Your teacher placed a 3.5 kg block at the position marked with a “ + ” (horizontally, 0.5 m from the origin) on a large incline outlined on the graph below and let it slide, starting from rest. ***There are two images included!***
Answer:
x = 10.75 m
Explanation:
For this problem we will solve it in two parts, the first using energy and the second with kinematics
Let's use the energy work relationship to find the velocity of the block as it exits the ramp
W = [tex]Em_{f}[/tex] - Em₀
Starting point. Higher
Em₀ = U = m g h
the height from the edge of the ramp of the graph has a value
h = 9-3 = 6 m
Final point. At the bottom of the ramp
Em_{f} = K = ½ m v²
Friction force work
W = - fr d
The friction force has the formula
fr = μ N
On the ramp, we can use Newton's second law
N - W cos θ = 0
N = W cos θ
where the angle is obtained from the graph
tan θ = (9-3) / (0.5-4) = -6 / 3.5
θ = tan⁻¹ (-1,714)
θ = -59.7º
the distance d is
d = √ (Δx² + Δy²)
d = √ [(0.5-4)² + (9-3)²]
d = 6.95 m
for which the work is
W = - μ mg cos 59.7 d
we substitute
W = Em_{f} -Em₀
- μ mg cos 59.7 d = ½ m v² - m g h
In the graph o text the value of the friction coefficient is not observed, suppose that it is μvery = 0.2
- μ g cos 59.7 d = ½ v² - g h
v² = 2g (h - very d coss 59.7)
let's calculate
v² = 2 9.8 (6 - 0.2 6.95 cos 59.7)
v = √ 103.8546
v = 10.19 m / s
in the same direction as the ramp
in the second part we use projectile launch kinematics
let's look for the components of velocity
v₀ₓ = vo cos -59.7
[tex]v_{oy}[/tex] = vo sin (-59,7)
v₀ₓ = 10.19 cos (-59.7) = 5.14 m / s
v_{oy} = 10.19 if (-59.7) = -8.798 m / s
Let's find the time to get to the floor (y = o)
y = y₀ + v_{oy} t - ½ g t²
to de groph y₀=3 m
0 = 3 - 8.798 t - ½ 9.8 t²
t² - 1.796 t - 0.612 = 0
we solve the quadratic equation
t = [1.796 ±√(1.796² + 4 0.612)] / 2
t = [1,795 ± 2,382] / 2
t₁ = 2.09 s
t₂ = -0.29 s
since time must be a positive quantity the correct value is t = 2.09 s
we calculate the horizontal displacement
x = v₀ₓ t
x = 5.14 2.09
x = 10.75 m
The motion of the box, after it exits the incline is the motion and trajectory
of a projectile.
Horizontal distance from the right-hand edge of the incline to the point of
contact with the floor is approximately 1.24613 m.
Reasons:
Mass of the block, m = 3.5 kg
Coefficient of kinetic friction, μ = 1.2
Location of the = 0.5 m from the origin
Required:
Horizontal distance between the block's point of contact with the floor and
the bottom right-hand edge of the incline.
Solution:
Let θ represent the angle the incline make with the horizontal.
The normal reaction of the incline on the block, [tex]F_N[/tex] = m·g·cos(θ)
Work done on friction = [tex]F_N[/tex]×μ×Length of the incline, L
Rise of the incline = 10 - 3 = 7
Run of the incline = 4
L = √(6.125² + 3.5²) = [tex]\dfrac{7 \times \sqrt{65} }{8}[/tex]
Let ΔP.E.₁ represent the potential energy transferred to kinetic energy
and work along the incline, we have;
Energy of the block at the bottom of the incline, M.E.₂, is found as follows;
K.E.₂ = mgh - m·g·μ·cos(θ)·L
[tex]K.E. =\frac{1}{2} \times 3.5 \times v^2 = 3.5 \times 9.81 \times 6.125 - 3.5 \times 9.81 \times 1.2 \times \dfrac{4}{\sqrt{65} } \times \dfrac{7 \times \sqrt{65} }{8}[/tex]
v ≈ 6.1456 m/s
The vertical component of the velocity is therefore;
[tex]v_y = v \cdot sin(\theta)[/tex]
[tex]v_y = 6.1456 \times \dfrac{7}{\sqrt{65} } \approx 5.33588[/tex]
From the equation, h = u·t + 0.5·g·t² derived from Newton's Laws of motion, we have;
ΔP.E.₁ = 3.5×9.81×7
3 = 5.33588·t + 0.5×9.81·t²
Factorizing, the above quadratic equation, we get;
The time it takes the block to reach the floor, t ≈ 0.40869 seconds
Horizontal component of the velocity is [tex]v_x \approx 6.1456 \times \dfrac{4}{\sqrt{65} } \approx 3.04908[/tex]
The horizontal distance, x = vₓ × t
∴ x = 3.04908 × 0.40869 ≈ 1.08194
Horizontal distance from the right-hand edge of the incline to the point of
contact with the floor, x ≈ 1.24613 m.
