A. During long jump athlete runs before taking the jump by doing so he provides himself a larger inertia.
What is inertia?
Inertia is the reluctance of an object to stop moving once in motion or start moving when it is at rest.
When an athlete runs before taking the jump, he is trying to increase his inertia, that is his reluctance to stop, thereby increasing his forward motion or jump.
Thus, during long jump athlete runs before taking the jump by doing so he provides himself a larger inertia.
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20. For each improvement in glider design, engineers follow
O A. the written instructions that are provided in the hang glider build kit.
O B. an iterative process of testing, modifying, retesting, and modifying again.
O C. a complicated process of checks and balances while obtaining financing.
O D. a mathematical process, rejecting designs that don't follow blueprint dimensions.
Turn In
For the questions below, include units if applicable. If necessary, use a separate sheet of paper for 1, 6c and 7c. Tire pressure is in part a function of the temperature of the tire.
1. Based on everyday experience, state (in words) the relationship between tire pressure and temperature. Look at the data below and see if the numbers support your statement.
2. Prepare a hand-drawn plot of the two variables on the reverse side of this worksheet. Include a title, axis labels (with units), and a trendline. Estimate the tire pressure when the temperature is 18.6°C: Estimate the temperature of the air in the tire when the pressure is 37.0 psi: 3.
a. Prepare a plot using graphing software. Include a title, axis labels (with units), the equation of the best-fit Line and the R? value on the graph.
b. Re-write the equation of the best-fit line substituting "Temperature" for x and "Pressure" for y directly on the graph.
c. Attach the fully labeled graph to this worksheet.
4. What is the value of the slope for the relationship between temperature and pressure?
5. Determine the percent error using the definition of percent error: Use 0.145 psi/" for the "Actual" value of the slope. %error = Actual-Experimental % Error Actual
6. Based on your computer-generated graph,
a. visually estimate the tire pressure when the temperature is 18.6°C:
b. calculate the tire pressure at this temperature using the equation of the best fit line: the graph to ensure that this value is reasonable.
c. compare the calculated pressure to the two visually interpolated values (Steps 2 and 6a). Comment on any discrepancies.
7. Based on your computer-generated graph,
a. visually estimate the temperature of the air in the tire when the pressure is 37.0 psi:
b. calculate the temperature of the air in the tire at this pressure: Use the graph to ensure that this value is reasonable.
c. compare the calculated temperature to the two visually interpolated values (Steps 2 and 7a). Comment on any discrepancies.
Data:
Temperature (x) Tire Pressure, psi (y)
12.9°C 3.39 x 10
15.4C 34.25
-2.10 F 2.68 x 10
19.5 °C 3.50 x 10
29.6 'F 36.53
Answer:
All answer are explained below in the explanation section.
Explanation:
1. The pressure varies proportionally with the change in temperature. It can also be observed in our daily lives.
As for example, a pressure cooker uses the same principal to cook food faster. With the increasing temperature, the pressure inside the cooker increases.
Thus after a while, the excess pressure inside is released through the top nozzle. The data shown below supports that pressure and temperature varies linearly.
2. Hand drawn plot is attached in the attachment please refer to the attachment for the hand drawn plot.
Tire pressure at temperature 18.6 degree C is ~ 35 psi.
Temperature at air pressure of 37 psi is ~26.1 degree C
3. a.) Necessary values are included in the stat box. It is attached in the attachment please refer to the attachment.
3. b) The equation becomes: Pressure = 0.176 x temperature + 32.32
3. c) It is already done in part a of this question.
4. The value of the slope estimated from the linear fit is 0.176 +/- 0.094.
5. % Error = [tex]\frac{Actual - Experiment}{Actual} x 100[/tex]
Plugging in the values, we get:
Actual = 0.145, Experimental = 0.176. Thus, percentage error is given by:
% Error = 21.33%
6. a.) Visual estimation of tire pressure at t = 18.6 degree C is ~ 35 psi
6. b.) Estimation of pressure from the best fit line is given by 35.6 psi, which is consistent with the eye estimation value.
6. c.) The eye estimation and the estimation from the line fit are quite comparable. The discrepancy of +/-0.5 psi is within the percentage error calculated in 5.
