 0.012kg
And Velocity V = 16m/s
The workdone = the kinetic energy of the split ball
WD = 1/2mv^2
Substitutes m and V into the formula
WD = 1/2 × 0.012 × 16^2
WD = 1.536 Joule
C.) The maximum force acts on the spit ball will be at maximum kinetic energy.
Since work done = force × distance
Where distance = 12.5 cm
F × S = 1/2mv^2
Substitutes all the parameters
F × 0.0125 = 1.536
Make F the subject of formula
F = 1.536/0.0125
F = 122.88 N
The maximum force F0, that acts on the spitball is therefore equal to 123 N approximately.
We have that for the Question "(a) Sketch a plot of the force of his breath as a function of position along the straw, labeling the force at x = 0 as F0.
(b) If the spitball begins from rest and leaves the straw with a speed of 16 m/s, how much work is done on the spitball?
(c) What is the maximum force F0, that acts on the spitball?"
It can be said that
a) The sketch is attachedb) The workdone = [tex]1.536J[/tex]c) Maximum force = [tex]6.4N[/tex]From the question we are told
mass of spitball = 12g through a 25.0 cm straw
Generally the equation for workdone is mathematically given as
[tex]= \frac{1}{2}mv^2 - 0\\\\= \frac{1}{2} * 12*10^{-3} * 16^2\\\\= 1.536J[/tex]
Maximum force
[tex]w = \frac{1}{2}*\frac{x_0}{2}*\frac{F_0}{2} + x_0*\frac{F_0}{2}\\\\w = \frac{5}{8}x_0F_0[/tex]
Therefore,
[tex]F_0 = \frac{8w}{5x_0}\\\\F_0 = \frac{8*1.536}{5*25*10^[-2]}\\\\F_0 = 6.4N[/tex]
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Which of these are scientific questions? Check all that apply. How will climate change affect forests? Which planet is the prettiest? How did life on Earth begin? Why did dinosaurs go extinct? Which volcano is the most amazing?
Answer:
The scientific questions here are:
a) How will climate change affect forests
b) How did life on Earth begin
c) Why did dinosaurs go extinct
Explanation:
Scientific question are logical quantifiable questions, whose answers can be measured. A good scientific question must have answers that can be tested by a carefully designed experiment or measurement. Some qualities like "prettiest" and "amazing" cannot be tested for nor are they measurable, and hence, they do not make a testable component of good scientific question.
Let us treat a helicopter rotor blade as a long thin
rod, as shown in Fig. 8–49. (a) If each of the three rotor
helicopter blades is 3.75 m long and has a mass of 135 kg,
calculate the moment of inertia of the three rotor blades
about the axis of rotation. (b) How much torque must the
motor apply to bring the blades from rest up to a speed
of 6.0 rev/s in 8.0 s?
Rotor
Answer:
(a) 1900 kg m²
(b) 8950 Nm
Explanation:
(a) The moment of inertia of a rod about its end is I = ⅓mL².
For 3 rods of mass m = 135 kg and length L = 3.75 m, the total moment of inertia is:
I = 3 (⅓ (135 kg) (3.75 m)²)
I = 1900 kg m²
(b) Net torque = moment of inertia × angular acceleration
∑τ = Iα
First, find the angular acceleration.
ω₀ = 0 rad/s
ω = 6.0 rev/s (2π rad/rev) = 37.7 rad/s
t = 8.0 s
α = (37.7 rad/s − 0 rad/s) / 8.0 rad/s = 4.71 rad/s²
∑τ = Iα
∑τ = (1900 kg m²) (4.71 rad/s²)
∑τ = 8950 kg m² / s²
∑τ = 8950 Nm
Stopping distance of vehicles When brakes are applied to a moving vehicle, the distance it travels before stopping is called stopping distance. It is an important factor for road safety and depends on the initial velocity (v0) and the braking capacity, or deceleration that is caused by braking. A car travelling at speed 72km/hr suddenly applies the brake with the deceleration of 5m/s2. Find the stopping distance of the car.
Answer:
Stopping distance = 40m
Explanation:
Given the following :
Initial speed of vehicle before applying brakes = 72km/hr
Converting km/hr to m/s:
72km/hr = [(72 * 1000)m] / (60 * 60)
72km/hr = 72,000m / 3600s
72km/hr = 20m/s
Deceleration after applying brakes (-a) (negative acceleration) = - 5m/s^2
From the 3rd equation of motion:
v^2 = u^2 + 2as
Where v = final Velocity ; u= Initial Velocity ; a = acceleration and s = distance
Final velocity when the car stops will be 0
Therefore ;
v^2 = u^2 + 2as
0 = 20^2 + 2(-5)(s)
0 = 400 - 10s
10s = 400
s = 400/10
s = 40m
Therefore, the stopping distance of the car = 40 meters
A calculator displays a result such as 1,365 248 0 107 kg. The estimated uncertainty in the result is 2%. How many digits should you include as significant when you write the result? Choose one:
1) zero,
2) one,
3) two,
4) three,
5) four
6) five,
7) the number cannot be determined.
