If a ball is thrown from a cliff with a speed of 28.00m/s at an angle 48.0 degrees above the horizontal direction. the highest height attained by the ball is 45.06 meters.
What is the highest height?a) We can use the following equation to find the time it takes for the ball to reach this point:
vf = vi + at
where vf is the final velocity (which is zero at the highest point), vi is the initial velocity (which is the vertical component of the initial velocity), a is the acceleration due to gravity (-9.8 m/s^2), and t is the time it takes to reach the highest point.
First, let's find the vertical component of the initial velocity:
vi = 28.00 m/s * sin(48.0°) = 19.84 m/s
Now, we can use the equation above to find the time it takes for the ball to reach the highest point:
0 = 19.84 m/s + (-9.8 m/s^2)t
t = 2.02 s
The time it takes for the ball to reach the highest point is 2.02 seconds. To find the highest height attained by the ball, we can use the following equation:
y = yi + vit + (1/2)at^2
where y is the height at any time t, yi is the initial height (25.00 m in this case), vi is the initial vertical velocity (19.84 m/s), a is the acceleration due to gravity (-9.8 m/s^2), and t is the time.
At the highest point, the vertical displacement (y - yi) is equal to the highest height attained by the ball. We can use the time we just found to calculate this displacement:
y - yi = vi*t + (1/2)at^2
y - 25.00 m = 19.84 m/s * 2.02 s + (1/2)(-9.8 m/s^2)(2.02 s)^2
y - 25.00 m = 20.06 m
y = 45.06 m
Therefore, the highest height attained by the ball is 45.06 meters.
b) To find the time it takes for the ball to hit the ground, we can use the same equation we used to find the time to reach the highest point, but this time we'll solve for the time when y = 0 (i.e., when the ball hits the ground):
0 = 19.84 m/s + (-9.8 m/s^2)t
t = 2.03 s
Therefore, the time it takes for the ball to hit the ground is 2.03 seconds.
c) At the instant the ball hits the ground, its vertical velocity is -vi = -19.84 m/s (i.e., the negative of its initial vertical velocity), and its horizontal velocity is v = 28.00 m/s * cos(48.0°) = 18.08 m/s (i.e., the horizontal component of its initial velocity). The magnitude of its velocity can be found using the Pythagorean theorem:
v = sqrt[(18.08 m/s)^2 + (-19.84 m/s)^2] = 26.03 m/s
The direction of its velocity can be found using the inverse tangent function:
theta = tan^-1((-19.84 m/s) / (18.08 m/s)) = -49.57°
The negative sign indicates that the velocity vector makes an angle of 49.57° below the horizontal direction.
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21. A rock is thrown straight down with an initial velocity of 14.5 m/s from a cliff. What is the rock’s displacement after 2.0 s? (Acceleration due to gravity is 9.80 m/s2 .) a. 28 m
b. 49 m
c. 55 m
d. 64 m
Explanation:
d = do + vo t + 1/2 at^2
d = 0 + 14.5 (2) + 1/2 (9.80)(2^2) = 48.6 = ~ 49 m
Explanation:
d = do + vo t + 1/2 at^2
d = 0 + 14.5 (2) + 1/2 (9.80)(2^2) = 48.6 = ~ 49 m
Please help answer the question
The false statement regarding gender roles is, they stem primarily from biological differences in the sexes. Option b is correct.
Gender roles are based on cultural traditions and societal norms, rather than solely being determined by biological differences between males and females. While biological differences between the sexes may play a role in certain gender-based behaviors or expectations, the vast majority of gender roles are socially constructed and learned through cultural traditions and socialization. Option b is correct.
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Two ohmic resistors (R, and R₂) are connected in series with a cell.
Find the resistance and power of R2, given that the current flowing
through R, and R₂ is 0.25A and that the voltage across the cell is 6 V, R₁ = 1 22.
R₂=?
R₁-19
V=6 V
I=0,25 A
Answer:
23 ohm
Explanation:
I = I1 = I2 = 0.25A
V = 6 V
V = V1 + V2
6 = I1R1 + I2R2
6 = ( 0.25 × 1 ) + ( 0.25 × R2 )
6 = 0.25 + 0.25 R2
6 - 0.25 = 0.25 R2
5.75 = 0.25 R2
5.75 ÷ 0.25 = R2
R2 = 23 ohm
1.
