Answers
Related Questions
You push a cart with mass 15 kg forward, giving it an acceleration of 3 m/s2
How much force did you apply?
Answers
Answer:
45 N
Explanation:
F= ma (ie force is found by multiplying the mass of the object by its accerelation)
thus, F = 15 X 3 = 45 N
Physics Momentum topic question. I will mark brainliest please help.
Answers
Answer:
10 m/s
Explanation:
Given
mass of ball 1, m1 = 1 kgmass of ball 2, m2 = 0.25 kginitial velocity of ball 1, u1 = 10 m/sinitial velocity of ball 2, u2 = 0 m/s [stationary]final velocity of ball 1, v1 = 7.5 m/smomentum of ball 2 after collision = 2.5 kg m/sSolving :
We do not require all of this informationOnly require points 2 and 6Momentum = mass x velocity⇒ velocity = 2.5 / 0.25⇒ velocity = 10 m/sThe mass of the planet Mars is 6.39 x 10^23 kg. Using Newton's Law of Gravitation, calculate the force of gravity between the planet Mars and the 74 kg Mars Rover drone on the surface if the distance between the center of Mars and surface is 2129.9 km. Show all work.
Need it ASAP!!!!!!!!!!!!!!!!!!!!!!!!!!!1
Answers
Answer:
F = 695.25 N
Explanation:
The force between Mars and Rover can be given by Newton's Law of Gravitation can be written as follows:
F = Gm₁m₂/r²
where,
F = Force of Gravity = ?
G = Universal Gravitational Constant = 6.67 x 10⁻¹¹ N.m²/kg²
m₁ = mass of rover = 74 kg
m₂ = mass of mars = 6.39 x 10²³ kg
r = distance between the centers of mars and rover = 2.1299 x 10⁶ m
Therefore,
F = (6.67 x 10⁻¹¹ N.m²/kg²)(74 kg)(6.39 x 10²³ kg)/(2.1299 x 10⁶ m)²
F = 695.25 N
An army tank division leaves base and travels 30 miles at [W30*S] and then turns and travels 70 miles at [W10*N]. What is their total displacement from base at the end of the trip?
Answers
The tank division's total displacement from the base is approximately 75.9 miles at a bearing of W67.4S.
How to calculate the displacement?To calculate the total displacement of the tank division, we need to find the vector sum of the two legs of their journey.
We can see that the tank division travelled 30 miles to the west (W30) and then 70 miles to the north (N70), so their total displacement is the vector sum of these two legs.
To add vectors, we need to break them down into their horizontal and vertical components.
For the first leg, the tank division travelled 30 miles to the west, so its horizontal component is -30 (since it's to the left of the base) and its vertical component is 0 (since it didn't travel up or down).
For the second leg, the tank division travelled 70 miles to the north, so its horizontal component is 0 (since it didn't travel left or right) and its vertical component is 70 (since it travelled directly north).
Now we can add these components to get the total displacement:
Horizontal component = -30 + 0 = -30
Vertical component = 0 + 70 = 70
So the total displacement is a vector with a horizontal component of -30 and a vertical component of 70.
We can use the Pythagorean theorem to find the magnitude of this vector:
|displacement| = √((-30)² + 70²) ≈ 75.9 miles
And we can use trigonometry to find the direction of this vector:
\(\theta = tan^{-1}\dfrac{70} { -30}\)
θ ≈ -67.4°
So the tank division's total displacement from the base is approximately 75.9 miles at a bearing of W67.4S.