Answer:
4) three
Explanation:
Assuming you mean 1.365248×10⁷, 2% of that is:
0.02 (1.365248×10⁷) = 0.027305×10⁷
So the number is:
1.365248×10⁷ ± 0.027305×10⁷
We need to round this number so that there is uncertainty only in the last digit.
1.37×10⁷ ± 0.03×10⁷
There are three significant figures in 1.37.
The robot HooRU is lost in space, floating around aimlessly, and radiates heat into the depths of the cosmos at the rate of 13.5 W. HooRU's surface area is 1.51 m^2 and the emissivity of its surface is 0.209. Ignore the radiation HooRU absorbs from the cold universe. What is HooRU's temperature?
Answer:
165.73 K
Explanation:
The computation of HooRU's temperature is shown below:-
As per the stefan's law, the power radiated by black body radiations which is
[tex]P = eA\sigma T^4[/tex]
where
A indicates surface area
e indicates emissitivity
T indicates temperature
now, we will put the values in the above equation
[tex]13.5 = 0.209 \times 1.51 \times \sigma \times T^4[/tex]
After solving the above equation we will get temperature which results
= 165.73 K
Therefore for computing the HooRU's temperature we simply applied the above formula.
Find the force acting on it and the acceleration. 15 points. Will give brainliest!
Answer:
[tex]F_{net} = 1905 N[/tex]
[tex]\boxed{a = 7.62 m/s^2}[/tex]
Explanation:
For net force:
Firstly, finding the force of friction:
[tex]F_{k} =[/tex] [tex](micro)_{k} m g cos \theta[/tex]
Where [tex](micro)_{k}[/tex] is the coefficient of friction, m = 250 kg and g = 9.8 m/s²
[tex]F_{k} = (0.17)(25)(9.8) cos (52)\\F_{k} = (41.65)(0.616)\\F_{k} = 25.59 \ N[/tex]
Now, Finding of the pulling box:
[tex]F = mgsin\theta[/tex]
[tex]F = (250)(9.8) Sin (52)\\F = 2450 * 0.788\\F = 1930.6[/tex]
So, The net Force is
[tex]F _{net} = F - F_{k}[/tex]
[tex]F_{net} = 1930.6 -25.6\\[/tex]
[tex]F_{net} = 1905 N[/tex]
For Acceleration:
[tex]F_{net} = m a[/tex]
For a, it is:
=> [tex]a = \frac{F_{net}}{m}[/tex]
=> a = 1905 / 250
=> a = 7.62 m/s²
A piano has a mass of 99 kg. What is the weight of the piano?
Explanation:
weight of the piano = mg
w = 99 x 10 =990 N
The power source provides a current of 1.86 A at a potential difference of 3.90 V. Calculate the power of the power source. Use the equation:
power = potential difference × current
Choose the correct unit from the box below
C W J
Answer:
W
Explanation:
The unit for Power which is (Volt X Current) is Watts. and the symbol for Watts is W.
A point charge +Q is located on the x axis at x = a, and a second point charge –Q is located on the x axis at x = –a. A Gaussian surface with radius r = 2a is centered at the origin. The flux through this Gaussian surface is
Answer:
Net flux through the surface is zero.
Explanation:
Recall that the net electric flux through a closed surface depends on the net charge enclosed inside that surface.
In our case, there are two point charges of exactly opposite charge (net charge - zero), which are located inside the Gaussian surface of radius "2 a" centered at the origin - both charges are located at a distance "a" from the origin of coordinates, therefore inside the Gaussian surface.
Then the net flux through the surface is also ZERO.
PLEASEEE HELP, thank you :)
Answer:
The answer is B.
Explanation:
Given that the current (Ampere) in a series circuit is same so we can ignore it. We can assume that the total voltage is 60V and all the 3 resistance are different, 20Ω, 40Ω and 60Ω. So first, we have to find the total resistance by adding :
Total resistance = 20Ω + 40Ω + 60Ω
= 120Ω
Next, we have to find out that 1Ω is equal to how many voltage by dividing :
120Ω = 60V
1Ω = 60V ÷ 120
1Ω = 0.5V
Lastly, we have to calculate the voltage at R1 so we have to multiply by 20 (R1) :
1Ω = 0.5V
20Ω = 0.5V × 20
20Ω = 10V
How is a less-intense wave different from a more-intense wave?
It has fewer decibels.
O It has a higher pitch.
O It has more volume.
It has more energy.
Answer: It has fewer decibels.
Explanation:
In a sound-wave, the intensity is defined as the power carried by the wave. The decibel is a measure of the ratio between two quantities. And in acoustics is used as the unit of the sound pressure level, which is related to the intensity of the wave, then:
As the intensity increases, we also should notice an increase in the decibels.
How is a less-intense wave different from a more-intense wave?