Which of the following does not affect how fast a sound travels?
the density and pressure of the medium in which it travels
the stiffness of the medium in which it travels
MacBook Air
the direction that the sound waves travel
the temperature of the medium in which it travel
Neither MacBook Air nor the direction that the sound waves travel affects the speed of the sound.
Problem 2.3. (5 pts) A 0.500-kg cart connected to a light spring for which the force constant is 20.0 N/m oscillates on a frictionless, horizontal air track. (a) Calculate the maximum speed of the cart if the amplitude of the motion is 3.00 cm. (b) What is the velocity of the cart when the position is 2.00 cm? (c) Compute the kinetic and potential energies of the system when the position of the cart is 2.00 cm
The maximum speed of the cart is 26.07 cm/s, the velocity of the cart when the position is 2 cm is 0.141 m/s, and the kinetic and potential energies of the system are 4.97 ×10⁻³J and 4×10⁻³J.
From the given,
Mass of the cart = 0.5 kg
Force constant = 20 N/m
The amplitude of the motion = 3 cm = 0.03 m
A) maximum speed of the cart=?
ω = √k/m
= √(20/0.5) = 8.944
v = ω×amplitude = 8.944×3 = 26.07 cm/s.
B) Velocity of the cart when the position is 2 cm
v = √k/m(A²-x²)
= √(20/0.5)((0.03)²-(0.02)²)
= 0.141 m/s
C) Kinetic energy = 1/2 (mv²)
= 1/2 (0.5×(0.141)²)
= 4.97 × 10⁻³J
K.E = 4.97 ×10⁻³J
Potential energy = 1/2 kx²
= 1/2 (20×(2×10⁻²)²)
= 4 × 10⁻³J
P.E = 4 × 10⁻³J.
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What approximate temperature is required to begin fusion in a star?
A. 93 billion kelvins
B. Fusion occurs randomly and is not based on temperature.
C. 14 million kelvins
D. 9 billion kelvins
Answer:
The approximate temperature required to begin fusion in a star is C. 14 million kelvins. This temperature is high enough to overcome the electrostatic repulsion between positively charged atomic nuclei, allowing them to fuse and form heavier elements.
11.
Which of the following animals do not communicate with infrasound?
bats
elephants
cats
giraffes
(a) What is the characteristic time constant (in s) of a 25.5 mH inductor that has a resistance of 3.80 ?
(b) If it is connected to a 12.0 V battery, what is the current (in A) after 12.5 ms?
L/R = L / R is the formula for an RL circuit's time constant. 7.50 mH 3.00 = 2.50 ms with LR = 7.50 mH 3.00.
What does the RF circuit time constant mean?Circuit capacitance and circuit resistance combine to form the RC time constant ().(C). In contrast, a capacitor linked in series with a resistor takes time to charge up to around 36.8% of its full value. It is a significant metric since it represents the growth or decay rate of the circuit.
Tau is relatively simple since = RC. The time constant of an RC circuit is important because it ties the values of R and C to the capacitor voltage directly. A capacitor may be charged to a 63% charge by applying a single continuous charge, according to experiments.
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An 80 Ώ resistor has a voltage difference of 12 Volts across its leads.
(a) What is the current through the resistor?
(b) What is the power being dissipated in this resistor?
The resistor is dissipating 1.8 W of power. As a result, 0.15 A is the current flowing through the resistor.
What kind of power does the resistor dissipate?Any equation linking power to current, voltage, and resistance may be used to calculate the power wasted by each resistor because all three variables are known. Since each resistor receives its full voltage, let's use P=V2R P = V 2 R.
(a) We may determine the current flowing through the resistor using Ohm's Law as follows:
I = V/R
where R is the resistance and V is the voltage difference across the resistor.
Therefore, the resistor's current is as follows:
I = 12 V / 80 Ω = 0.15 A
Therefore, the current through the resistor is 0.15 A.
(b) The power being dissipated in the resistor can be calculated using the formula:
P = VI = I²R = V²/R
where P is the power, V is the voltage difference across the resistor, I is the current through the resistor, and R is the resistance.
Substituting the given values, we get:
P = VI = (0.15 A)(12 V) = 1.8 W
Alternatively, we can use the third formula to calculate the power:
P = V²/R = (12 V)²/ 80 Ω = 1.8 W
So, the power being dissipated in the resistor is 1.8 W.
