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Explanation:
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a vector has components x=6 m and y=8 m. what is its magnitude and direction?
Answer: 10m
Explanation:
The magnitude of the vector would be 10
[tex]\sqrt{6^{2}+8^{2} } =10[/tex]
If you jumped out of a plane, you would begin speeding up as you fall downward. Eventually, due to wind resistance, your velocity would become constant with time. While your velocity is constant, the magnitude of the force of wind resistance is
Answer:
Mg or your weight.
Explanation:
When your velocity is constant, the net force acting on you is 0. That means the upwards force of air resistance must fully balance the downwards force of gravity on you, which is Mg.
A block is supported on a compressed spring, which projects the block straight up in the air at velocity . The spring and ledge it sits on then retract. You can win a prize by hitting the block with a ball. When should you throw the ball and in what direction to be sure the ball hits the block? (Assume the ball can reach the block before the blochk reaches the ground and that the ball is thrown from a height equal to the release position of the block.)
A. At the instant when the block is at the highest point, directed at the spring.
B. At the instant when the block is at the highest point, directed at the block.
C. At the instant when the block leaves the spring, directed at the spring.
D. At the instant when the block leaves the spring, directed at the block.
E. When the block is back at the spring's original position, directed at that position.
Answer:
B. At the instant when the block is at the highest point, directed at the block.
Explanation:
Motion of an object is the change in the position of the object with respect to time. On the earth, gravity has a great influence on the motion of an object (especially in a vertical direction).
When the block is projected up in the air, it moves with a varying velocity until the velocity becomes zero due to gravity. Which make the object to rest a little in the air (when velocity = gravity) and starts to fall freely.
To ensure hitting the block by the ball, it is thrown at the block when the block is at its highest point in the air. Since the block would be at rest at this instant before it start to fall at a constant acceleration under gravity.
A tank with a constant volume of 3.72 m3 contains 22.1 moles of a monatomic ideal gas. The gas is initially at a temperature of 300 K. An electric heater is used to transfer 4.5 × 104 J of energy into the gas. It may help you to recall that CV = 12.47 J/K/mole for a monatomic ideal gas, and that the number of gas molecules is equal to Avagadros number (6.022 × 1023) times the number of moles of the gas.
a) What is the temperature of the gas after the energy is added?___K
b) What is the change in pressure of the gas?____Pa
c) How much work was done by the gas during this process?____J
Answer:
a) 463.29 K
b) 8065.65 Pa
c) 0 J
Explanation:
The parameters given are;
Volume of the tank, V = 3.72 m³
Number of moles of gas present in the tank, n = 22.1 moles
Temperature of the gas before heating, T₁ = 300 k
Heat added to the gas, ΔQ = 4.5 × 10⁴ J
Specific heat capacity at constant volume, [tex]c_v[/tex], for monatomic gas = 12.47 J/K/mole
Avogadro's number = 6.022 × 10²³ particles per mole
a) ΔQ = n × [tex]c_v[/tex] × ΔT
Where:
ΔT = T₂ - T₁
T₂ = Final temperature of the gas
Hence, by plugging in the values, we have;
4.5 × 10⁴ = 22.1 × 12.47 × (T₂ - 300)
[tex]T_{2} - 300 = \frac{4.5\times 10^{4}}{22.1\times 12.47}[/tex]
T₂ = 300 + 163.29 = 463.29 K
b) The pressure of the gas is found from the relation;
P×V = n×R×T
[tex]P = \dfrac{n \times R \times T}{V}[/tex]
Where:
P = Pressure of the gas
R = Universal gas constant = 8.3145 J/(mol·K)
T = Temperature of the gas
V = Volume of the gas = 3.72 ³ (constant)
n = Number of moles of gas present = 22.1 moles (constant)
Hence the change in pressure is given by the relation;
[tex]\Delta P = \dfrac{n \times R \times (T_2 - T_1)}{V} = \dfrac{n \times R \times \Delta T}{V}[/tex]
Plugging in the values, we have;
[tex]\Delta P = \dfrac{22.1 \times 8.3145 \times 163.29}{3.72} = 8065.65 \, Pa[/tex]
c) Work done, W, by the gas is given by the area under the pressure to volume graph which gives;
W = f(P) × ΔV
The volume given in the question is constant
∴ ΔV = 0
Hence, W = f(P) × 0 = 0 J
No work done by the gas during the process.