7. a.) Visual estimation of temperature of the air for a tire-pressure of 37 psi is ~ 26 degree C.
7. b.) Estimation of temperature from best fit value of line is = 26.64 degree C
7 c) The values from eye estimation and evaluated from the fit are quite consistent within a random fluctuation of +/- 0.64 degree C.
what is permittivity
Answer:
Permittivity, also called electric permittivity, is a constant of proportionality that exists between electric displacement and electric field intensity.
he nucleus of 8Be, which consists of 4 protons and 4 neutrons, is very unstable and spontaneously breaks into two alpha particles (helium nuclei, each consisting of 2 protons and 2 neutrons). (a) What is the force between the two alpha particles when they are 6.60 ✕ 10−15 m apart? N (b) What is the initial magnitude of the acceleration of the alpha particles due to this force? Note that the mass of an alpha particle is 4.0026 u. m/s2
Answer:
A) F = 21.134 N
B) a = 3180.76 × 10^(24) m/s²
Explanation:
A) We are given;
Mass of alpha particle; m = 4.0026 u
Now, 1u = 1.66 × 10^(-27) kg
Thus; m = 4.0026 × 1.66 × 10^(-27)
Distance apart; r = 6.60 × 10^(−15) m
Charge on the alpha particle is;
q = 2e = 2 × 1.6 × 10^(-19) C
Formula for the force between the two alpha particles is;
F = kq1.q2/r²
k = 8.99 × 10^(9) N.m²/C²
q1 = q2 = 2 × 1.6 × 10^(-19) C
F = 8.99 × 10^(9) × (2 × 1.6 × 10^(-19))²/(6.60 × 10^(−15))²
F = 21.134 N
B) acceleration is given by;
a = F/m
Thus; a = 21.134/(4.0026 × 1.66 × 10^(-27))
a = 3180.76 × 10^(24) m/s²
Specify whether the boiling point, as determined in the miniscale boiling-point apparatus, is the temperature a.of the liquid at the timebubbles first emerge slowly from the liquid. b.at the vapor-liquid interface above the surface of the boiling liquid while a drop of liquid c.is suspended from the thermometer. d.of the liquid at the timebubbles emerge rapidly from the liquid. e.of the heating source at the timebubbles emerge rapidly from the liquid.
Answer:
a. of liquid at the time bubbles first emerge slowly from the liquid.
Explanation:
Boiling point of liquid happens due to heat energy. This is an exothermic reaction as heat is released in to the environment. The initial boiling vapors slowly move away from the liquid and as the temperature increases the vapors start moving quickly.
help me pls it’s a usa test prep pretty easy
Answer:
Im 99.99999% sure its c
Explanation:
i cant see the pictures too well
What is the correct definition of amplitude
Answer:
In my textbook's words-
Amplitude, in physics, the maximum displacement or distance moved by a point on a vibrating body or wave measured from its equilibrium position. It is equal to one-half the length of the vibration path.
Explanation:
The correct definition of amplitude is that it is a maximum displacement
that occurs on a vibrating body from one point to the other.
The initial point of the wave is regarded as its equilibrium position which is
equal to one-half the length of the vibration path.
Amplitude helps to calculate the peak value of different types of waves
such as water waves and in electrical appliances so as to know the peak
current suitable for it.
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Drag the tiles to the correct boxes to complete the pairs
Match the particles with their characteristics.
subatomic particles with a positive charge
subatomic particles with a negative charge
subatomic particles with no charge
made of atoms
neutrons
electrons
protons
malaria
Answer:
1. Protons.
2. Electrons.
3. Neutrons.
4. Molecules.
Explanation:
1. Protons: subatomic particles with a positive charge. They are bound together in the nucleus of an atom due to strong nuclear forces.
2. Electrons: subatomic particles with a negative charge. Electrons can be defined as subatomic particles that are negatively charged and as such has a magnitude of -1.
3. Neutrons: subatomic particles with no charge. The negative charge of the electrons cancels the positive charge of the protons.
4. Molecules: they are made of atoms.
Generally, molecules attach on the inside of a mineral to give it shape. Therefore, the molecule of a mineral is a crystal three-dimensional regular structure (arrangement) of chemical particles that are bonded together and determines its shape.