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What does the term wavelength refer to?
the distance between the equilibrium position and a crest
the distance between the equilibrium position and a trough
the time taken to complete one cycle
the distance between two consecutive crests or troughs
Answers
Answer:
the distance between two consecutive crests or troughs
Answer #49 please and thank you
Answers
when Force (N) is 10.0 Length (m) is 0.60
when Force (N) is 8.0 Length (m) is 0.40
when Force (N) is 4.0 Length (m) is 0.20
when Force (N) is 4.0 Length (m) is 0.20
when Force (N) is 2.0 Length (m) is 0.10
chatgpt
49. To find the length of a pendulum that has a period of 2.3 seconds on the Moon, where the gravitational acceleration (g) is 1.6 N/kg, we can use the formula:
Period (T) = 2π√(Length (L) / g)
Substituting the given values:
2.3 = 2π√(L / 1.6)
To solve for L, we can rearrange the formula:
L = (2.3 / (2π))^2 * 1.6
L ≈ 0.781 meters (or 78.1 centimeters)
So, the pendulum must be approximately 0.781 meters (or 78.1 centimeters) long to have a period of 2.3 seconds on the Moon.
50. Ranking Task:
To rank the pendulums according to their periods, we need to consider both the length and mass of each pendulum.
Ranking from least to greatest period:
1. A: 10 cm long, mass = 0.25 kg
2. C: 20 cm long, mass = 0.25 kg
3. B: 10 cm long, mass = 0.35 kg
There is a tie between pendulums A and C, as they have the same length but different masses.
Very large forces are produced in joints when a person jumps from some height to the ground. (a) Calculate the magnitude of the force (in N) produced if a 62.0 kg person jumps from a 0.800 m-high ledge and lands stiffly, compressing joint material 1.50 cm as a result. (Be certain to include the weight of the person.) N (b) In practice the knees bend almost involuntarily to help extend the distance over which you stop. Calculate the magnitude of the force (in N) produced if the stopping distance is 0.300 m. N (c) Compare both forces with the weight of the person.
Answers
Answer:
a) F = 3.3 10⁴ N, b) F = 2.2 10³ N, c) force when rigid is 15 times greater than when bending the knees
Explanation:
For this exercise we can use the relationship between work and the variation of kinetic energy
K₀ = ½ m v²
the final kinetic energy is zero because the person is stationary
W = (∑ F) x
W = W x - F w
the weight is in the same direction of the displacement therefore the work is positive and the force applied, by the floor, is in the opposite direction to the displacement, consequently the work is negative
we substitute
( W- F ) x = 0-K₀
F = W + K₀ /x
F = mg + \(\frac{1}{2} \frac{mv^2 }{2x}\)
F = m ( g+ \(\frac{v^2 }{2x }\) )
Let's use kinematics to find the velocity of the person when reaching the floor
v² = v₀² - 2g (y + y₀)
the initial velocity is true and when reaching the ground y = 0
v² = -2 g (0-yo)
we calculate
v = \(\sqrt{2 ] 9.8 \ 0.800}\)
v = - 3.96 m/s
the direction of this velocity is vertical down
let's calculate
a) x = 1.50 cm = 0.0150 m
F = 62.0 (3.96² / 2 0.0150 + 9.8)
F = 3.3 10⁴ N
b) x = 30 cm = 0.30 m
F = 62.0 (3.96² / 2 0.30 + 9.8)
F = 2.2 10³ N
c) to compare the force let's look for the relationship between the two
\(\frac{F_{rigid} }{ F_{flexible} }\) = 3.3 10⁴ / 2.2 10³
\frac{F_{rigid} }{ F_{flexible} } = 15
therefore see that the force when rigid is 15 times greater than when bending the knees
1. Compare the kinetic energy distributions for the heavy vs. light particles at the same
temperature. Are these the same or different? What about the speed distributions?
2. Compare the kinetic energy distributions for the heavy vs. light particles at different
temperatures. Are these the same or different? What about the speed distributions?
3. Compare the kinetic energy distributions for the mixture to those of the heavy-only and light-
only gases at the same temperature. Are these the same or different? What about the speed
distributions?
4. Summarize your observations about the relationships between molecular mass (heavy vs.
light), kinetic energy, particle speed, and temperature.
Answers
Only when the average speed of the heavy particles is lower than that of the light particles will the average kinetic energy of the light particles equal the average kinetic energy of the heavy particles.
How do the kinetic energy of the light and heavy particles compare?Only when the average speed of the heavy particles is lower than that of the light particles will the average kinetic energy of the light particles equal the average kinetic energy of the heavy particles.