A beam of light is incident upon a flat piece of glass (n = 1.50) at an angle of incidence of 30.00. Part of the beam is transmitted and part is reflected. Determine the angle between the reflected and transmitted rays
Answer:
130.528779365 degrees
Explanation:
The angle of incidence is 30 degrees. From this, we can use Snell's Law to calculate the angle of refraction.
n1/n2 = sin(theta2)/sin(theta1)
let theta1 be 30 degrees, and n1 be the refractive index of air = 1
1/1.5 = sin(theta2)/sin(30deg)
solve:
sin(theta2) = 2/3 sin(30deg) = 1/3
theta2 = arcsin (1/3) = 19.4712206345 degrees
The angle of reflection will always be equal to the angle of incidence, in this case, 30 degrees.
Because these angles are measured relative to the normal, the angle formed between the two rays is the difference between the normal line (180 degrees) and the sum of the two angle measures.
Angle between = 180-30-19.4712206345 = 130.528779365 degrees
The angle between the reflected and transmitted rays 130.5287 degrees
What is the refraction of light?The angle of incidence is 30 degrees. From this, we can use Snell's Law to calculate the angle of refraction.
[tex]\dfrac{n_1}{n_2} = \dfrac{sin(\theta_2)}{sin(\theta_1)}[/tex]
let [tex]\theta_1[/tex] be 30 degrees, and n1 be the refractive index of air = 1
[tex]\dfrac{1}{1.5} = \dfrac{sin(\theta_2)}{sin(30)}[/tex]
solve:
[tex]sin(\theta_2) = \dfrac{2}{3} sin(30) = \dfrac{1}{3}[/tex]
[tex]\theta_2 = sin ^{-1}\dfrac{1}{3} = 19.4712 \ degrees[/tex]
The angle of reflection will always be equal to the angle of incidence, in this case, 30 degrees.
Because these angles are measured relative to the normal, the angle formed between the two rays is the difference between the normal line (180 degrees) and the sum of the two angle measures.
Angle between = 180-30-19.4712206345 = 130.528779365 degrees
Hence the angle between the reflected and transmitted rays 130.5287 degrees
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3. A ray of light incident on one face of an equilateral glass prism is refracted in such a way that it emerges from the opposite surface at an angle of 900 to the normal. Calculate the i. angle of incidence. ii. minimum deviation of the ray of light passing through the prism [n_glass=1.52]
Answer:
i) angle of incidence;i = 29.43°
ii) δm = 38.92°
Explanation:
Prism is equilateral so angle of prism (A) = 60°
Refractive index of glass; n_glass = 1.52
A) Let's assume the incident angle = i and Critical angle = θc
We know that, sin θc = 1/n
Thus;
sin θc = 1/n_glass
θc = sin^(-1) (1/n_glass)
θc = sin^(-1) (1/1.52)
θc = 41.14°
Now, the angle of prism will be the sum of external angle that is critical angle and reflected angle.
Thus;
A = r + θc
r = A - θc
So;
r = 60° - 41. 14°
r = 18.86°
From, Snell's law. If we apply it to this question, we will have;
(sin i)/(sin r) = n_glass
Where;
i is angle of incidence and r is angle of reflection.