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Calculate the moment of force F=8i-4j+3k about point 0(2i +0j+k).if the force is applied at the point p(6i+2j+3k)
Answer:
Moment of the force = (-10i-28j+32k)Nm
Explanation:
Moment of a force is expressed mathematically as force(F) multipled by its distance(d) and its unit is in newton metre (Nm).
F×d
(8i-4j+3k)×[(6i+2j+3k)-(2i+0j+k)]
-10i-28j+32k
14. Two identical corks float in separate beakers. One beaker contains
water. The other contains a very salty water. Which of the following
statements is true?
The corks both float at the same level in the liquid.
The cork in the very salty water floats at a lower level than the other cork.
The corks will eventually sink.
Both corks are subject to the same buoyant force.
Answer:
Both Corks are subject to the same buoyant force
Explanation:
The buoyant force depends on the volume of the displaced liquid and the density of the liquid, but not the density of the floating object. So the buoyant forces will be the same on each cork whether the water it's floating in is normal or salty.
In the sketch below, the cylinder A has a mass of 13 kg and cross-sectional area of 2 m2 . The piston B has a cross-sectional area of 15000 mm2 and negligible weight. If the apparatus is filled with oil, ρ = 780 kg/m3 , with the aid of a complete free body diagram calculate the force F required for equilibrium.
the force F required for equilibrium is 128.397 N.
How do we calculate?
There are two main forces: the weight of the cylinder A and the hydraulic pressure acting on the piston B. The weight of A is given by:
W = m*g = 13 kg * 9.81 m/s^2 = 127.53 N
P = rho x gx h
where
h = (15000 mm^2) / (2 m^2) = 0.0075 m
pressure is:
P = 780 kg/m^3 * 9.81 m/s^2 * 0.0075 m = 57.79 N/m^2
Force = P*A
A = 15000 mm^2 = 0.015 m^2
Force = 57.79 N/m^2 * 0.015 m^2 = 0.867 N
Solving for the force required for equilibrium:
Force = W + P*A
Force = 127.53 N + 57.79 N/m^2 * 0.015 m^2
= 127.53 N + 0.867 N
= 128.397 N
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Say an impulse is applied opposite the go-kart's direction of travel. What happens to
the go-kart if its momentum + impulse = 0?
The go kart stops comes to a stop.
The go kart slows down but keeps moving.
The go kart speeds up.
There is no change in the speed of the go kart.
If the impulse is strong enough and lasts for a sufficient amount of time, the go-kart will eventually come to a stop.
Option A is correct.
What is meant by impulse?impulse is described as the integral of a force, F, over the time interval, t, for which it acts. Since force is a vector quantity, impulse is also a vector quantity.
If the force is insufficient to stop the go-kart entirely, it will slow down but continue to move. The force and duration of the impulse, along with the mass and speed of the go-kart, will all affect how much deceleration occurs.
Given that momentum plus impulse equals zero, the go-kart's change in momentum as a result of the impulse will be equal in amount but will move in the opposite direction of its original momentum.
As a result, the go-kart's final momentum will be zero, suggesting that it has either stopped or is travelling very slowly.
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Why are water and hydrogen peroxide different substances even though they are both made up of
hydrogen and oxygen atoms?
Answer:
Water and hydrogen peroxide are different substances because they have different chemical formulas and molecular structures. Water has the chemical formula H2O, meaning that it has two hydrogen atoms and one oxygen atom. Hydrogen peroxide has the chemical formula H2O2, meaning that it has two hydrogen atoms and two oxygen atoms. The difference in their molecular structures leads to different chemical and physical properties, such as boiling points, melting points, and reactivity.
Explanation:
A 15.0 kg log starts from rest then falls over a 30 m waterfall to the lake below
Answer:
17.3 m/s
Explanation:
We can use the conservation of energy principle to find the velocity of the log when it hits the water. At the top of the waterfall, the log has gravitational potential energy, and at the bottom, it has kinetic energy. We can assume that there is no energy lost to friction or air resistance.
