Answers
As the board is raised by an angle θ, the block will be held in place by 3 forces:
• its weight, pointing downward (magnitude w )
• the normal force of the board pushing up on the block, pointing in the direction perpendicular to the board (mag. n)
• static friction, pointing in the direction parallel to the board, opposite the direction the block would slip (mag. f )
Decompose the vectors into components that are parallel and perpendicular to the board (taking the direction of n to be the positive direction perpendicular to the board, and the direction of f to be the negative directoin parallel to it), so that by Newton's second law, we have
• net parallel force:
∑ F = w (//) + f
∑ F = m g sin(θ) - µ n = 0
where µ = 0.45 is the coefficient of static friction, g = 9.80 m/s² is the mag. of the acceleration due to gravity, and m = 15.0 kg is the mass of the block.
• net perpendicular force:
∑ F = n + w (⟂)
∑ F = n - m g cos(θ) = 0
Solve for n in the equation for net perpendicular force:
n = m g cos(θ)
Substitute this into the equation for net parallel force:
m g sin(θ) - 0.45 m g cos(θ) = 0
Solve for θ :
sin(θ) - 0.45 cos(θ) = 0
sin(θ) = 0.45 cos(θ)
tan(θ) = 0.45
θ = tan⁻¹(0.45)
θ ≈ 24.2°
So the maximum angle the board can be lifted before the block starts to slide is about 24.2°, since the coefficient of static friction µ is such that
f = µ n
where f is the maximum magnitude of the static friction force.
Related Questions
In winter morning, as soon as we wake the air inside the room is cold but if up, the out and return to the same room, we we goo feel warm, why?
Answers
Answer:
it is all because of nature
As a 3.0 kg bucket is being lowered into a 10 m deepwell, starting from top, the tension in the rope is 9.8 N. theacceleration of the bucket will be:____________A) 6.5 m/s2 downwardB) 9.8 m/s2 downwardC) zeroD) 3.3 m/s2 upwardE) 5.6 m/s2 upward
Answers
Answer:
A) 6.5 m/s²
Explanation:
Mass of the bucket, m = 3.0 kg
depth of the well, d = 10 m
tension on the rope, T = 9.8 N
The net downward force on the bucket is given as;
T = mg - ma
where;
a is downward acceleration of the bucket
9.8 = (3 x 9.8) - 3a
9.8 = 29.4 - 3a
3a = 29.4 - 9.8
3a = 19.6
a = 19.6 / 3
a = 6.53 m/s² downwards
Therefore, the acceleration of the bucket is 6.53 m/s² downwards
A person holds a ladder horizontally at its center. Treating the ladder as a uniform rod of length 4.15 m and mass 7.98 kg, find the torque the person must exert on the ladder to give it an angular acceleration of 0.396 rad/s2.
Answers
Answer:
4.535 N.m
Explanation:
To solve this question, we're going to use the formula for moment of inertia
I = mL²/12
Where
I = moment of inertia
m = mass of the ladder, 7.98 kg
L = length of the ladder, 4.15 m
On solving we have
I = 7.98 * (4.15)² / 12
I = (7.98 * 17.2225) / 12
I = 137.44 / 12
I = 11.45 kg·m²
That is the moment of inertia about the center.
Using this moment of inertia, we multiply it by the angular acceleration to get the needed torque. So that
τ = 11.453 kg·m² * 0.395 rad/s²
τ = 4.535 N·m
The Torque will be "4.535 N.m".
Given:
Mass of ladder,
m = 7.98 kgLength of ladder,
L = 4.15 m
The moment of inertia will be:
→ [tex]I = \frac{mL^2}{12}[/tex]
[tex]= \frac{7.98\times (4.15)^2}{12}[/tex]
[tex]= \frac{7.98\times 17.2225}{12}[/tex]
[tex]= 11.45 \ kg.m^2[/tex]
hence,
The torque will be:
→ [tex]\tau = 11.453\times 0.395[/tex]
[tex]= 4.535 \ N/m[/tex]
Thus the above approach is correct.
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A source of heat at 1000 K transfers 1000 kW of power to a power generation device, while producing 400 kW of useful work. Determine the second law efficiency of the system, if the environment is at 300 K.