Let's make i the subject;
i = sin^(-1) (n_glass × sin r)
i = sin^(-1) (1.52 × sin 18.86)
i = sin^(-1) 0.4914
i = 29.43°
B) The formula to calculate minimum deviation would be from;
μ = [sin ((A + δm)/2)]/(sin A/2)
Where;
μ is Refractive index
δm is minimum angle of deviation
A is angle of prism
Now Refractive index is given by a formula; μ = (sin i)/(sin r)
So; μ = (sin 29.43)/(sin 18.86)
μ = 1.52
Thus;
1.52 = [sin ((60 + δm)/2)]/(sin 60/2)
1.52 * sin 30 = sin ((60 + δm)/2)
0.76 = sin ((60 + δm)/2)
sin^(-1) 0.76 = ((60 + δm)/2)
49.46 × 2 = (60 + δm)
98.92 - 60 = δm
δm = 38.92°
N capacitors are connected in parallel to form a "capacitor circuit". The capacitance of first capacitor is C, second one is C/2 and third one is C/4, forth one is C/8 and so on. Namely, capacitance of a capacitor is one-half of the previous one. What is the equivalent capacitance of this parallel combination when N goes to inifinity?
Answer:
2C
Explanation:
The equivalent capacitance of a parallel combination of capacitors is the sum of their capacitance.
So, if the capacitance of each capacitor is half the previous one, we have a geometric series with first term = C and rate = 0.5.
Using the formula for the sum of the infinite terms of a geometric series, we have:
Sum = First term / (1 - rate)
Sum = C / (1 - 0.5)
Sum = C / 0.5 = 2C
So the equivalent capacitance of this parallel connection is 2C.
Jason takes off from rest across level water on his jet-powered skis. The combined mass of Jason and his skis is 75 kg (the mass of the fuel is negligible). The skis have a thrust of 200 N and a coefficient of kinetic friction on water of 0.10. Unfortunately, the skis run out of fuel after only 75 s. What is Jason's top speed?
Answer:
v = 126 m / s
Explanation:
Let's analyze this exercise a little, they give us the thrust that is the applied force and the time that it lasts, and they ask us for the final speed, so we can use the Impulse ratio and the variation of the amount of movement
I = F t = Dp
F t = pf -p₀
Now let's use Newton's second law to find the net thrust
F = E - fr
the friction force has the formula
fr = μ N
let's write Newton's second law on the y-axis
N-W = 0
N = W
we substitute
fr = μ mg
we look for the net out
F = 200 - μ mg
With the skater starting from rest, the initial speed is zero (vo = 0)
we substitute
(200 - very m g) t = m v
v = (200 µm - very g) t
let's calculate
v = (200/75 - 0.10 9.8) 75
v = 126 m / s
I need help physics
Which of the following statements is true of a gas?
It has a fixed volume, but not a fixed shape
It has closely packed molecules
It can change into a liquid by adding heat
It takes the shape and size of a container
Answer:
it takes the shape and size of the container that it is in
Explanation:
Answer:
it takes the shape and size of a container
The amount of friction divided by the weight of an object forms a unit less number called the
Answer:
Coefficient of friction.
Explanation:
The amount of friction divided by the weight of an object is equal to the coefficient of friction. It is a dimensional less number. It can be given by :
[tex]F=\mu N[/tex]
N is normal force.
[tex]\mu[/tex] = coefficient of friction
[tex]\mu=\dfrac{F}{N}[/tex]
Water flows at 0.850 m/s from a hot water heater, through a 450-kPa pressure regulator. The pressure in the pipe supplying an upstairs bathtub 3.70m above the heater is 414-kPa. What's the flow speed in this pipe?