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Select the correct answer.
The motion of a car on a position-time graph is represented with a horizontal line. What does this indicate about the car's motion?
A. It's not moving.
B.It's moving at a constant speed.
C.It's moving at a constant velocity
D.It's speeding up.
Answer:
It isn't moving
Explanation:
I NEED THIS ASAP!!
Which formula defines the unit for electrical power?
Answer:
1 W = 1 V x 1 A
Explanation:
Other dude is wrong this is right
A mass of 100 g is tied to the end of an 80.0-cm string and swings in a vertical circle about a fixed center under the influence of gravity. The speed of the mass at the top of the swing is 3.50 m/s. What is the speed of the mass at the bottom of its swing?
Answer:
the speed of the mass at the bottom of its swing is 6.61m/s
Explanation:
Applying energy conservation
[tex]\frac{1}{2}m(Vlowest)^2 = mg(2R) + \frac{1}{2}m(Vtop)^2[/tex]
There is no potential energy at the bottom as the body will have a kinetic energy there.
h= 2R = 1.6m as the diameter of the circle will represent the height in the circle.
g = 9.8m/s^2
m will cancel out, so the net equation becomes.
[tex]\frac{(Vbottom)^2}{2} = 2gR + \frac{(Vtop)^2}{2}[/tex]
= [tex]2*9.8*0.8 + \frac{(3.5)^2}{2}[/tex]
= 15.68+ 6.125
[tex]\frac{(Vbottom)^2 }{2}[/tex] = 21.805
(Vb)^2 = 2*21.805
= 43.64
Vb = 6.61m/s
A student throws a 110 g snowball at 6.5 m/s at the side of the schoolhouse, where it hits and sticks.
What is the magnitude of the average force on the wall if the duration of the collision is 0.19 s ?
Answer:
3.6NExplanation:
Impulse is the change of momentum of an object when the object is acted upon by a force for an interval of time.
the expression is Ft=mv
where F= force
m= mass
t= time
v= velocity
Step one:
given data
mass m= 110g= 0.11kg
velocity v= 6.5m/s
time t= 0.19seconds
Step two:
we also know that the force on impulse is given as
Ft=mv
F=0.11*6.5/0.19
F=0.715/0.19
F=3.76N
The magnitude of the average force on the wall if the duration of the collision is 0.19 is 14N
The propeller of an aircraft accelerates from rest with an angular acceleration α = 7t + 8, where α is in rad/s2 and t is in seconds. What is the angle in radians through which the propeller rotates from t = 1.00 s to t = 6.10 s?
Answer:
The value is [tex]\theta =407.3 \ radian[/tex]
Explanation:
From the question we are told that
The angular acceleration is [tex]\alpha = (7t + 8) \ rad/ s^2[/tex]
The first time is [tex]t_1 = 1.00 \ s[/tex]
The second time [tex]t_2 = 6.10 \ s[/tex]
Generally the angular velocity is mathematically represented as
[tex]w = \int\limits {\alpha } \, dt[/tex]
=> [tex]w = \int\limits {7t + 8 } \, dt[/tex]
=> [tex]w =\frac{ 7t^2}{2} + 8 t[/tex]
Generally the angular displacement is mathematically represented as
[tex]\theta = \int\limits^{t_2}_{t_1} { w} \, dt[/tex]
=> [tex]\theta = \int\limits^{t_2}_{t_1} { \frac{7t^2}{2} + 8t } \, dt[/tex]
=> [tex]\theta = { \frac{7t^3}{6} + \frac{8t^2}{2} } | \left \ t_2} \atop {t_1}} \right.[/tex]
=> [tex]\theta = { \frac{7t^3}{6} + 4t^2} } | \left \ 6.10} \atop {1}} \right.[/tex]
=> [tex]\theta =[ { \frac{7}{6}[6.10 ]^3 + 4[6.10]^2} } ] -[ { \frac{7}{6}[1 ]^3 + 4[1]^2} } ][/tex]
=> [tex]\theta =407.3 \ radian[/tex]
The components of lifetime fitness include all of the following components except
Answer:it’s A
Explanation:
because i took the quiz
Answer:
D is the correct answer, not A
Explanation:
A twirlers baton is 0.76 m long and spins around its center. The end of the baton has a centripetal acceleration of 47.8 m/s2?