Due to the fact that these molecules are structurally arranged or ordered and are repeated by different symmetrical and translational operations they determine the shape of minerals.
What can you conclude about the electric potential and the field strength at the two noted points between the two electrodes? What can you conclude about the electric potential and the field strength at the two noted points between the two electrodes? The potential is greater at point B; the field strength is greater at point A. The potential is greater at point B; the field strength is greater at point B. The potential is greater at point A; the field strength is greater at point B. The potential is greater at point A; the field strength is greater at point A
Answer: The potential is greater at point B; the field strength is greater at point B.
Explanation:
The thing that can be concluded about the electric potential and the field strength at the two noted points between the two electrodes is that the potential is greater at point B; the field strength is greater at point B.
We should note that electrodes are used in the provision of current which typically takes place through a nonmetal objects.
the ____ is a particle with one unit of positive change
a. proton
b. positron
c. electron
d. nucleus
Answer:
a proton because it has a positive charge
Answer:
The answer is
B)
When rubbing a balloon against your head, you notice the balloon pulling your hair away from your head. What best explains why the balloon and your hair are attracted to each other?
They become oppositely charged, which causes them to be attracted to each other.
They become similarly charged, which causes them to be attracted to each other.
They stick together because of the friction between the two objects.
They are made of different materials, which is why they attract each other.
Answer:
They become oppositely charged, which causes them to be attracted to each other.
Answer: number A
Explanation:
If a positive charge and a negative charge interact, their forces act in the same direction, from the positive to the negative charge. As a result opposite charges attract each other: The electric field and resulting forces produced by two electrical charges of opposite polarity. Have a nice day <3
Which example is correctly matched with its type of friction?
A. Pushing a car that isn't moving is an example of slkiding friction.
B. A plane flying through the air is an example of static friction.
OC.
A skateboard wheels on cement is an example of rolling friction.
OD.
A sled sliding down a grassy hill is an example of fluid friction.
Answer:
A. pushing a car that isn't moving
If a total 50 J of work are done on an object, it's energy...
Answer:
0.0119502868 kilocalorie
Explanation:
Answer:
increases by 50
Explanation:
Which statement describes what will most likely occur when warm air cools and the temperature drops to the
point?
A.air will contain more water vapor. B. Dew will form on leaves C.clouds will disappear. D. Water vapor in the air will evaporate
Answer:
The person who did the comment is correct, it B - Dew will form on leaves
Explanation:
Answer:
B
Explanation:
Valeriie.07 tap in g
PLEASE HELP! WILL GIVE BRANILIEST TO FIRST REAL ANSWER If one marble is rolling three times as fast as a second marble of the same mass, the kinetic energy of the first marble is how many times larger when compared to the kinetic energy of the second marble?
a) 4
b) 9
c) 6
d) 3
(i already know its not 3)
Answer:
9
Explanation:
Suppose that you connect the terminals of two batteries of different emfs positive to positive and negative to negative (opposing each other) in a circuit. If you wanted to add in a capacitor to charge it from the batteries, would you be able to get more charge onto the capacitor or less charge, than if there was only one battery. (hint: start this problem by aligning the batteries positive to negative, and think of it from conservation of energy perspective).
Answer:
Answer is explained in the explanation section below.
Explanation:
This question is very basic and easy. The answer to this question is:
Answer: If both batteries are connected we would get less amount of charge as compared to connected a single battery.
Reasoning:
If both batteries are connected in a manner of positive terminal to positive terminal and negative terminal to negative terminal then a capacitor is added to charge it from the batteries then, total electromotive force (emf) would decrease.
As a result, the capacitor added would get less amount of charge stored. But capacitor added will get more amount of charge stored when a single battery is connected.