Answer:
The velocity is [tex]v_2= 0.45 \ m/s[/tex]
Explanation:
From the question we are told that
The initial speed of the hot water is [tex]v_1 = 0.85 \ m/s[/tex]
The pressure from the heater [tex]P_1 = 450 \ KPa = 450 *10^{3} \ Pa[/tex]
The height of the hot water before flowing is [tex]h_1 = 0 \ m[/tex]
The height of bathtub above the heater is [tex]h_2 = 3.70 \ m[/tex]
The pressure in the pipe is [tex]P_2 = 414 KPa = 414 *10^{3} \ Pa[/tex]
The density of water is [tex]\rho = 1000 \ kg/m^3[/tex]
Apply Bernoulli equation
[tex]P_1 + \rho gh_1 +\frac{1}{2} \rho v_1^2 = \rho g h_2 + \frac{1}{2}\rho v_2 ^2[/tex]
Substituting values
[tex](450 *10^{3}) + (1000 * 9.8 * 0) + (0.5 * 1000 * 0.85^2) = (1000 * *9.8*3.70) + (0.5*1000*v_2^2 )[/tex]
=> [tex]v_2^2 = \frac{ (450 *10^{3}) + (1000 * 9.8 *0 ) + (0.5 * 1000 * 0.85^2) -[ (1000 * *9.8*3.70) ]}{0.5*1000}[/tex]
=> [tex]v_2= \sqrt{ \frac{ (450 *10^{3}) + (1000 * 9.8 * 0) + (0.5 * 1000 * 0.85^2) -[ (1000 * *9.8*3.70) ]}{0.5*1000}}[/tex]
=> [tex]v_2= 0.45 \ m/s[/tex]
What is the period of a wave if the frequency is? 5 Hz
Answer: If the woodpecker drums upon a tree 5 times in one second, then the frequency is 5 Hz; each drum must endure for one-fifth a second, so the period is 0.2 s.
In an RC-circuit, a resistance of R=1.0 "Giga Ohms" is connected to an air-filled circular-parallel-plate capacitor of diameter 12.0 mm with a separation distance of 1.0 mm. What is the time constant of the system?
Answer:
[tex]\tau = 1\ ms[/tex]
Explanation:
First we need to find the capacitance of the capacitor.
The capacitance is given by:
[tex]C = \epsilon_0 * area / distance[/tex]
Where [tex]\epsilon_0[/tex] is the air permittivity, which is approximately 8.85 * 10^(-12)
The radius is 12/2 = 6 mm = 0.006 m, so the area of the capacitor is:
[tex]Area = \pi * radius^{2}\\Area = \pi * 0.006^2\\Area = 113.1 * 10^{-6}\ m^2[/tex]
So the capacitance is:
[tex]C = \frac{8.85 * 10^{-12} * 113.1 * 10^{-6}}{0.001}[/tex]
[tex]C = 10^{-12}\ F = 1\ pF[/tex]
The time constant of a rc-circuit is given by:
[tex]\tau = RC[/tex]
So we have that:
[tex]\tau = 10^{9} * 10^{-12} = 10^{-3}\ s = 1\ ms[/tex]
What is the highest point at which weather will generally occur?
Answer:
At thestratosphere: it 20- 25km
Sara walks part way around a swimming pool. She walks 50 yards north, then
20 yards east, then 50 yards south. The magnitude of her total displacement
during this walk is
yards.
Answer:
20 Yards
Explanation:
|---20----|
| |
| 50 |50
|---D--->|
Start End
Total displacement(D) 20 yards (East).
A student writes down several steps of scientific method. Put the steps in the best order
Answer:
Make a hypothesis, conduct an experiment, Analyze the experimental data..
Two large insulating parallel plates carry charge of equal magnitude, one positive and the other negative, that is distributed uniformly over their inner surfaces. Rank the points 1 through 5 according to the magnitude of the electric field at the points, least to greatest.
A. 1, 2, 3, 4, 5
B. 2, then 1, 3, and 4 tied, then 5
C. 1, 4, and 5 tie, then 2 and 3 tie
D. 2 and 3 tie, then 1 and 4 tie, then 5
E. 2 and 3 tie, then 1, 4, and 5 tie
Answer:
The correct answer is C 1, 4, and 5 tie, then 2 and 3 tie
Explanation:
Solution
The electric field due to sheets E₁ positive =б/2E₀
E₂ is negative = б/2E₀
Now,
At the point 1, 4, 5 the electric field due to the sheets are in the opposite direction
At the point 1, the net field = -E₁ + E₂ =0
At the point A, the net field = -E₁ - E₂ = 0
Now,
At nay point inside between them, the electric field is seen to be at the same direction.
