Answers
I don't know if there is other given information that's missing here, so I'll try to fill in the gaps as best I can.
Let m be the mass of the object and v₀ its initial velocity at some distance x up the plane. Then the velocity v of the object at the bottom of the plane can be determined via the equation
v² - v₀² = 2 a x
where a is the acceleration.
At any point during its motion down the plane, the net force acting on the object points in the same direction. If friction is negligible, the only forces acting on the object are due to its weight (magnitude w) and the normal force (mag. n); if there is friction, let f denote its magnitude and let µ denote the coefficient of kinetic friction.
Recall Newton's second law,
∑ F = m a
where the symbols in boldface are vectors.
Split up the forces into their horizontal and vertical components. Then by Newton's second law,
• net horizontal force:
∑ F = n cos(θ + 90º) = m a cos(θ + 180º)
→ - n sin(θ) = - m a cos(θ)
→ n sin(θ) = m a cos(θ) ……… [1]
• net vertical force:
∑ F = n sin(θ + 90º) - w = m a sin(θ + 180º)
→ n cos(θ) - m g = - m a sin(θ)
→ n cos(θ) = m (g - a sin(θ)) ……… [2]
where in both equations, a is the magnitude of acceleration, g = 9.80 m/s², and friction is ignored.
Then by multiplying [1] by cos(θ) and [2] by sin(θ), we have
n sin(θ) cos(θ) = m a cos²(θ)
n cos(θ) sin(θ) = m (g sin(θ) - a sin²(θ))
m a cos²(θ) = m (g sin(θ) - a sin²(θ))
a cos²(θ) + a sin²(θ) = g sin(θ)
a = g sin(θ)
and so the object attains a velocity of
v = √(v₀² + 2 g x sin(θ))
If there is friction to consider, then f = µ n, and Newton's second law instead gives
• net horizontal force:
∑ F = n cos(θ + 90º) + f cos(θ) = m a cos(θ + 180º)
→ - n sin(θ) + µ n cos(θ) = - m a cos(θ)
→ n sin(θ) - µ n cos(θ) = m a cos(θ) ……… [3]
• net vertical force:
∑ F = n sin(θ + 90º) + f sin(θ) - w = m a sin(θ + 180º)
→ n cos(θ) + µ n sin(θ) - m g = - m a sin(θ)
→ n cos(θ) + µ n sin(θ) = m g - m a sin(θ) ……… [4]
Then multiply [3] by cos(θ) and [4] by sin(θ) to get
- n sin(θ) cos(θ) + µ n cos²(θ) = - m a cos²(θ)
n cos(θ) sin(θ) + µ n sin²(θ) = m g sin(θ) - m a sin²(θ)
and adding these together gives
µ n (cos²(θ) + sin²(θ)) = m g sin(θ) - m a (cos²(θ) + sin²(θ))
µ n = m g sin(θ) - m a
m a = m g sin(θ) - µ n
m a = m g sin(θ) - µ m g cos (θ)
a = g (sin(θ) - µ cos (θ))
and so the object would instead attain a velocity of
v = √(v₀² + 2 g x (sin(θ) - µ cos (θ)))
Related Questions
Having established that a sound wave corresponds to pressure fluctuations in the medium, what can you conclude about the direction in which such pressure fluctuations travel?A) The direction of motion of pressure fluctuations is independent of the direction of motion of the sound wave.B) Pressure fluctuations travel perpendicularly to the direction of propagation of the sound wave.C) Pressure fluctuations travel along the direction of propagation of the sound wave.D) Propagation of energy that passes through empty spaces between the particles that comprise the mediumDoes air play a role in the propagation of the human voice from one end of a lecture hall to the other?a) yesb) no
Answers
Answer:
None of them: the direction of the pressure fluctuations is parallel to the direction of motion of the wave
Explanation:
1. What does the pH scale measure?
Answers
Answer:
The pH scale measures of how acidic or basic water is.
The pH scale also measures whether there is more hydronium or hydroxide in a solution.
Explanation:
The range goes from 0-14, with 7 being neutral. Less than 7 indicates acidity and more than seven indicates the substance is a base.