Four electrons and one proton are at rest, all at an approximate infiitne distance away from each other. This original arrangment of the four particles is defined as having zero electrical potential energy No work is required to bring one electron from infitinty to a location defined as the origin, while the other three particles remain at infiniuty. This is because no voltage exists near the origin until the first electron arrives. (a) Now, with the first electron remaining fixed at the origin, how much work is required to bring one of the remaining electrons from infinity to the coordinate (0 m, 2.00 m)? The other three particles remain at infinity. If this second electron was subsequently released, how fast would it be traveling once it returned to infinity? (b) Nļw, considering the two electrons fixed 2.00 m apart, how much work is required to bring the third electron from infinity to the coordinate (3.00 m, 0 m)? The other two particles remain at infinity. If this third electron was subsequently released, how fast would it be traveling once it returned to infinity? (c) Now considering the three fixed electrons at the coordinates described above. How much work is required to bring the last electron from infinity to the coordinate (3.00 m, 4.00 m)? If this forth electron was subsequently released, how fast would it be traveling once it returned to infinity? (d) Now considering the three fixed electrons at the coordinates described above. Finally, how much work is required to bring the proton from infinity to a coordinate of (1.00 m, 1.00 m)? If the proton is subsequently released and we assume that minimum separation distance between a proton and an electron is 1.00 pm, then how fast will the proton be traveling once it crashes into an electron?
Answer:
a) W = 1.63 10⁻²⁸ J, b) W = 1.407 10⁻²⁷ J, c) W = 1.68 10⁻²⁸ J,
d) W = - 4.93 10⁻²⁸ J
Explanation:
a) In this problem we have an electron at the origin, work is requested to carry another electron from infinity to the point x₂ = 0, y₂ = 2.00m
If we use the law of conservation of energy, work is the change in energy of the system
W = ΔU = U_∞ -U
the potential energy for point charges is
U =k [tex]\sum \frac{q_i q_j}{r_{ij} }[/tex]
in this case we only have two particles
U = k [tex]\frac{q_1q_2}{r_{12} }[/tex]
the distance is
r₁₂ = [tex]\sqrt{(x_2-x_1)^2 + ( y_2-y_1)^2 }[/tex]
r₁₂ =[tex]\sqrt{ 0 + ( 2-0)^2}[/tex]Ra 0 + (2-0)
r₁₂ = √2= 1.4142 m
we substitute
W = k \sum \frac{q_i q_j}{r_{ij} }
let's calculate
W = [tex]\frac{ 9 \ 10^9 (1.6 \ 10^{-19})^2 }{1.4142}[/tex] 9 109 1.6 10-19 1.6 10-19 / 1.4142
W = 1.63 10⁻²⁸ J
b) the two electrons are fixed, what is the work to bring another electron to x₃ = 3.00 m y₃ = 0
in this case we have two fixed electrons
U = k [tex]( \frac{q_1q_3}{r_{13} } + \frac{q_2q_3}{r_{23} } )[/tex]
in this case all charges are electrons
q₁ = q₂ = q₃ = q
W = U = k q² [tex]( \frac{1}{r_{13} } + \frac{1}{r_{23} } )[/tex]
the distances are
r₁₃ = [tex]\sqrt{(3-0)^2 + 0}[/tex]RA (3.00 -0) 2 + 0
r₁₃ = 3
r₂₃ = [tex]\sqrt{ 3^2 + 2^2}[/tex]Ra (3 0) 2 + (2 0) 2
r₂₃ = √13
r₂₃ = 3.606 m
let's look for the job
W = U
let's calculate
W =[tex]{9 \ 10^3 ( 1.6 10^{-19})^2 }({\frac{1}{3} + \frac{1}{3.606} } )[/tex]