At the 2, 3 points the field is seen at the right
Thus,
E net = E₁ + E₂
= б/2E₀ + σ/2E₀
=б/E₀
Note: Kindly find an attached copy of the complete question to the solution
The correct answer is option C
The rank of the points according to the magnitude of the electric field is 1, 4, and 5 tie, then 2 and 3 tie
The magnitude of the electric field:
Let sheet 1 has positive surface charge density and sheet 2 has a negative surface charge density
The electric field (without direction) due to sheets will be
E₁ =σ/2E₀
E₂= σ/2E₀
Now,
At the point 1, 4, 5 the electric field due to the sheets is given by:
E = E₁ - E₂
E = σ/2E₀ - σ/2E₀
since the positive charge plate will have electric field lines away from the sheet and the negative charge plate will have electric field lines towards the sheet
E = 0
Now,
At points 2, 3 which are between the plates,
The net electric field is:
E = E₁ + E₂
since the electric field due to both the plates will be from positive to negative ( towards the negatively charged plate)
E = σ/2E₀ + σ/2E₀
E = σ/E₀
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Which of the followings is true about EMF?
a. an induced emf is caused by a changing magnetic flux.
b. an emf can only be induced in a conducting loop by moving the loop through an area that has a constant magnetic field.
c. an induced emf can be observed by measuring the current that is created.
d. an induced emf and conventional induced current are in opposite directions.
Answer:
a. TRUTH
b. FALSE
c. TRUTH
d. FALSE
Explanation:
The emf (electromagnetic force) is generated in a loop or solenoid by the change in the magnetic flux in a closed conductor path (for example, a wire).
This can be noted in the following formula, which is known as the Lenz's law:
[tex]emf=-N\frac{d\Phi_B}{dt}=-N\frac{d(AB)}{dt}[/tex] (1)
Then, the change, in time, of the area of the conductor, or the change in the magnitude of the magnetic field, the induced emf acquires different values. Furthermore, the loops have a resistance, then, a current can be measured when an emf is induced.
Based on this information you have:
a. an induced emf is caused by a changing magnetic flux. TRUTH
b. an emf can only be induced in a conducting loop by moving the loop through an area that has a constant magnetic field. FALSE
c. an induced emf can be observed by measuring the current that is created. TRUTH
d. an induced emf and conventional induced current are in opposite directions. TRUTH (the minus sing in the equation (1) )
6. When a positive charge is released and moves along an electric field line, it moves to a position of A) lower potential and lower potential energy. B) lower potential and higher potential energy. C) higher potential and lower potential energy. D) higher potential and higher potential energy.
Answer:
Since you would have to do work on the charge to bring it back to its original position, the charge moves to a position of lower potential and lower potential energy.
The positive charge is released from a point such that it will move along an uniform electric field to the position of lower potential and lower potential energy. Therefore, option (A) is correct,
When a positive charge (say +Q) is released from a point (say A) and moves in an uniform electric field to reach the point (say B), then some work is done on the charge. This work done is given as,
[tex]W=+Q(V_{A}-V_{B})[/tex]
Here, [tex]V_{A}[/tex] and [tex]V_{B}[/tex] are the potential differences between the points A and B respectively..
This means the charge is moving from higher potential to lower potential. And since it is moving along the uniform electric field, therefore the electric potential energy of charged system is decreased.
Thus, we conclude that on releasing the positive charge from a point, it starts moving along the electric field towards the direction of lower electric potential and lower electric potential energy. Hence, option (A) is correct.
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Concerned with citizen complaints of price gouging during past hurricanes, Florida's state government passes a law setting a price ceiling for a bottle of water equal to the market equilibrium price during normal times. After all, it seems unfair that sellers of water gain because of a hurricane.