A 0.31 s
B 0.56 s
C 4.3s
D 70s
Answer:
C. 4.3 seconds
Explanation:
B 0.56 s is the time period of a twirlers baton.
What is Centripetal Acceleration?Centripetal acceleration is defined as the property of the motion of an object which traversing a circular path.
Any object that is moving in a circle and has an acceleration vector pointed towards the center of that circle is known as Centripetal acceleration.
The centripetal acceleration is given by:
a = 4π²R/T²
Given values are:
a = 47.8 m/s²
D = 0.76 m so , R = 0.76/2 = 0.38m
Using this formula,
47.8*T² = 4π² x0.38
T² = [tex]\frac{4*3.14^2*0.38}{47.8}[/tex]
T = 0.56 s
Therefore,
A twirlers baton is 0.76 m long and spins around its center. The end of the baton has a centripetal acceleration of 47.8 m/s2 which have time period of 0.56 s.
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.
Find the mass of an object on planet F if its weight is 650 N (g = 13m/s^2)
Answer:
the object's mass is 50 kg
Explanation:
We use Newton's second law to solve for the mass:
F = m * a , then m = F / a
In our case, the acceleration is the gravitational acceleration on the planet, and the force is the weight of the object on the planet. So we get:
m = w / a = 650 N / 13 m/s^2 = 50 kg
Then, the object's mass is 50 kg.
A boxer is punching the heavy bag. The impact of the glove with the bag is 0.10s. The mass of the glove and his hand is 3kg. The velocity of the glove just before impact is 25m/s. What is the average impact force exerted on the glove?
Answer:
750NExplanation:
Impulse is the change of momentum of an object when the object is acted upon by a force for an interval of time.
the expression is Ft=mv
where F= force
m= mass
t= time
v= velocity
Step one:
given data
mass m=3kg
velocity v= 25m/s
time t= 0.10seconds
Step two:
we also know that the force on impulse is given as
Ft=mv
F=3*25/0.10
F=75/0.10
F=750N
The magnitude of the average force on the heavy bag if the duration of the collision is 0.1 is 750N
We will now determine the indexes of refraction for two Mystery materials, A and B. These materials can be selected from the list of materials on the right. Be sure to set your laser pointer to a frequency of 589 nm. Questions:A. Devise an experiment for determining the indices of refraction for these. Explain your methodology. B. What are the indices of refraction for the two mystery materials, A and B?
Answer:
A) refraction experiment n = n₁ sin θ₁ / sin θ₂
B) n_A = 1.19 , n_B = 1.53
Explanation:
A) This exercise is a method to measure the refractive index of materials, a very useful and simple procedure is to create a plate of known thickness from each material, place the material on a paper with angle measurements (protractor), incline the laser beam and measure the angles of incidence and refraction (within the material), repeat for about three different angles of incidence and use the equation of refraction to determine the index
n₁ sin θ₁ = n₂ sinθ₂
n₂ = n₁ sin θ₁₁ /sin θ₂
If the medium surrounding the plate is air, its refractive index is n₁ = 1, the final expression is
n = n₁ sin θ₁ / sin θ₂
B) For this part, no data are given in the exercise, but we can take 50º as the angle of incidence and measure the angle of refraction. Suppose it is 40º for material A and 30º for material B, the refractive index would be
material A
n_A = sin 50 / sin 40
n_A = 1.19
material B
n_B = sin 50 / sin30
n_B = 1.53
gravities limit is under which sphere as the perimeter?
g When the movable mirror of the Michelson interferometer is moved a small distance X while making a measurement, 246 fringes are counted moving into the field of the viewing mirror. What is X if the wavelength of the light entering the interferometer is 562 nm
Answer:
X = 69.1 x 10⁻⁶ m = 69.1 μm
Explanation:
The relationship between the motion of the moveable mirror and the fringe count of the Michelson's Interferometer is given by the following formula:
d = mλ/2
where,
d = distance moved by the mirror = X = ?
m = No. of Fringes counted = 246
λ = wavelength of light entering interferometer = 562 nm = 5.62 x 10⁻⁷ m
Therefore,
X = (246)(5.62 x 10⁻⁷ m)/2
Therefore,
X = 69.1 x 10⁻⁶ m = 69.1 μm
A medicine ball has a mass of 5kg and is thrown with a speed of 3 m/sec what is it's kinetic energy
The speed of a space shuttle is 10 / express this in /�
Answer:
268.22m/s
Explanation:
Given;
10mile/min to m/s
We need to convert between the two units;
1 mile = 1609.34m
60s = 1min
Now;
10 x [tex]\frac{mile}{min}[/tex] x [tex]\frac{1min}{60s}[/tex] x [tex]\frac{1609.34m}{1mile}[/tex]
= 268.22m/s
Sona wants to install room heater in her living room. She had only two options, either to install heater at the top of the window or near the ground level. . Which method of installing room heater would be the effective way . Why or Why not ?