W = 1.407 10⁻²⁷ J
c) the three electrons are fixed, we bring the four electron to x₄ = 3.00m,
y₄ = 4.00 m
W = U = k [tex]( \frac{q_1q_4}{r_{14 }} + \frac{q_2q_4}{r_{24} } + \frac{q_3q_4}{r_{34} } )[/tex]
all charges are equal q₁ = q₂ = q₃ = q₄ = q
W = k q² [tex](\frac{1}{r_{14} } + \frac{1}{r_{24} } + \frac{1}{r_{34} } )[/tex]
let's look for the distances
r₁₄ = [tex]\sqrt{3^2 +4^2}[/tex]
r₁₄ = 5 m
r₂₄ = [tex]\sqrt{3^2 + ( 4-2)^2}[/tex]
r₂₄ = √13 = 3.606 m
r₃₄ = [tex]\sqrt{(3-3)^2 + (4-0)^2}[/tex]
r₃₄ = 4 m
we calculate
W = 9 10⁹ (1.6 10⁻¹⁹)² [tex]( \frac{1}{5} + \frac{1}{3.606} + \frac{1}{4} )[/tex]
W = 1.68 10⁻²⁸ J
d) we take the proton to the location x5 = 1m y5 = 1m
W = U = k [tex]( \frac{q_1q_5}{r_{15} } + \frac{q_2q_5}{r_{25} } + \frac{q_3q_5}{r_{35} } + \frac{q_4q_5}{r_{45} } )[/tex]
in this case the charges have the same values but charge 5 is positive and the others negative, so the products of the charges give a negative value
W = - k q² [tex]( \frac{1}{r_{15} } + \frac{1}{r_{25} } + \frac{1}{r_{35} } + \frac{1}{r_{45} } )[/tex]
we look for distances
r₁₅ = [tex]\sqrt{ 1^2 +1^2}[/tex]Ra (1-0) 2 + (1-0) 2
r₁₅ = √ 2 = 1.4142 m
r₂₅ = [tex]\sqrt{ (2-1)^2 +1^2}[/tex]
r₂₅ = √2 = 1.4142 m
r₃₅ = [tex]\sqrt{ ( 3-1)^2 +1^2}[/tex]
r₃₅ = √5 = 2.236 m
r₄₅ = [tex]\sqrt{ (3-1)^2 + (4-1)^2}[/tex]
r₄₅ = √13 = 3.606 m
we calculate
W = - 9 10⁹ (1.6 10⁻¹⁹)² [tex]( \frac{1}{1.4142} +\frac{1}{1.4142} + \frac{1}{2.236} + \frac{1}{3.606} )[/tex]
W = - 4.93 10⁻²⁸ J
uppose that the terminal speed of a particular sky diver is 150 km/h in the spread-eagle position and 320 km/h in the nosedive position. Assuming that the diver's drag coefficient C does not change from one position to the other, find the ratio of the effective cross-sectional area A in the slower position to that in the faster position (Aslower / Afaster).
Answer:
4.55
Explanation:
The terminal speed of a diver is given by:
[tex]v_t=\sqrt{\frac{2mg}{C\rho A} } \\\\Where\ m=mass\ of \ driver,d=acceleration\ due\ to\ gravity,C=drag\ \\coefficient,A=cross\ sectional\ Area.\\\\Therefore:\\\\A=\frac{2mg}{C \rho v_t^2} \\\\For\ area\ with\ terminal\ speed\ in\ spread\ angle\ position(v_s):\\\\A_s=\frac{2mg}{C \rho v_s^2} \\\\For\ area\ with\ terminal\ speed\ in\ nose\ dive\ position(v_n):\\\\A_n=\frac{2mg}{C \rho v_n^2}\\\\Therefore\ since\ g,m,C,\rho\ are\ constant:\\\\[/tex]
[tex]\frac{A_s}{A_n}= \frac{\frac{2mg}{C \rho v_s^2}}{\frac{2mg}{C \rho v_n^2}}\\\\\frac{A_s}{A_n}= \frac{v_n}{v_s} \\\\v_n=320\ km/h,v_s=150\ km/h\\\\\frac{A_s}{A_n}=\frac{320^2}{150^2} =4.55[/tex]
Find the GCF of each set of numbers.
12, 21, 30
Math
Answer:
3 is the GCF for all these numbers if thats what you're asking
Please help I will fail
Answer:
6. A
7. C
8. B
9. The average speed is the distance (a scalar quantity) per time ratio. Speed is ignorant of direction. The average velocity is the displacement or position change (a vector quantity) per time ratio.
Please help! Will mark brainliest.
Answer:
1122.8
Explanation:
12.73 kg x 9.8 m/s^2 x 9m
=1122.786
Rounded=1122.8
The force between two charges when they are 2 cm apart is
0.036 N. If the sum of two charges is 10uC, what are the
charges? (1/4ttɛo=9x109 Nm-C-2).