2
10 points
Find the total displacement of each of the motions.
a) You walk 45 m W, then 34 mW
b) You drive 5 km N, then 7 km S
c) You cycle 350 m E, then 800 m W, then 200 m E
d) You fly 850 km N then 850 km S
Answers
Answer:
a) s = 79 m W
b) s = 2 km S
c) s = 250 m W
d) s = 0 km
Explanation:
We take the following sign convention for the directions:
North (N) ---> positive
South (S) ---> negative
East (E) ---> negative
West (W) ---> positive
a)
45 m W, 34 m W
s = 45 m + 34 m
s = 79 m W
b)
5 km N, 7 km S
s = 5 km - 7 km
s = - 2 km
s = 2 km S
c)
350 m E , 800 m W, 200 m E
s = -350 m + 800 m - 200 m
s = 250 m
s = 250 m W
d)
850 km N, 850 km S
s = 850 km - 850 km
s = 0 km
A car is moving at an average speed of 20 meters per second. This is equivalent to
Answers
Answer:
44.73 MP/H or 71.98 KM/H
Explanation:
car driving on a circular test track shows a constant speedometer reading of 100 kph for one lap. a. Describe the car's speed during this time. b.
Answers
Answer:
Speed = 100 km/h
Explanation:
Given:
Speedometer reading = 100 kph for one lap
Assume;
Time taken to complete one lap = 1 hour
Computation:
Speed = Distance / Time
Speed = 100 / 1
Speed = 100 km/h
Which term refers to the ability to do work?
o energy
power
force
motion
PLEAEE HURRY IM DOING MY EXAM PLEASE HELP WILL MARK BRAINLIEST
Answers
Answer:
Energy
Explanation:
work is actually a transfer of energy. When work is done to an object , energy is transferred to that object.
The ability to do work is called energy.
What is work ?"Work is the energy transferred to or from an object via the application of force along a displacement. In its simplest form, it is often represented as the product of force and displacement."
What is energy ?"Energy is defined as the “ability to do work, which is the ability to exert a force causing displacement of an object.” energy is just the force that causes things to move. Energy is divided into two types: potential and kinetic."
Know more about energy here
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an object falls from a hovering helicopter and hits the ground at a speed of 30m per seconds. how long does it take the object to reach the ground and how far does it fall? sketch a velocity-time graph for the object ( ignore air resistance
Answers
Answer:
45.9m
Explanation:
Given parameters:
Final velocity = 30m/s
Initial velocity = 0m/s
Unknown:
Time it takes for the object of fall = ?
Height of fall = ?
Solution:
For the first problem, we use the equation below to solve for t;
V = U + gt
V is the final velocity
U is the initial velocity
g is the acceleration due to gravity
t is the time taken
30 = 0 + 9.8 x t
30 = 9.8t
t = [tex]\frac{30}{9.8}[/tex] = 3.1s
Now, height of fall;
V² = U² + 2gH
30² = 0² + 2 x 9.8 x H
900 = 19.6H
H = 45.9m
An engineer is designing the runway for an airport. Of the planes that will use the airport, the lowest acceleration rate is likely to be 3 m/s2. The takeoff speed for this plane will be 65 m/s. All airplanes will start from rest(0m/s). Assuming this minimum acceleration, what is the minimum allowed length for the runway for take off?
Answers
Answer:
x = 704 [m]
Explanation:
To solve this problem we must use the following equation of kinematics.
[tex]v_{f} ^{2} =v_{o} ^{2} +2*a*x[/tex]
where:
Vf = final velocity = 65 [m/s]
Vo = initial velocity = 0 (starts from rest)
a = acceleration = 3 [m/s²]
x = distance [m]
Now replacing we have:
65² = 0 + 2*3*x
4225 = 6*x
x = 704 [m]
Which interaction contributes to the greenhouse effect?
A (Gases in the atmosphere absorb heat.
B (Dust particles scatter and reflect light from the Sun.
C (Green visible light is trapped in Earth’s atmosphere.
D (Light travels through a thick part of the atmosphere at sunrise and sunset.
Answers
Answer:
A
Explanation:
Answer:
A
Explanation:
Gases in the atmosphere absorb heat.
You know when you have a blanket around you and some heat gets trapped in but some still gets out. Thats basically what it is.
Plus I got it right in multiple questions including the test!
I hope that reassured you!
Have a good night!
At an accident scene on a level road, investigators measure a car's skid mark to be 98 m long. It was a rainy day and the coefficient of friction was estimated to be 0.38. a) Use these data to determine the speed of the car when the driver slammed on (and locked) the brakes.b) Why does the car's mass not matter?