A current of 3.75 A in a long, straight wire produces a magnetic field of 2.61 μT at a certain distance from the wire. Find this distance.
Given :
Current, I = 3.75 A .
Magnetic Field, [tex]B = 2.61\times 10^{-4}\ T[/tex]
To Find :
The distance from the wire.
Solution :
We know,
[tex]B = K\dfrac{2i}{d}\\\\d = 10^{-7}\times \dfrac{2\times 3.75}{2.61\times 10^{-4}}\\\\d = 0.00287\ m \\\\d = 2.87\times 10^{-3}\ m[/tex]
Hence, this is the required solution.
If a ball rolls across a table to the left with constant speed, which of the following is true about the force(s) on the ball? (3a1)
Question 10 options:
There cannot be any forces applied to the ball.
There must be exactly one force applied to the ball.
The net force applied to the ball is zero.
The net force applied to the ball is directed to the right.
Answer:
C. The net force applied to the ball is zero.
Explanation:
From Newton's second law of motion;
F = ma
Where F is the force on an object, m is its mass and a is its acceleration.
Therefore, the force on an object is a product of its mass and acceleration as it travel from one point to another.
Since acceleration relates to the rate of change in velocity to time. Then when the object moves at uniform velocity (especially along a straight path), its acceleration is zero.
So that;
F = m x 0
= 0
No force is applied on the object.
Therefore for the ball in the given question, the net force applied to the ball is zero because it rolls with constant speed along a straight path.
An extraterrestrial creature is standing in front of plane mirror. The height of this creature is H and we know that this creature has eyes positioned h below the top of its head. This creature sees its reflection which fit exactly the mirror, it means, this creature can just see the top of head and the bottom of its feet (or whatever it uses for motion). We can conclude that the top of a mirror is exactly:________
a. H/2 above the ground
b. H above the ground
c. (H-h/2) above the ground
d. (H-h) above the ground
e. We can not guess anything without information about the nature of this creature.
Answer:
c. (H-h/2) above the ground
Explanation:
The mirror must be at least half as tall as the alien, and its base must be located at half of the distance between the alien's eyes and the ground (assuming that the alien doesn't float or levitate).
This question is about the Law of Reflection which states that the angle of reflection = angle of incidence.
I attached an image that can help you understand the concept, although the alien is not included.
When two RF signals on the same frequency arrive at a receiver at the exact same time and their peaks and valleys are in alignment, what is true about these signals?
Answer:
The two RF signals are in phase.
Explanation:
A wave is a disturbance that travels through a medium which transfers energy from one point to another in the medium without causing any permanent displacement of the particles of the medium.
Characteristics of waves include frequency, wavelength, velocity, etc.
Two types of waves are longitudinal and transverse wave. Radio Frequency (RF) signals travel in the form of transverse waves which have regions of maximum and minimum displacements called crests and troughs.
Travelling waves with the same frequency may be said to be in phase or out of phase depending on whether their crests/peaks or troughs/valleys are reached at the same instant of time.
When two RF signals on the same frequency arrive at a receiver at the exact same time and their peaks and valleys are in alignment or in step, they are said to be in phase.
The phase of a wave involves the relationship between the position of the amplitude peaks and valleys of two waveforms.
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
Answer:
None of them: the direction of the pressure fluctuations is parallel to the direction of motion of the wave
Explanation:
Section 4.1- Newton's First Law
Answer:
Newton's first law states that every object will remain at rest or in uniform motion in a straight line unless compelled to change its state by the action of an external force. This is normally taken as the definition of inertia. ... If that velocity is zero, then the object remains at rest.
Explanation:
Answer:
Newton's First Law is about inertia; objects at rest stay at rest unless acted upon and objects in motion continue that motion in a straight line unless acted upon. The amount of inertia an object has is simply related to the mass of the object.
In 1993, Wayne Brian threw a spear at a record distance of 201.24 m. (This is not an official sports record because a special device was used to “elongate” Brian’s hand.) Suppose Brian threw the spear at a 35.0° angle with respect to the horizontal. What was the initial speed of the spear? 2. Find the maximum height and time of flight of the spear in problem #1.