As the temperature rises, the particles accumulate kinetic energy and quicken. The actual average speed of the particles is influenced by both their mass and temperature; at a given temperature, larger particles travel more slowly than lighter ones.
Given that the formula for calculating a particle's kinetic energy is
Ek = 1/2 mu²,
The formula for particle speed is \($$c = [3RT/M]^{1/2\).
The graphs of kinetic energy and particle speed show that the heavier particles only have higher peaks, whilst the lighter particles only have lower peaks.
It is clear from the graphs and the temperatures employed that the graphs' shapes were nearly identical. It does not appear to be significantly impacted by temperature.
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Which of the following atoms contain a nucleus with no neutrons.
helium
hydrogen
deuterium
tritium
Answers
Answer:
Hydrogen
Explanation:
(H) atom does not have any neutrons in it's tiny nucleus.
Answer: C. Hydrogen
Explanation: Now I can answer the question lol, that bot didn't let me.
50
1. Force = ? N mass = 65 kg acceleration = 25 m/s2 (Record your answer
by number only and don t.include units...)
Answers
Answer: el pepe
Explanation:
Answer:
8125 N.
Explanation:
F = M A
M is mass
A is acceleration
F = 65 X 25
F = 8125 N.
PLEASE ANSWER FASG I WILL MARK BRAINELIST PLEASEEEEE
The number of protons in the nucleus of an atom determines the species of the atom, i.e., the element to which the atom belongs. An atom has the same number of protons and neutrons. But the electron number cannot be used instead because (5 points)
a. electrons are not within the nucleus
b. electrons are negatively charged
c. electrons can be removed from or added to an atom
d. electrons are lighter than protons
Answers
The electron number cannot be used instead because electrons can be removed from or added to an atom (option C)
Why the electron number cannot be used instead?The element of an atom is determined by its proton count, while the electron count can exhibit variability. Take, for instance, a sodium atom, which encompasses 11 protons and 11 electrons. However, it has the capacity to relinquish one electron, transforming into a sodium ion housing only 10 electrons.
This occurs due to the relatively loose binding of electrons to the nucleus, enabling their removal through the influence of an electric field or alternative mechanisms.
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A wagon weighing 1000kg moves 50km/h on smooth rails. Later, a mass of 250 kg is placed in the wagon what is the velocity with which it moves?
Answers
The final velocity V is 40 km/h.
The final velocity V.
Mass of wagon m = 1000 kg
Initial velocity of wagon v = 50 km/h
Mass dropped velocity M = 250 kg
The final velocity =V
Initial system linear momentum \(P_{i}\) = mv
=1000*50
=5*\(10^{4}\) kg km/h
The system with the final velocity (wagon + mass dropped) be V .
Final system linear momentum \(P_{f}\) = (m + M) V
=(1000+250)V
=1250 V
Basic principle of conservation of linear momentum,
\(P_{f}\) = \(P_{i}\)
1250V=5*\(10^{4}\)
V=\(\frac{5*10^{4} }{1250}\)
V= 40 km/h
So, the final velocity V is 40 km/h.
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Planet X has a mass 3.38 times that of the Earth and a radius 4.84 times the radius of the Earth. What is the ratio of the acceleration due to gravity on the surface of Planet X to the acceleration due to gravity on the surface of the Earth?
Answers
The ratio of acceleration due to gravity on planet X and on Earth is 8 : 5.
What is the ratio of the acceleration due to gravity?
Acceleration due to gravity is calculated by using the following formula.
g = ( GM ) / ( R² )
where;
G is universal gravitation constantM is the mass of the planetR is the radius of the planetThe acceleration due to gravity of the planet described in the question is calculated as;
g = ( G x 3.38 M ) / ( 4.84R )²
g = ( 3.38 / 20.7 ) ( GM/R² )
g = 0.163 ( GM/R² )
Ratio of acceleration due to gravity on planet X and on Earth;
= 0.163 ( GM/R² ) : ( GM/R² )
= 0.163 : 1
= 16.3 : 10
= 16: 10
= 8 : 5
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In a 41 s interval, 580 hailstones strike a glass window of area 1.346 m2 at an angle 31◦ to the window surface. Each hailstone has a mass of 7 g and speed of 6.7 m/s. If the collisions are elastic, find the average force on the window. Answer in units of N.