Answer:idk
Explanation:idk
Answer:
shortage of 50 water bottles
$2
30
Explanation:
Some types of spiders build webs that consist of threads made of dry silk coated with a solution of a variety of compounds. This coating leaves the threads, which are used to capture prey, hygroscopic - that is, they attract water from the atmosphere. It has been hypothesized that this aqueous coating makes the threads good electrical conductors. To test the electrical properties of coated thread, researchers placed a 5-mm length of thread between two electrical contacts. The researchers stretched the thread in 1-mm increments to more than twice its original length, and then allowed it to return to its original length, again in 1-mm increments. Some of the resistance measurements are shown.If the conductivity of the thread results from the aqueous coating only, how does the cross-sectional area A of the coating compare when the thread is 13 mm long versus the starting length of 5 mm? Assume that the resistivity of the coating remains constant and the coating is uniform along the thread.If the conductivity of the thread results from the aqueous coating only, how does the cross-sectional area of the coating compare when the thread is 13 long versus the starting length of 5 ? Assume that the resistivity of the coating remains constant and the coating is uniform along the thread.A13mm is about 1/10 A5mm.A13mm is about 1/4 A5mm. === correct answer... I figured it out. R = pL/A. L is 2.5 times. Therefore, A must be 1/4 times.A13mm is about 2/5 A5mm.A13mm is the same as A5mm.
Answer:
A13 mm is about 1/4 A5 mm
Explanation:
Find the attachment
You are comparing a reaction that produces a chemical change and one that produces a physical change. What evidence could you use to determine which type of change is occurring?
Answer: A chemical change results from a chemical reaction, while a physical change is when matter changes forms but not chemical identity. Examples of chemical changes are burning, cooking, rusting, and rotting. Examples of physical changes are boiling, melting, freezing, and shredding. Often, physical changes can be undone, if energy is input.
Explanation: hope this helps have a good day
Answer:
If the reaction is a chemical change, new substances with different properties and identities are formed. This may be indicated by the production of an odor, a change in color or energy, or the formation of a solid.
someone please help me with this thanks
Now consider a different electromagnetic wave, also described by: Ex(z,t) = Eocos(kz - ω t + φ) In this equation, k = 2π/λ is the wavenumber and ω = 2π f is the angular frequency. In this case, though, assume φ = +30o and Eo = 1 kV/m. What is the value of Ex(z,t) when z/λ = 0.25 and ft = 0.125?
Answer:
Explanation:
Ex(z,t) = Eocos(kz - ω t + φ)
k = 2π/λ , ω = 2π f
φ = +30° , E₀ = 10³ V .
z/λ = 0.25 , ft = 0.125
Ex(z,t) = Eocos(2πz/λ - 2πf t + φ)
Putting the values given above
Ex(z,t) = 10³ cos ( 2π / 4 - 2π x .125 + 30⁰ )
= 1000cos (90⁰ - 45+30)
= 1000 cos 75
=258.8 V .
A Ferris wheel has radius 5.0 m and makes one revolution every 8.0 s with uniform rotation. A person who normally weighs 670 N is sitting on one of the benches attached at the rim of the wheel. What is the apparent weight (the normal force exerted on her by the bench) of the person as she passes through the highest point of her motion? ( type in your answer with no units in form xx0)
Answer:
The apparent weight of the person as she pass the highest point is [tex]N = 458.8 \ N[/tex]
Explanation:
From the question we are told that
The radius of the Ferris wheel is [tex]r = 5.0 \ m[/tex]
The period of revolution is [tex]T = 8.0 \ s[/tex]
The weight of the person is [tex]W = 670 \ N[/tex]
Generally the speed of the wheel is mathematically represented as
[tex]v = \frac{2 \pi r}{T }[/tex]
substituting values
[tex]v = \frac{2 * 3.142 * 5}{8 }[/tex]
[tex]v = 3.9 3 \ m/s[/tex]
The apparent weight (the normal force exerted on her by the bench) at the highest point is mathematically evaluated as
[tex]N = mg - \frac{mv^2}{r}[/tex]
Where m is the mass of the person which is mathematically evaluated as
[tex]m = \frac{W}{g}[/tex]
substituting values
[tex]m = \frac{670}{9.8}[/tex]
[tex]m = 68.37 \ kg[/tex]
So
[tex]N = 68.37 * 9.8 - \frac{68.37 * {3.93}^2}{5}[/tex]
[tex]N = 458.8 \ N[/tex]
9. How do air masses move?
Answer:
Air masses move with the global pattern of winds. In most of the United States, air masses generally move from west to east. They may move along with the jet stream in more complex and changing patterns.
an object's resistance to any change in motion is the_________ of the object.