Answer:
[tex]q_1=9.9998\mu C[/tex] and [tex]q_2=0.0002\mu C[/tex]
Or
[tex]q_1=0.00016\mu C[/tex] and [tex]q_2=9.99984\mu C[/tex]
Explanation:
We are given that
Force between two charges=0.036 N=[tex]36\times 10^{-3}N[/tex]
Distance between two charges, r=2cm=[tex]2\times 10^{-2}[/tex]m
1m=100cm
Sum of two charges=[tex]10\mu C[/tex]
Let one charge=[tex]q_1=q\mu C=q\times 10^{-6}C[/tex]
[tex]q_2=(10-q)\times 10^{-6} C[/tex]
We know that
Electric force between two charges
[tex]F=\frac{kq_1q_2}{r^2}[/tex]
Where [tex]k=\frac{1}{4\pi \epsilon_0}=9\times 10^{9}[/tex]
Using the formula
[tex]36\times 10^{-3}=9\times 10^{9}\times \frac{q\times 10^{-6}\times(10-q)\times 10^{-6}}{(2\times 10^{-2})^2}[/tex]
[tex]\frac{144\times 10^{-7}}{9\times 10^{9}\times 10^{-12}}=q(10-q)[/tex]
[tex]0.0016=10q-q^2[/tex]
[tex]q^2-10q+0.0016=0[/tex]
[tex]10000q^2-100000q+16=0[/tex]
[tex]q=\frac{100000\pm\sqrt{(100000)^2-4\times 10000\times 16}}{2\times 10000}[/tex]
Using the formula
[tex]x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
[tex]q=9.999[/tex] and [tex]q=0.00016[/tex]
[tex]q_2=10-9.9998=0.0002[/tex]
[tex]q_2=10-0.00016=9.99984[/tex]
Hence, two charges are
[tex]q_1=9.9998\mu C[/tex] and [tex]q_2=0.0002\mu C[/tex]
Or
[tex]q_1=0.00016\mu C[/tex] and [tex]q_2=9.99984\mu C[/tex]
Which hand is negatively charged?
Answer:
Left
Explanation:
Answer:
Your Left hand is negatively charged, and receives energy. It emits the energy that "allows things to happen''.
Explanation:
did some research
Which one of Newton’s Laws best explains a bottle flip?
Animals conduct_______.
A. cellular respiration
B. photosynthesis
C. both cellular respiration and photosynthesis
Potential energy is energy due to the:
a. motion of an object.
b. height of an object.
c. temperature of an object.
d. speed of an object.
Answer:I will say d
Explanation: because Potential energy is the energy stored within an object, due to the object's position, arrangement or state. Potential energy is one of the two main forms of energy, along with kinetic energy.
Student pushes a 50 N block across the floor for a distance of 15 m how much work was done to move the block
Answer:
750 J
Explanation:
We have a student that pushes a 50N block across the floor for a distance of 15m. The question is asking how much work was done to move the block.
To solve this, we must know that we are looking for a certain thing called joules. And to get the answer, we must follow the formula of W = FS
F being the force and S being the distance.
W = FS
W = (50)(15)
W = 750
Therefore, 750 joules is our answer.
Which two statements below are central ideas in the article, "How Gross Is Your Bathroom"?
a. What you can't see might hurt you.
b. Different numbers of bacteria are hiding on various surfaces around your bathroom.
c. Most bacteria are harmless, and some are even good for you.
d. Your bathroom is filled with germs that you might not know anything about, including
viruses and bacteria.
The engine in an imaginary sportThe engine in an imaginary sports car can provide constant power to the wheels over a range of speeds from 0 to 70 miles per hour (mph). At full power, the car can accelerate from zero to 30.0 mph in time 1.00 s .s car can provide constant power to the wheels over a range of speeds from 0 to 70 miles per hour (mph).
Required:
a. At full power, how long would it take for the car to accelerate from 0 to 58.0mph?
b. A more realistic car would cause the wheels to spin in a manner that would result in the ground pushing it forward with a constant force (in contrast to the constant power in Part A). If such a sports car went from zero to 29.0mph in time 1.50s , how long would it take to go from zero to 58.0mph ?
Answer:
a. 1.93 s b. 3 s
Explanation:
a. At full power, how long would it take for the car to accelerate from 0 to 58.0mph?