I really don't know how to do any of this please help me :(
Answer:
V₀ = 45.81 m/s
H = 70.45 m
T = 5.36 s
Explanation:
The motion of the spare is projectile motion. Therefore, we will first use the formula of range of projectile:
R = V₀² Sin 2θ/g
where,
R = Range of Projectile = 201.24 m
V₀ = Initial Speed = ?
θ = Launch Angle = 35°
g = 9.8 m/s²
Therefore,
201.24 m = V₀²[Sin 2(35°)]/9.8 m/s²
V₀ = √[(201.24 m)/(0.095 m/s²)
V₀ = 45.81 m/s
Now, for maximum height:
H = V₀² Sin² θ/g
H = (45.81 m/s)² Sin² 35°/9.8 m/s²
H = 70.45 m
For the total time of flight:
T = 2 V₀ Sin θ/g
T = 2(45.81 m/s) Sin 35°/9.8 m/s²
T = 5.36 s
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?
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
A material that provides resistance to the flow of electric current is called a(n):
circuit
conductor
insulator
resistor
Answer:
it's an insulator
Explanation:
Insulators provides resistance
Answer:
C. insulator
Explanation:
if you increase the frequency of a wave by 5x whats it’s period?
We know that Period of a wave is the inverse of its Frequency
So, Period = 1 / Frequency
From the above, we can say that Period is inversely proportional to Frequency and hence, any change in Frequency will be the inverse change in the period
Therefore, we can say that if the frequency is increased by 5 times, the period will increase by 1/5 times
If a penny is dropped from rest from a building takes 2 seconds to hit the ground, calculate the velocity of the penny right before it touches the ground?
a. 19.6 m/s
b 9.8 m/s
c. 0 m/s
d 29.4 m/s
Answer:
20m/s
Explanation:
u = 0m/s
t = 2s
a = +g = 10m/s²
t = 2d
v = ?
v = ut + 1/2at²
v = 0(2) + 1/2(10)(2)²
v = 0 + 5(4)
v = 20m/s
On a surface of a planet of radius R and mass M the acceleration due to gravity is 7m/s?. Consider another planet of radius 2R and mass 0.4M. What would the acceleration due to gravity be on this new planet? Show your calculations.
Answer:
0.7 m/[tex]s^{2}[/tex]
Explanation:
From Newton's law of universal gravitation,
F = [tex]\frac{GMm}{r^{2} }[/tex]
and from Newton's second law of motion,
F = mg
So that;
mg = [tex]\frac{GMm}{r^{2} }[/tex]
⇒ g = [tex]\frac{GM}{r^{2} }[/tex]
For the first planet,
7 = [tex]\frac{GM}{R^{2} }[/tex]
⇒ G = [tex]\frac{7R^{2} }{M}[/tex] .............. 1
For the second planet,
g = [tex]\frac{0.4GM}{(2R)^{2} }[/tex]
= [tex]\frac{0.4GM}{4R^{2} }[/tex]
⇒ G = [tex]\frac{4gR^{2} }{0.4M}[/tex] ............. 2
Equating 1 and 2, we have;
[tex]\frac{7R^{2} }{M}[/tex] = [tex]\frac{4gR^{2} }{0.4M}[/tex]
g = [tex]\frac{7R^{2} *0.4M}{4R^{2}M }[/tex]
= [tex]\frac{7*0.4}{4}[/tex]
= [tex]\frac{2.8}{4}[/tex]
g = 0.7
Therefore, the acceleration due to gravity on the new planet is 0.7 m/[tex]s^{2}[/tex].
A 36.3 kg cart has a velocity of 3 m/s. How much kinetic energy does the object have?
Answer:
163.35
__________________________________________________________
We are given:
Mass of the object (m) = 36.3 kg
Velocity of the object (v) = 3 m/s
Kinetic Energy of the object:
We know that:
Kinetic Energy = 1/2(mv²)
KE = 1/2(36.3)(3)² [replacing the variables with the given values]
KE = 18.15 * 9
KE = 163.35 Joules
Hence, the cart has a Kinetic Energy of 163.35 Joules
explain the relationship among visible light, the electromagnetic spectrum, and sight.
Explanation:
The electromagnetic spectrum is the name given to the full range of frequencies and/or wavelengths that electromagnetic phenomena may have.
Human eyes respond to a small range of wavelengths in that spectrum. That response is called sight. Because humans can see that electromagnetic energy, it is called visible light.