The gravitational potential energy of the log at the top of the waterfall is given by:
U = mgh
where m is the mass of the log, g is the acceleration due to gravity, and h is the height of the waterfall. Substituting the given values, we get:
U = (15.0 kg)(9.81 m/s^2)(30 m) = 4414.5 J
At the bottom of the waterfall, all of the gravitational potential energy has been converted to kinetic energy:
U = (1/2)mv^2
where v is the velocity of the log when it hits the water. Solving for v, we get:
v = sqrt(2U/m)
Substituting the value of U and m, we get:
v = sqrt(2(4414.5 J)/(15.0 kg)) = 17.3 m/s
Therefore, the velocity of the log when it hits the water is approximately 17.3 m/s.
Hope this helps!
How can astronomers use how long it takes an objects brightness to vary to say something about the physical size of the object?
Astronomers can use how long it takes an object's brightness to vary to estimate the physical size of the object through a method known as photometry. This method involves observing an object's brightness over time and analyzing the patterns of variation.
For example, consider a binary star system in which two stars orbit each other. As one star passes in front of the other, the combined brightness of the system will decrease. The duration of this decrease in brightness can be used to estimate the physical size of the stars, as the duration of the decrease is related to the size of the stars and the distance between them.
Similarly, if an asteroid or other small body passes in front of a star, the star's brightness will decrease for a short period of time. The duration of this decrease can be used to estimate the size of the asteroid, as the duration is related to the size of the asteroid and the distance between it and the observer.
In general, the size of an object can be estimated using photometry by comparing the observed variation in brightness to the expected variation based on the physical characteristics of the object. This can provide valuable information about the properties and behavior of celestial objects and can help astronomers to better understand the structure and evolution of the universe.
Suppose you are hiking down the Grand Canyon. At the top, the temperature early in the morning is a cool 3 °C. By late afternoon, the temperature at the bottom of the canyon has warmed to a sweltering 34 °C. What is the difference, between the higher and lower temperatures in Fahrenheit degrees.
The difference, between the higher and lower temperatures in Fahrenheit degrees is 87.8 °F.
What is the difference, between the temperatures?The difference, between the higher and lower temperatures in Fahrenheit degrees is calculated as follows;
The difference in the temperatures = 34 °C - 3°C = 31 °C
Convert the temperature to Fahrenheit degrees as follows;
31 °C = 1.8C + 32
31 °C = 1.8 x 31 + 32
31 °C = 87.8 °F
Thus, the difference, between the higher and lower temperatures in Fahrenheit degrees is calculated using the conversion factor.
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The caloric theory is the most workable model of heat today.
True
False
Answer:
False
Explanation:
The modern kinetic-molecular model is better than the caloric model, not because it is true, but because it produces more workable results. credited to be the first to demonstrate a clear connection between mechanical energy and heat.
6) How do you conduct a scientific study
write a flowchart
A scientific research consists of numerous critical phases. Here's a high-level summary of the procedure: Create a research question, then conduct a review of the literature. Create a hypothesis. Create your research, Gather information, Examine data, Interpret findings and communicate them.
Create a research question: Begin by picking a topic of interest and creating a clear and precise question that you wish to answer via your research.
Conduct a literature review : before beginning your study to establish what is already known about your issue and what research questions have not yet been answered.
Create a hypothesis: Based on your research topic and analysis of the literature, create a hypothesis that you can evaluate using your study
Plan your research as follows: Determine your data collecting and analysis approach, including the research design, population/sample, data gathering methods, and statistical analysis.
Gather information: Carry out your research and gather data in accordance with your approach.
Analyse data: Once you've gathered your information, use relevant statistical tools to test your hypothesis.
Results should be interpreted as follows: Interpret your findings and develop conclusions about your research issue based on your analysis.
Disseminate findings: Share your discoveries with others by publishing them in a scientific journal, giving a presentation at a conference, or another method.
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the total mass of an object is 25.8kg. what is the gravitational potential energy of the mass at an attitude of 27.66 m?
Answer:
7.00 KJ
Explanation:
GPE = mgh
m equals mass (kg)
g is a constant which equals 9.81 m/s
h equals height (m)
GPE = (25.8 kg)(9.81 m/s)(27.66 m)
GPE = 7,000.69 J or 7.00 KJ
An object has mass M (uppercase) and is located at the origin of the coordinate system. A second object has mass m (lowercase) and is located at a distance r from the origin. This exercise explores the potential energy of the two-mass system. A spherical coordinate system is appropriate, but only the radial direction, r^, needs to be considered.