Since the car accelerates from 0 to 30 mph in 1.00 s, we find its acceleration, a from a = (v - u)/t where u = 0 m/s, v = 30 mph and t = 1.00s = 1/3600 h
So, substituting the values of the variables into the equation, we have
a = (v - u)/t
a = (30 mph - 0 mph)/ 1/3600 h
a = 30 mph × 3600 /h
a = 108000 mph²
So, we find the time it takes the car to accelerate to 58 mph from 0 mph from
t = (v' - u')/a where u = 0 mph, v = 58 mph and a = 108000 mph²
So, substituting the value of the variables into the equation, we have
t = (v' - u')/a
t = (58 mph - 0 mph)/108000 mph²
t = 58 mph/108000 mph²
t = 5.37 × 10⁻⁴ h
t = 5.37 × 10⁻⁴ × 3600 s
t = 1.93 s
b. A more realistic car would cause the wheels to spin in a manner that would result in the ground pushing it forward with a constant force (in contrast to the constant power in Part A). If such a sports car went from zero to 29.0mph in time 1.50s , how long would it take to go from zero to 58.0mph ?
Since the car accelerates from 0 to 29 mph in 1.50 s, we find its acceleration, a from a = (v - u)/t where u = 0 m/s, v = 29 mph and t = 1.05s = 1/3600 h
So, substituting the values of the variables into the equation, we have
a = (v - u)/t
a = (29 mph - 0 mph)/ 1.5/3600 h
a = 29 mph × 3600/1.5 /h
a = 104400/1.5 mph²
a = 69600 mph²
So, we find the time it takes the car to accelerate to 58 mph from 0 mph from
t = (v' - u')/a where u = 0 mph, v = 58 mph and a = 69600 mph²
So, substituting the value of the variables into the equation, we have
t = (v' - u')/a
t = (58 mph - 0 mph)/69600 mph²
t = 58 mph/69600 mph²
t = 8.33 × 10⁻⁴ h
t = 8.33 × 10⁻⁴ × 3600 s
t = 3 s
A block of mass m = 150 kg rests against a spring with a spring constant of k = 880 N/m on an inclined plane which makes an angle of θ degrees with the horizontal. Assume the spring has been compressed a distance d from its neutral position.
Required:
a. Set your coordinates to have the x-axis along the surface of the plane, with up the plane as positive, and the y-axis normal to the plane, with out of the plane as positive.
b. Denoting the coefficient of static friction by μs, write an expression for the sum of the forces in the x-direction just before the block begins to slide up the inclined plane. Use defined quantities and g in your expression ΣFx = 25%
c. Assuming the plane is frictionless, what will the angle of the plane be, in degrees, if the spring is compressed by gravity a distance 0.1 m?
d. Assuming θ = 45 degrees and the surface is frictionless, how far will the spring be compressed, d in meters?
Answer:
b) k Δx - W cos θ - μ mg cos θ = m a , c) θ = 86.6º, d) Δx = 1.18 m
Explanation:
a) In the attachment we can see a diagram of the forces in this problem and the coordinate axes for its decomposition.
F is the force applied by the spring, while it is compressed, this force disappears when the block leaves the spring
b) Let's apply Newton's second law for when the spring is compressed
let's use trigonometry to break down the weight
sin θ = Wₓ / W
cos θ = W_y / W
Wₓ = W sin θ
W_y = W cos θ
Y axis
N - W_y = 0
N = W_y
N = W cos θ
X axis
F -Wₓ -fr = ma
the force applied by the spring is given by hooke's law
F = k Δx
friction force has the expression
fr = μ N
fr = μ W cos θ
we substitute
k Δx - W cos θ - μ mg cos θ = m a ( 1)
c) If the plane has no friction, what is the angle so that Δx = 0.1m
We write the equation 1, with fr = 0 and since the system is still a = 0
k Δx - W cos θ -0 = 0
cos θ = [tex]\frac{k \Delta x}{ m g}[/tex]
cos θ = [tex]\frac{880 \ 0.1}{ 150 \ 9.8}[/tex]
cos θ = 0.0598
θ = cos⁻¹ 0.0598
θ = 86.6º
d) In this part they give the angle θ = 45º and there is no friction, they ask the compression
the acceleration is zero, we substitute in 1
k Δx - W cos θ - 0 = 0
Δx = [tex]\frac{mg \ cos \ \theta}{k}[/tex]
Δx = [tex]\frac{ 150 \ 9.8 \ cos45}{880}[/tex]
Δx = 1.18 m