An object's resistance to any change in motion is the Inertia of the object.
A skateboarder, starting from rest, rolls down a 12.8-m ramp. When she arrives at the bottom of the ramp her speed is 8.89 m/s. (a) Determine the magnitude of her acceleration, assumed to be constant. (b) If the ramp is inclined at 32.6 ° with respect to the ground, what is the component of her acceleration that is parallel to the ground?
Answer:
a) a = 3.09 m/s²
b) aₓ = 2.60 m/s²
Explanation:
a) The magnitude of her acceleration can be calculated using the following equation:
[tex] V_{f}^{2} = V_{0}^{2} + 2ad [/tex]
Where:
[tex]V_{f}[/tex]: is the final speed = 8.89 m/s
[tex]V_{0}[/tex]: is the initial speed = 0 (since she starts from rest)
a: is the acceleration
d: is the distance = 12.8 m
[tex] a = \frac{V_{f}^{2}}{2d} = \frac{(8.89 m/s)^{2}}{2*12.8 m} = 3.09 m/s^{2} [/tex]
Therefore, the magnitude of her acceleration is 3.09 m/s².
b) The component of her acceleration that is parallel to the ground is given by:
[tex] a_{x} = a*cos(\theta) [/tex]
Where:
θ: is the angle respect to the ground = 32.6 °
[tex] a_{x} = 3.09 m/s^{2}*cos(32.6) = 2.60 m/s^{2} [/tex]
Hence, the component of her acceleration that is parallel to the ground is 2.60 m/s².
I hope it helps you!
A skateboarder, starting from rest, rolls down a 12.8-m ramp the magnitude of the skateboarder's acceleration is approximately 3.07 [tex]m/s^2[/tex], the component of her acceleration that is parallel to the ground is approximately 1.66 [tex]m/s^2[/tex].
(a) The following kinematic equation can be used to calculate the skateboarder's acceleration:
[tex]v^2 = u^2 + 2as[/tex]
[tex](8.89)^2 = (0)^2 + 2a(12.8)[/tex]
78.72 = 25.6a
a = 78.72 / 25.6
a = 3.07 [tex]m/s^2[/tex]
(b) Trigonometry can be used to calculate the part of her acceleration that is parallel to the ground. We are aware that the ramp's angle with the ground is 32.6°.
[tex]a_{parallel }= a * sin(\theta)[/tex]
Plugging in the values:
[tex]a_{parallel[/tex] = 3.07 [tex]m/s^2[/tex]* sin(32.6°)
[tex]a_{parallel[/tex]≈ 1.66 [tex]m/s^2[/tex]
Therefore, the component of her acceleration that is parallel to the ground is approximately 1.66 [tex]m/s^2[/tex].
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This problem explores the behavior of charge on conductors. We take as an example a long conducting rod suspended by insulating strings. Assume that the rod is initially electrically neutral. For convenience we will refer to the left end of the rod as end A, and the right end of the rod as end B. In the answer options for this problem, "strongly attracted/repelled" means "attracted/repelled with a force of magnitude similar to that which would exist between two charged balls.A small metal ball is given a negative charge, then brought near (i.e., within about 1/10 the length of the rod) to end A of the rod. What happens to end A of the rod when the ball approaches it closely this first time?
Answer:
rod end A is strongly attracted towards the balls
rod end B is weakly repelled by the ball as it is at a greater distance
Explanation:
When the ball with a negative charge approaches the A end of the neutral bar, the charge of the same sign will repel and as they move they move to the left end, leaving the rod with a positive charge at the A end and a negative charge of equal value at end B.
Therefore rod end A is strongly attracted towards the balls and
rod end B is weakly repelled by the ball as it is at a greater distance