Answers
Answer:
a. V = 19.1m/s
b. The mass of the car does not matter
Explanation:
A.
KE = 1/2mv² = fd --------(1)
Fd = umgd ---------(2)
Therefore,
1/2mv² = umgd ---------(3)
M will cancel itself out from both sides of equation 3.
Then we will have:
1/2v² = ugd
Then we cross multiply to make v² the subject of the formula
V² = 2ugd
V = √2ugd -------(4)
U = 0.38
g = 9.81
d = 98
When we input these values into equation 4, we will have:
V = √2x0.38x9.81x98
V = √730.6488
V = 27.03m/s
B.
The mass of the car does not actually matter as the mass was cancelled out on the both sides of equation 3
A hydraulic car jack needs to be designed so it can lift a 2903.57 lb car assuming that a person can exert a force of 24.41 lbs. If the piston the person is pushing on had a radius of 3.26 cm, what should the diameter of the piston be that is used to raise the car?
Answers
Answer:
Diameter of the piston would be 0.71 m (71.1 cm)
Explanation:
From the principle of pressure;
[tex]\frac{F_{1} }{A_{1} }[/tex] = [tex]\frac{F_{2} }{A_{2} }[/tex]
Let [tex]F_{1}[/tex] = 2903.57 lb, [tex]F_{2}[/tex] = 24.41 lbs, [tex]r_{2}[/tex] = 3.26 cm = 0.0326 m.
[tex]A_{2}[/tex] = [tex]\pi r^{2}[/tex]
= [tex]\frac{22}{7}[/tex] x [tex](0.0326)^{2}[/tex]
= 0.00334 [tex]m^{2}[/tex]
So that:
[tex]\frac{2903.57}{A_{1} }[/tex] = [tex]\frac{24.41}{0.00334}[/tex]
[tex]A_{1}[/tex] = [tex]\frac{2903.57*0.00334}{24.41}[/tex]
= 0.3973
[tex]A_{1}[/tex] = 0.4 [tex]m^{2}[/tex]
The radius of the piston can be determined by:
[tex]A_{1}[/tex] = [tex]\pi r^{2}[/tex]
0.3973 = [tex]\frac{22}{7}[/tex] x [tex]r^{2}[/tex]
[tex]r^{2}[/tex] = [tex]\frac{0.3973*7}{22}[/tex]
= 0.1264
r = [tex]\sqrt{0.1264}[/tex]
= 0.3555
r = 0.36 m
Diameter of the piston = 2 x r
= 2 x 0.3555
= 0.711
Diameter of the piston would be 0.71 m (71.1 cm).
Select all correct answers....Covalent compounds
Answers
that delivers oxygen to your body and In the video your blood is compared to a picks up CO2 to be released out when you breath. PLEASE I NEED A ANSWER
Answers
What specific changes in two climate variables are expected to lead to major decreases in soil moisture southern Africa and the Mediterranean region?
Answers
Answer:
Less precipitation, droughts9: How might agriculture in southern Europe change by the end of the century if conditions follow the RCP8.
Explanation:
Precipitation and droughts are the specific changes in two climate variables that are expected to lead to major decreases in soil moisture.
What is drought?
Drought is defined as a period of protracted water scarcity, whether it is due to atmospheric surface water, or groundwater constraints.
Droughts can last months or years, although they can be proclaimed in as little as 15 days.
It has the potential to have a significant influence on the afflicted region's ecology and agriculture as well as harm the local economy.
Precipitation and droughts are the specific changes in two climate variables that are expected to lead to major decreases in soil moisture in southern Africa and the Mediterranean region.
Hence Precipitation and droughts are the specific changes in two climate variables.
To learn more about the drought refer to the link;
https://brainly.com/question/26693108
a car accelerates at a constant rate from 15 m/s to 25 m/s while it travels a distance of 125 m. How long does it take to achieve this speed?
Answers
25m/s -15m/s/ 125m
10m/s /125m
=0.08s
I hope it’s correct !
The time taken by the car to achieve the final speed is 6.25 seconds.
What is the equation of motion?The equations of motion can be defined as the equation that represents the relationship between the time, velocity, acceleration, and displacement of a moving object.