Answers
Answer:
N = hailstones / sec = 580 / 41 = 14.1 stones / sec
mass = .007 kg
v = 6.7 m/s * sin 31 = 3.45 speed of stones perpendicular to surface
Δp = 2 m Δv change in momentum dur to striking window
F = N Δp force required to repel hailstones
F = 2 N m Δv = .68 N force on window pane
Pressure = force / area (don't need window area for force)
subtract 7.987 m - 0.54 m and the final answer must be in decimal form
Answers
Answer:
7.447
Explanation:
PLEASE HELP ME ANSWER THE PHYSICS QUESTIONS ON MY PROFILE!!!
i will give brainliest to the first to answer!!! this one and the other ones
Two freight cars, each with a mass of 291,001 kg, collide and stick together. One was initially moving at 2.4 m/s and the other was at rest. What is their final speed?
Answers
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Compare and contrast gravitational and elastic potential energy, and give an example of each.
Answers
Answer:
See explanation
Explanation:
Potential energy is the energy that is stored in an object due to its state, arrangement or position. It can also be described as any energy that has the potential to do work. The two types of potential energy are:
Gravitational potential energy andElastic potential energyDifferences are:
Gravitational potential energy emanates from the gravitational attraction between masses while Elastic potential energy emanates from the electrostatic repulsion between molecules and atoms.Gravitational potential energy tries to pull the center of masses of objects very close while Elastic potential energy tries to keep atoms and molecules making up an object so as to maintain particle equilibrium.Gravitational potential energy is the energy an object possesses due to its location in a gravitational field while Elastic potential energy is the energy an object gains after going through distortion.Similarity is:
They are both types of potential energies making them have the potential to do work.Examples of Gravitational potential energy:
A rock sitting at the edge of a cliffExamples of Elastic potential energy:
A stretched elastic string in a bow.A) In terms of electrolysis, it’s been said from multiple sources online that “Using water's density and relative atomic populations, it is estimated by a mass balance that approximately 2.38 gallons of water are consumed as a feedstock to produce 1 kg of hydrogen gas (14.13 liters), assuming no losses.”
B) However, 1 Gallon of water is said to contain approximately 4,707 liters of hydrogen.
How can both statements be correct under normal atmospheric conditions, since even with 80% efficiency of current PEM electrolyzers the first statement (A) is nowhere near the +4,000 liters of the second approximation (B)?
Answers
Answer:
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students attach a force probe in the middle of string a to measure ta and then use a different force probe to provide the applied force f to the box of mass m1. with the box of mass m3 held in place by one student, a second student pulls to the left on the force probe that provides the applied force f. as the second student pulls with a steady force, and with the boxes remaining at rest, the following pairs of readings from the two force probes are recorded at different times. Time F(N) TA (N) ti 10.6 11 10 10.4 10.2 10.8 10 11 t5 10.6 11 Based on the measurements above, how do the magnitudes of the two force quantities compare? The two quantities exactly agree numerically. The two quantities agree within experimental uncertainty but do not exactly agree numerically. The two quantities disagree by an amount that is larger than the experimental uncertainty. The two quantities cannot be compared because the two force probes have different levels of precision.
Answers
The magnitudes of the two force quantities after comparing the two quantities agree within experimental uncertainty but do not agree numerically.
What is applied force?One of the most prevalent forms of force is applied force, which is the force we exert on objects with our hands, legs, or any other item. As an illustration, push a chair with some force to move it in a certain direction.
According to Newton's second equation of motion, an object's force is equal to its mass times its acceleration, or F = m × a.
Use Newtons for force, kilograms for mass, and meters per second squared for acceleration when applying this formula.