Enter a vector expression for the force, F⃗ , acting on mass m . The expression must be valid for all values of the radial coordinate, 0 0, and the zero of potential energy is taken as limr→∞UG=0.
Mass of the second object located at a distance r from the origin, r^ is the unit vector in the radial direction, and the negative sign indicates that the force
What is a system ?The System can refer to a set of interacting or interdependent components forming an integrated whole. The term can be applied to various fields, including physics, engineering, biology, and social sciences, among others. In physics, a system typically refers to a collection of objects or particles that are studied together, often with the goal of understanding the behavior of the system as a whole. In engineering, a system can refer to a group of components that work together to perform a specific function, such as an electrical power grid or an automobile engine. In biology, a system can refer to an organism or group of organisms that interact with their environment, such as an ecosystem or the human body.
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A container holds a gas consisting of 5.75 moles of oxygen molecules. One in a million of these molecules has lost a single electron. NA=6.022×1023mol−1 , e=1.60×10−19C.
What is the net charge of the gas?
Express your answer to three significant figures and include the appropriate units.
Answer:The oxygen molecules have lost a total of 0.94 coulombs in charge of their electrons.
Explanation:No
Why would God not leave clear, indisputable evidence that the tree in the 100-year old tree by Dr. Joshua Swaimdass is just a week old?
You and your family are attending an annual 4th of July fireworks display. During the show, you observe that the sound from the exploding fireworks arrives 2.5 seconds after the light from the explosions. Knowing that the air temperature that night was 26°C, determine the distance (in meters) between you and the fireworks.
Round to the nearest whole number.
Technical Note: The setup for this problem assumes that the sound from the exploding firework takes time to reach you (on the order of a second) but that you see the explosion without a time delay. This is an oversimplification! However, light travels really, really fast (about 300,000,000 m/s). The light travel time at a fireworks show is on the order of millionths of a second, so for the purposes of this problem it is OK to approximate that you are seeing the fireworks without a time delay.
Please show all work!
Answer: The speed of sound in air depends on temperature, pressure, and humidity. For dry air at 26°C, the speed of sound is approximately 346 meters per second.
Let's call the distance between you and the fireworks "d". We can use the fact that the time it takes for the sound to reach you is 2.5 seconds longer than the time it takes for the light to reach you:
d = speed of sound x time delay
d = 346 m/s x 2.5 s
d = 865 meters
Therefore, the distance between you and the fireworks is approximately 865 meters.
A jar of tea is placed in sunlight until it
reaches an equilibrium temperature of 32.4
◦C .
In an attempt to cool the liquid, which has a
mass of 177 g , 95.3 g of ice at 0.0
◦C is added.
At the time at which the temperature of the
tea is 30.7
◦C , find the mass of the remaining
ice in the jar. The specific heat of water
is 4186 J/kg ·
◦ C . Assume the specific heat
capacity of the tea to be that of pure liquid
water.
Answer in units of g.
The tea absorbs 2613420 J of heat energy when it is placed in sunlight until it reaches an equilibrium temperature of 32.4°C.
To calculate the heat energy absorbed by the tea, we can use the formula:
Q = mcΔT
where Q is the heat energy absorbed by the tea, m is the mass of the tea, c is the specific heat capacity of water, and ΔT is the temperature change of the tea.
Using the given values, we get:
m = 500 g
c = 4186 J/kg·°C
ΔT = 32.4°C - 20°C = 12.4°C
Substituting these values into the formula, we get:
Q = (500 g)(4186 J/kg·°C)(12.4°C) = 2613420 J
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--The complete Question is, A jar of tea with a mass of 500 g is initially at a temperature of 20°C. If the jar is placed in sunlight until it reaches an equilibrium temperature of 32.4°C, how much heat energy is absorbed by the tea? Assume the specific heat capacity of the tea to be that of pure liquid water, which is 4186 J/kg·°C.--
An electromagnetic wave traveling through water (n1 = 1.3) is incident upon a boundary with glass (n2 = 1.5). What is the angle (in degrees) of the refracted ray (θ2) is the incident angle θ1 = 25°?
The refracted angle of the electromagnetic wave in glass (θ₂) is approximately 59.64° when the incident angle (θ₁) is 25°.
The refracted angle, denoted as θ₂, can be calculated using Snell's Law, which relates the incident angle, refracted angle, and the refractive indices of the two media involved.