The mathematical expressions for the equations of motions can be written as:
[tex]v= u+at\\S=ut+(1/2)at^2\\v^2-u^2=2aS[/tex]
Given, the initial speed of the car, u = 15 m/s
The final speed of the given car, v = 25m/s
The distance covered by car, S = 125 m
From the third equation of motion: v² = u²+ 2aS
(25)² = (15)² + 2×a× 125
a = 1.6 m/s²
From the first equation of motion we can find the time to achieve the final speed:
v = u+ at
25 = 15 + (1.6) × t
t = 6.25 sec
Therefore, 6.25 seconds will be taken by the car to catch the final speed.
Learn more about the equation of motion, here:
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WHAT IS TRANS ATLANTIC SLAVE TRADE
Answers
A radio signal has a frequency of 1.023 x 108 HZ. If the speed of the signal in air is 2.997 x 108m/s, what is the wavelength of the signals? а 7.15 m b 5.23 m C 2.93 m d 0.93 m
Answers
Answer:
2.93 m (which agrees with answer "C" on the list)
Explanation:
Recall that the speed of the wave equals the product of the wave's length times its frequency. Therefore, the wavelength is going to be the quotient of the speed of the signal divided its frequency:
Wavelength = 2.997 10^8 / 1.023 10^8 = 2.93 m
A typical elevator car with people has a mass of 1500.0 kg. Elevators are currently approaching speeds of 20.0 m/s - faster than the speed.
Required:
What is the upward force required if the elevator moves upward 200.0 meters before reaching 20.0 m/s?
Answers
Answer:
1500NExplanation:
Force = mass * acceleration
Given
Mass = 1500kg
Get the acceleration using the equation of motion;
v² = u²+2aS
20² = 0+2s(200)
400 = 400a
a = 400/400
a = 1m/s²
Get the upward force required
F = 1500 * 1
F = 1500N
Hence the upward force required if the elevator moves upward 200.0 meters before reaching 20.0 m/s is 1500N
match the variables to its definition
Answers
Answer:
See connections below
Explanation:
1 [tex]\Rightarrow[/tex] b
2 [tex]\Rightarrow[/tex] a
3 [tex]\Rightarrow[/tex] d
4 [tex]\Rightarrow[/tex] i
5 [tex]\Rightarrow[/tex] g
6 [tex]\Rightarrow[/tex] h
7 [tex]\Rightarrow[/tex] c
8 [tex]\Rightarrow[/tex] e
9 [tex]\Rightarrow[/tex] f
A car traveling initially at a speed of 20 m/s accelerates to a speed of 31 m/s over a distance of 45 meters.
What is the magnitude of the car's acceleration?
Answers
Answer:abc defg hijk lmnop qrs tuv wx y and z
Explanation: now i know my abc's
A satellite was in two separate crashes. In both crashes, the satellite had the same mass. Engineers want to know about the speed and direction of the satellite after the crashes. Why would the crash affect the motion of the satellite, and which crash caused a greater change in motion for the satellite?
WILL GIVE BRAINLIEST
Answers
Answer:
The fastest satellite must change orbit
The most massive body (m₁) transfers more momentum to the satellite,
Explanation:
For this problem we consider a system formed by the satellite and each of the bodies with which it collides, in this system the forces during the collision are internal, the amount of movement must be conserved. Let's write the momentum is two instants
Most massive body (m1)
initial. Before the crash
p₀₁ = M v + m₁ v₁
after the crash
[tex]p_{f1}[/tex] = M v´ + m₁ v₁´
how momentum is conserved
p₀ = p_{f}
Lighter body (m2)
p₀₂ = M v + m₂ v₂
p_{f2} = M v´ + m₂ v₂´
Let's clarify that the speed of the satellite and the object do not have the same direction, in general these shocks are elastic.
We can see that p₀₁> p₀₂
Let us analyze the two cases when the body collides, The most massive body (m₁) transfers more momentum to the satellite, therefore there must be a greater change in its momentum and velocity.
The fastest satellite must change orbit, thus rotating at a different distance from Earth
please help i will mark brainliest
what does a speedometer measure?
a. accerlation
b. velocity
c. speed
d. average speed.
Answers
Answer:
c. speed
Explanation:
Speedometer is a device used to measure the speed of a vehicle. I am pretty sure this is the correct option.
If a ball rolls down an incline with a starting velocity of 0m/s and a final velocity of 6m/s
and it takes a total of 1.4 seconds, calculate its acceleration.