Given that, time F(N) TA(N)
t₁ 10.6 11
t₂ 10.4 10
t₃ 10.2 10
t₄ 10.8 11
t₅ 10.6 11
Thus, The mean value of F is: 10.52 N
The mean value of TA is: 10.6 N
So, the two quantities agree within experimental uncertainty but do not agree numerically.
Thus, the two quantities cannot be compared because the two force probes have different levels of precision.
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When a skater pulls her arms in, it
reduces her moment of inertia from
2.12 kg m² to 0.699 kg-m². If she was
initially spinning 3.25 rad/s, what is
her final angular velocity?
Answers
The skater's final angular velocity is approximately 9.86 rad/s.
The skater's final angular velocity can be calculated using the principle of conservation of angular momentum. The equation for angular momentum is given by:
L = Iω
where L is the angular momentum, I is the moment of inertia, and ω is the angular velocity.
Initially, the skater has an angular momentum of:
L_initial = I_initial * ω_initial
Substituting the given values:
L_initial = 2.12 kg m² * 3.25 rad/s
The skater's final angular momentum remains the same, as angular momentum is conserved:
L_final = L_initial
The final moment of inertia is given as 0.699 kg m². Therefore, the final angular velocity can be calculated as:
L_final = I_final * ω_final
0.699 kg m² * ω_final = 2.12 kg m² * 3.25 rad/s
Solving for ω_final:
ω_final = (2.12 kg m² * 3.25 rad/s) / 0.699 kg m²
Hence, the skater's final angular velocity is approximately 9.86 rad/s.
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You connect three resistors with resistances R, 2R, and 3R in parallel. The equivalent resistance of the three resistors will have a value that is:_______
a. less than R.
b. between R and 2R.
c. greater than 3R.
d. between 2R and 3R.
Answers
Less than R, less than 2R, less than 3R, and less than any other possible hookup of any one, any two, or all three of these resistors.
car has a mass of 1200 kg. What is the car’s weight near the surface of the earth?
Answers
Explanation:
remember since they are asking the weight there is always gravity its 9.8m/s but approximately its 10m/s
What mistake did Farah make in this experiment? Farah conducted the following experiment to check whether fabrics of different colours take different times to dry. She took one piece each of red, white and blue cotton. They were all of the same size and quality. She wet each piece with the same amount of water and hung them from spring balances near a fan as shown above. She noted the weight of each piece of cotton. She then put the fan on and noted the weight of each piece of cotton at the end of every two minutes. The weight of all the pieces of cotton decreased as water evaporated from the them.
Answers
The mistake that Farah made in this experiment is that she hung up the pieces of cotton before putting the fan on, also the water evaporating can take longer or shorter even if they are all the same.
What are the consequences of mistakes in experiments?The consequences of errors or mistakes in the experiments may be determined by the fact that errors are differences between observed values and what is true in nature.
The error causes results that are inaccurate or misleading and can misrepresent nature. Scientifically accepted values are scientists' current best approximations, or descriptions, of nature.
Experimental error is the difference between a measured value and its true value. In other words, it is the inaccuracy or inaccuracies that stop us from seeing an absolutely correct measurement. Experimental error is very common and is to some degree inherent in every measurement.
Therefore, the mistake that Farah made in this experiment is that she hung up the pieces of cotton before putting the fan on, also the water evaporating can take longer or shorter even if they are all the same.
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Which law of thermodynamics does each of the following scenarios violate (if any)?
A machine that can turn 1000J of heat directly into 1000J of electricity
1.
The first law of thermodynamics
2.
The second law of thermodynamics
3.
The third law of thermodynamics
4.
It is allowed
Answers
Answer: The scenario violates the second law of thermodynamics.
Explanation: The second law states that heat cannot be converted into work without some loss of usable energy, and that the amount of usable energy in a closed system will always decrease over time. Therefore, the machine described in the scenario cannot exist because it would violate the second law by converting all of the heat into electricity without any loss of usable energy.