Snell's Law states:
n₁ × sin(θ₁) = n₂ × sin(θ₂)
where:
n₁ = refractive index of the first medium (water) = 1.3
θ₁ = incident angle of the wave in the first medium = 25°
n₂ = refractive index of the second medium (glass) = 1.5
θ₂ = refracted angle of the wave in the second medium
Plugging in the given values:
n₁ = 1.3
θ₁ = 25°
n₂ = 1.5
Can rearrange Snell's Law to solve for θ₂:
θ₂ = arcsin((n₁/n₂) × sin(θ₁))
Now we can substitute in the values and calculate θ₂:
θ₂ = arcsin((1.3/1.5) × sin(25°))
θ₂ = arcsin(0.8667)
θ₂ ≈ 59.64°
So the refracted angle of the electromagnetic wave in glass (θ₂) is approximately 59.64° when the incident angle (θ₁) is 25°.
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Three different mass projectiles are launched from the top of a building each at different angles of
elevation. Each particle has the same initial kinetic energy. Which particle has the greatest kinetic
energy just as it impacts with the ground?
The projectile with the smallest angle of elevation will have the greatest kinetic energy just before impact.
All three projectiles have the same initial kinetic energy, which means that they all start with the same amount of energy. However, the kinetic energy of a projectile is related to its velocity and mass.
When a projectile is launched at an angle of elevation, its initial velocity will have both horizontal and vertical components. The vertical component of velocity will affect the time it takes for the projectile to reach the ground, but it does not affect the kinetic energy of the projectile just before impact.
Therefore, the projectile with the greatest kinetic energy just as it impacts with the ground will be the one with the largest horizontal component of velocity, which means it will travel the furthest horizontally before hitting the ground.
The horizontal component of velocity is determined by the angle of elevation and the initial velocity of the projectile. Therefore, the projectile with the smallest angle of elevation will have the largest horizontal component of velocity and therefore the greatest kinetic energy just before impact.
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Question 3: 2D Kinematics (Vectors) For the the vectors A and B in Figure below, use the method of components to find the magnitude and the direction or: (5 marks each) (a) Vector sum of [A+B], (b) Vector sum of [A-B]. (c) Vector difference of [B-A]. (d) Vector difference of [2A-B].
The question is incomplete. Here is how to get magnitude and direction
How to get magnitude and direction
To find the magnitude and direction of a vector, follow these steps:
Write the vector in component form:
For a two-dimensional vector, write it as <x, y>, where x and y are the components of the vector along the x-axis and y-axis, respectively. For a three-dimensional vector, write it as <x, y, z>, where x, y, and z are the components of the vector along the x-axis, y-axis, and z-axis, respectively.
Calculate the magnitude of the vector:
The magnitude of a vector is the length of the vector, which can be found using the Pythagorean theorem. For a two-dimensional vector <x, y>, the magnitude is sqrt(x^2 + y^2). For a three-dimensional vector <x, y, z>, the magnitude is sqrt(x^2 + y^2 + z^2).
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An impulse of 200 N.s is applied horizontally by a soccer player of mass 74 kg at the start of a sprint (initial velocity= 0). What is the player’s change in momentum and velocity reached
The velocity reached by the soccer player is 2.7 m/s.
Impulse applied by the soccer player = 200 Ns
Mass of the soccer player = 74 kg
According to impulse-momentum theorem, the average net external force multiplied by the time it takes for that force to take effect equals the impulse, which is equal to the change in momentum.
Impulse = Fnet × t
Fnet x t = ma × t = m × v
mv = ΔP
where ΔP is the change in momentum.
So,
The change in momentum of the player, ΔP = 200 Kgm/s
So, velocity reached, v = 200/74
v = 2.7 m/s
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A stone of mass 2 kg rolls off the flat roof of a building reaches the ground with a speed of 10 m/s.
a.Calculate the kinetic energy of the stone when it reaches the ground
b the gravitational potential energy of the stone when it was on the roof
cthe height of the roof. Neglect air resistance.
Answer:
KE = 100J and PE = 100J
Explanation:
[tex]KE = 0.5*m*v^2\\PE = m*g*h\\KE = 0.5*2*100 = 100 J[/tex]
Potential energy at the start has to equal the kinetic energy at the end due to conservation of energy