The less-intense wave has fewer decibels.
Answer:
It has fewer decibels.
Explanation:
A student environmental group is creating a campaign for locally sourced energy resources.What would be best for them to feature in their campaign?a coal mine located in their countya farmer with a field of solar panelsa company building a gas pipeline through the towna rancher drilling for oil in a horse pasture
Answer:
A farmer with a field of solar panels.
Explanation:
The closest to a locally sources energy would have been
A coal mine located in their county.
But coal as an energy source is not environmentally friendly due to carbon emission, and should not be what the group should advocate for.
The best bet for them is
A farmer with a field of solar panels.
As solar panels are a source of green energy and green energy is what the environmental group should often and always advocate for
A 115 kg hockey player, Adam, is skating east whenever he tackles a 133 kg player, Bob, skating west at -1.59 m/s. Afterwards, they move together at .250 m/s east. What was Adam's velocity before the collision? (Unit = m/s)
Answer:
2.38 m/s
Explanation:
Momentum is conserved:
m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂
After the collision, they move at the same speed, so v₁ = v₂ = v.
m₁u₁ + m₂u₂ = (m₁ + m₂) v
Plugging in numbers:
(115 kg) u₁ + (133 kg) (-1.59 m/s) = (115 kg + 133 kg) (0.250 m/s)
u₁ = 2.38 m/s
PLEASE HELP ME ASAP. IT'S VERY IMPORTANT
Answer:
1) a. 52.41 m/s
b. The skier will be going 15.35 m/s slower
2) 103.68 m
3) 35,127 J
4) a. 88.825 kJ
(b) 16.36 %
5) 3,071.12 J
Explanation:
1) a. The given height of the hill, h = 140.0 m
The mass of the skier at the top of the hill, m = 85.0 kg
The acceleration due to gravity, g = 9.81 m/s²
The initial potential energy, P.E of the skier = m×g×h = 85.0×140.0×9.81 = 116739 J
From the principle of conservation of energy, we have;
The potential energy, P.E. lost = The gain in kinetic energy, K.E.
m×g×h = 1/2×m×v²
116739 J = 1/2×85.0×v²
v² = 116739/(1/2*85.0)= 2746.8 m²/s²
v = √(2746.8 m²/s²) = 52.41 m/s
b. From 70 m up, we have;
The initial potential energy, P.E., of the skier is now = 85.0×70×9.81 = 58,369.5 J
The potential energy, P.E. lost = The gain in kinetic energy, K.E.
58,369.5 J = 1/2×85.0×v²
v² = 58,369.5/(1/2*85.0) = 1373.4 m²/s²
v = 37.06 m/s
The skier will be going 52.41 - 37.06 = 15.35 m/s slower
The skier will be going 15.35 m/s slower
2) From the principle of conservation of energy, the amount of work done (energy used) = The (potential) energy gained by the load
The amount of work done by the electric hoist = 356,000 J
The mass of the load = 350.0 kg
The height to which the load is raised = h
The potential energy gained by the load = m×g×h = 350.0×9.81×h
356,000 J = 350.0×9.81×h
h = 356,000/(350.0*9.81) = 103.68 m
The height to which the load is lifted= 103.68 m
3) The initial potential energy of the roller coaster cart = 600*35.0*9.81 = 206010 J
The final potential energy = 600*28.0*9.81= 164808 J
The velocity at point 3 = 4.5 m/s
The kinetic energy at point 3 = 1/2*600*4.5^2 = 6075 J
The total energy at point 3 = 164808 + 6075 = 170,883 J
The energy loss = The initial potential energy at point 1 - Total energy at point 3
The energy loss = 206010 - 170,883 = 35,127 J
The heat energy due to friction that must have been produced between points 1 and 3 = 35,127 J
4) a. The heat energy absorbed = mass × specific heat capacity for water, [tex]C_{water}[/tex] × Temperature change
The mass of the water = 2.5×10² g = 0.25 kg
[tex]C_{water}[/tex] = 4,180 J/(kg·°C)
Initial temperature = 10.0°C
Final temperature = 95°C
The temperature change = 95.0°C - 10.0°C = 85.0°C
The heat energy absorbed = 0.25*4,180* 85 = 88,825 J = 88.825 kJ
(b) The percentage efficiency = (Heat absorbed/(Heat supplied)) × 100
The heat supplied = 543 kJ
The efficiency = (88.825/543) × 100 = 16.36 %
5) The mass of the box = 115 kg
Force acting on the rope = 255 N
The angle of inclination of the force to the horizontal = 24.5°
The distance the box is displaced = 15.0 m to the right
The work done = Force applied × distance moved in the direction of the force
The work done = Force applied × distance moved in the direction of the force
Given that the load moves a distance 15.0 m to the right,we have;
The component of the force acting in the direction of the movement of the load (to the right) is 225 × cos(24.5°) = 204.74 N
The work done = 204.7*15 = 3071.12 J
The amount of work done = 3,071.12 J