HI PLEASE HELP ON QUESTION ASAP USING AVERAGE (MEAN) TO ANSWER QUESTION! IF UR ANSWER AND EXPLAINATION IS CORRECT ILL RATE YOU FIVE STARS, A THANKS AND MAYBE EVEN BRAINLIEST. PLEASE MAKE SURE YOU ANSWER MY QUESTION USING AVERAGES.
1) a meal for 6 cost £12 per person. as it is one of the diners birthday , the other 5 decided to pay for his meal. how much do each of the five friends need to pay?
Answers
Each of the five friends needs to pay £12 to cover the cost of their own meals and contribute towards the birthday person's meal. Using mean allows us to distribute the cost equally among the friends, ensuring a fair division of expenses for the meal.
To determine how much each of the five friends needs to pay, we can use the concept of averages (mean) and divide the total cost by the number of people paying.
In this scenario, the total cost of the meal for 6 people is £12 per person. Since the other 5 friends have decided to pay for the birthday person's meal, they will collectively cover the cost of their own meals plus the birthday person's meal.
To calculate the total cost covered by the five friends, we can subtract the cost of one person's meal (since the birthday person's meal is being paid by the group) from the total cost. The cost of one person's meal is £12.
Total cost covered by the five friends = Total cost - Cost of one person's meal
= (£12 x 6) - £12
= £72 - £12
= £60
Now, to find out how much each of the five friends needs to pay, we divide the total cost covered by the five friends (£60) by the number of friends (5).
Amount each friend needs to pay = Total cost covered by the five friends / Number of friends
= £60 / 5
= £12
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If you weigh 690 N on the earth, what would be your weight on the surface of a neutron star that has the same mass as our sun and a diameter of 15.0 km ? Take the mass of the sun to be ms = 1.99×1030 kg , the gravitational constant to be G = 6.67×10−11 N⋅m2/kg2 , and the free-fall acceleration at the earth's surface to be g = 9.8 m/s2 . Express your weight wstar in newtons.
Answers
Answer:
W' = 1.66 x 10¹⁴ N
Explanation:
First, we will calculate the mass:
\(W = mg\)
where,
W = weight on earth = 690 N
m = mass = ?
g = acceleration due to gravity on earth = 9.8 m/s²
Therefore,
\(m = \frac{W}{g} = \frac{690\ N}{9.8\ m/s^2}\\\\m = 70.4\ kg\)
Now, we will calculate the value of g on the neutron star:
\(g' = \frac{GM}{R^2}\)
where,
g' = acceleration due to gravity on the surface of the neutron star = ?
G = Gravitational Constant = 6.67 x 10⁻¹¹ N.m²/kg²
M = Mass of the Neutron Star = 1.99 x 10³⁰ kg
R = Radius of the Neutron Star = 15 km/2 = 7.5 km = 7500 m
Therefore,
\(g' = \frac{(6.67\ x\ 10^{-11}\ N.m^2/kg^2)(1.99\ x\ 10^{30}\ kg)}{(7500\ m)^2}\\\\g' = 2.36\ x\ 10^{12}\ m/s^2\)
Therefore, the weight on the surface of the neutron star will be:
\(W' = mg'\\W' = (70.4\ kg)(2.36\ x\ 10^{12}\ m/s^2)\)
W' = 1.66 x 10¹⁴ N
String 1 in the figure has linear density 2.60 g/m and string 2 has linear density 3.30 g/m. A student sends pulses in both directions by quickly pulling up on the knot, then releasing it. She wants both pulses to reach the ends of the strings simultaneously.
What should the string length L1 be?
What should the string length L2 be?
Answers
Explanation:
We can use the formula for the speed of waves on a string:
v = sqrt(T/μ)
where v is the speed of the wave, T is the tension in the string, and μ is the linear mass density (mass per unit length) of the string.
Let's denote the tension in both strings by T. Since the pulses must reach the ends of both strings simultaneously, we must have:
L1/v1 = L2/v2
where L1 and L2 are the lengths of the strings, v1 is the speed of the wave on string 1, and v2 is the speed of the wave on string 2.