Answers
Answer:
If a ball rolls down an incline with a starting velocity of 0m/s and a final velocity of 6m/s
and it takes a total of 1.4 seconds, calculate its acceleration.
Answer:
Acceleration is 4.28 m/s²
Explanation:
Acceleration is change of speed in time. To solve this, we will assume that the acceleration is constant, meaning that every second the velocity increases for the same constant value.
a = ∆v/t
∆v is the difference between two measured velocities:
a = (v2 - v1) / t
v1 = 0m/s
v2 = 6m/s
t = 1.4 s
Now, we only plug in the given values:
a = (6 - 0) / 1.4
a = 6 m/s / 1.4 s
a = 4.28 m/s²
Why do stretching exercises increase flexibility more than cardio exercises?
Answers
when is thermal equilibrium achived between two identical objects
need help ASAP
Answers
Answer: When two objects in contact with each other are at different temperatures, they are said to be in thermal equilibrium.
Explanation: . When two objects not in contact with each other are at the same pressure, they are said to be in thermal equilibrium.
A medicine ball has a mass of 5kg and is thrown with a speed of 3 m/sec what is it's kinetic energy
Answers
KE = 1/2 (5kg)(3m/s)
KE = 22.5 J
Which statement explains how it is possible to carry books to school without changing the kinetic or potential energy of the books or doing any work?
a. by moving the book without acceleration and keeping the height of the book constant
b. by moving the book with acceleration and keeping the height of the book constant
c. by moving the book without acceleration and changing the height of the book
d. by moving the book with acceleration and changing the height of the book
Answers
Answer:
a. by moving the book without acceleration and keeping the height of the book constant
Explanation:
FOR CONSTANT KINETIC ENERGY:
The kinetic energy of a body depends upon its speed according to its formula:
ΔK.E = (1/2)mΔv²
So, for Δv = 0 m/s
ΔK.E = 0 J
So, for keeping kinetic energy constant, the books must be moved at constant speed without acceleration.
FOR CONSTANT POTENTIAL ENERGY:
The potential energy of a body depends upon its height according to its formula:
ΔP.E = mgΔh
So, for Δh = 0 m/s
ΔP.E = 0 J
So, for keeping potential energy constant, the books must be moved at constant height.
So, the correct option is:
a. by moving the book without acceleration and keeping the height of the book constant
A 8.45μC particle with a mass of 6.15 x 10^-5 kg moves perpendicular to a 0.493-T magnetic field in a circular path of radius 34.1 m. How much time will it take for the particle to complete one orbit?
a. 92.7 s
b. 0.0927 s
c. 9.27 s
d. 927 s
Answers
This question is incomplete, the complete question is;
A 8.45μC particle with a mass of 6.15 x 10⁻⁵ kg moves perpendicular to a 0.493-T magnetic field in a circular path of radius 34.1 m.
How much time will it take for the particle to complete one orbit?
a. 92.7 s
b. 0.0927 s
c. 9.27 s
d. 927 s
Answer:
it will take 92.7 seconds for the particle to complete one orbit.
Option a) 92.7 s is the correct option
Explanation:
Given that;
mass m = 6.15 x 10⁻⁵ kg
q = 8.45μC = 8.45 × 10⁻⁶ C
B = 0.493
we know that
Time period T = 2πr / V
where r = mv/qB
so T = 2πm/qB
we substitute
T = (2 × 3.14 × 6.15 x 10⁻⁵) / ( 8.45 × 10⁻⁶ × 0.493)
T = 0.0003862 / 0.000004165
T = 92.7 sec
Therefore it will take 92.7 seconds for the particle to complete one orbit.
Option a) 92.7 s is the correct option
Which possible component of initial energy is caused by molecular motion within a material?
Answer: thermal energy
Answers
Answer:
Thermal energy
Explanation:
The internal energy of a system is widely known as thermal energy. Now, thermal energy is also called heat energy and it is an internal energy of a component which is produced when an increase in temperature causes atoms and molecules within the component to move faster and start colliding with one other.
Therefore, the more heat the is applied to the component, the hotter the substance and the more its particles move which in turn leads to a higher thermal energy.
A football player runs down the field at a speed of 8 m/s how long will it take him to run 20 m?
Answers
The answer to this would be 2.5 seconds for the football player to run 20 meters.
I hope I did this problem correct and I hope that this helped you :)))