Using the formula above and solving for T, we can eliminate T from this equation to get:
sqrt(μ1/ T)/ L1 = sqrt(μ2/T)/ L2
Squaring both sides and rearranging, we obtain:
L2/L1 = sqrt(μ2/μ1)
Substituting the given values for μ1 and μ2, we get:
L2/L1 = sqrt(3.30/2.60) = 1.126
Solving for one of the lengths, say L1, in terms of the other, we get:
L1 = L2/1.126
Now we need to find the values of L1 and L2 that satisfy the condition that both pulses reach the ends of the strings simultaneously. To do this, we can use the fact that the time it takes for a wave to travel a distance L on a string is given by:
t = L/v
where v is the speed of the wave on the string.
Therefore, if the pulses are to arrive at the ends of the strings simultaneously, we must have:
L1/v1 + L2/v2 = 2L1/v1
Simplifying this equation using the relation L1 = L2/1.126 and the formula for v, we get:
sqrt(T/μ1)L2/1.126/2.60 + sqrt(T/μ2)L2/3.30 = 2L2/1.126sqrt(T/μ1)
Simplifying further and eliminating T, we obtain:
L2 = (2.60/3.30)^2(1.126) L1
Substituting the expression for L1 in terms of L2 that we found earlier, we get:
L2 = (2.60/3.30)^2(1.126) L2/1.126
Solving for L2, we find:
L2 = 2.196 L1
Finally, using the relation L1 = L2/1.126, we get:
L1 = 1.91 m
L2 = 4.20 m
Therefore, the length of string 1 should be 1.91 m and the length of string 2 should be 4.20 m in order for both pulses to reach the ends of the strings simultaneously.
I need help with this
Answers
A ball of mass 0.1kg is thrown vertically upwards with an initial velocityof 80 m/s. calculate the pontential energy (i) half way up (ii) at its maximum height. what is its kinetic energy as it leaves the ground
Answers
Answer:
Stated below:
Explanation:
Let's calculate the maximum height
.
H=v^2/2g=320mH=v
2
/2g=320m
PE=mgh=0.1*10*320=320 J
at halfway up PE will be half of max = 320/2=160 J
KE will be equal to PEmax=320 J.
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A particle's trajectory is described by x = (0.5t^3-2t^2) meters and y = (0.5t^2-2t), where time is in seconds. What is the particle's speed at t=5.0s ? What is the particle's direction of motion, measured as an angle from the x-axis, at t=5.0s ?
Answers
Differentiate the components of position to get the corresponding components of velocity :
\(v_x = \dfrac{\mathrm dx}{\mathrm dt} = \left(1.5\dfrac{\rm m}{\mathrm s^3}\right) t^2 - \left(4\dfrac{\rm m}{\mathrm s^2}\right)t\)
\(v_y = \dfrac{\mathrm dy}{\mathrm dt} = \left(1\dfrac{\rm m}{\mathrm s^2}\right)t-2\dfrac{\rm m}{\rm s}\)
At t = 5.0 s, the particle has velocity
\(v_x = \left(1.5\dfrac{\rm m}{\mathrm s^3}\right) (5.0\,\mathrm s)^2 - \left(4\dfrac{\rm m}{\mathrm s^2}\right)(5.0\,\mathrm s) = 17.5\dfrac{\rm m}{\rm s}\)
\(v_y = \left(1\dfrac{\rm m}{\mathrm s^2}\right)(5.0\,\mathrm s)-2\dfrac{\rm m}{\rm s} = 3.0\dfrac{\rm m}{\rm s}\)
The speed at this time is the magnitude of the velocity :
\(\sqrt{{v_x}^2 + {v_y}^2} \approx \boxed{17.8\dfrac{\rm m}{\rm s}}\)
The direction of motion at this time is the angle \(\theta\) that the velocity vector makes with the positive x-axis, such that
\(\tan(\theta) = \dfrac{3.0\frac{\rm m}{\rm s}}{17.5\frac{\rm m}{\rm s}} \implies \theta = \tan^{-1}\left(\dfrac{3.0}{17.5}\right) \approx \boxed{9.73^\circ}\)