Answers
Answer:
The value is [tex]\eta _2 = 0.57[/tex]
Explanation:
From the question we are told that
The temperature of the heat source is [tex]T_s = 1000 \ K[/tex]
The amount of power transferred is [tex]P_s = 1000 \ kW = 1000 *10^{3} \ W[/tex]
The work produced is [tex]W = 400 \ kW[/tex]
The temperature of the environment [tex]T_e = 300 \ K[/tex]
Gnerally the Carnot efficiency of the system is mathematically represented as
[tex]\eta_c = 1 -\frac{T_e}{T_s}[/tex]
=> [tex]\eta_c = 1 -\frac{300}{1000}[/tex]
=> [tex]\eta_c = 0.7[/tex]
Generally the first law efficiency of the system is mathematically represented as
[tex]\eta _1 = \frac{W}{P_s}[/tex]
=> [tex]\eta _1 = \frac{400}{1000}[/tex]
=> [tex]\eta _1 = 0.40[/tex]
Generally the second law efficiency of the system is mathematically represented as
[tex]\eta _2 = \frac{\eta_1}{\eta_c}[/tex]
=> [tex]\eta _2 = \frac{0.4}{0.7}[/tex]
=> [tex]\eta _2 = 0.57[/tex]
At the mail racing championship in England, the winner moved at an average velocity of 2.4 mm/s [ford] for 140 s. Determine the winning snail's displacement during this time interval. [
Answers
Answer:
Explanation: 1.2 mm
Time= 140 sec
Initial Velocity= 0
Average Velocity= 2.4 mm/s
Displacement= 0.5* (2.4/140) *140 = 1.2 mm
What is the voltage of a circuit that has a current of 3.7 amps and a resistance of 1.5 ohms.
Answers
Answer:
V = 5.55 volts
Explanation:
Given that,
Current, I = 3.7 A
Resistance, R = 1.5 ohms
We need to find the voltage of the circuit. Let V is the voltage. We can find it using Ohm's law as follows :
V = IR
Substituting all the values, we get :
[tex]V=3.7\times 1.5\\\\=5.55\ V[/tex]
So, the voltage of the circuit is 5.55 V,
A toy car in the figure below runs off the edge of a table that is h = 1.36 m high. The
car lands d= 0.88 m from the base of the table. How fast was the car going on the
table?
Answers
The toy car was going at a speed of 1.66 m/s on the table.
When the toy car runs off the edge of the table, it travels vertically as well as horizontally and it is an example of a horizontal projectile from a height.
The distance covered vertically will be equal to the height of the table which is 1.36m. And horizontal distance is given as d.
Vertical distance = H = 1.36m
Horizontal distance = d = 0.88m
Now, we for a free-falling body, in
Speed in vertical direction = u = 0 m/s
Distance = h = 1.36
Using the second equation of motion,
h = ut + 1/2gt²
Put in the value, we get
1.36 = (0)t + 1/2(9.8)t²
t² = 1.36/4.9
t² = 0.278
t = 0.53 seconds
Now distance traveled in a horizontal direction is given by
Distance in horizontal direction = Speed on table × time of travel
Put in the value, we get
0.88 = V × 0.53
V = 0.88/0.53
V = 1.66 m/s
So, the toy car was going at a speed of 1.66 m/s on the table.
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A car is stopped for a traffic signal. When the light turns green,
the car accelerates, increasing its speed from 0 to 5.20 m/s in
0.832 s. What are the magnitudes of (a) the linear impulse and
(b) the average total force experienced by a 70.0-kg passenger
in the car during the time the car accelerates?
Answers
Answer:
Impulse, p = 364 N·s
Force F = 437.5 N
Explanation:
First some definitions:
p = mv
Impulse, J is the change in momentum of a body
J = Δp = p₂ - p₁ = mv₂ - mv₁ = mΔv where the subscript 1 refers to initial values and subscript 2 to final values.
Part (a)
Since the car is initially at rest, its initial momentum is 0.
When the car reaches a velocity of 5.20 m/s, the momentum experienced by a 70 kg passenger is
Δv = 5.20 - 0 = 5.20 m/s
p = 70 kg x 5.20 m/s = 50.3248 kg m/s = 364 N·s
p = 384 N.s
Part (b)
Force is given by F=m(Δv/Δt) = 70 kg x (5.20 m/s / 0.832 s) = 437.5 N
F = 437.5 N
a sphere with a radius of 8cm carries a uniform volume charge density of 1.5 find the magnitude of the electric field
Answers
Answer:
E = 5.65 x 10¹⁰ N/C
Explanation:
First we need to find the total charge on the sphere. So, we use the following formula for that purpose:
[tex]q = \sigma V\\[/tex]
where,
q = total charge on sphere
V = Volume of Sphere = [tex]\frac{4}{3} \pi r^3 = \frac{4}{3} \pi (0.08\ m)^3 = 0.335\ m^3[/tex]
σ = volume charge density = 1.5 C/m³
Therefore,
[tex]q = (0.335\ m^3)(1.5\ C/m^3) \\q = 0.502 C[/tex]
Now, we use the following formula to find the electric field due to this charged sphere:
[tex]E = \frac{kq}{r^2}[/tex]
where.
E = Electric Field Magnitude = ?
k = Coulomb's Constant = 9 x 10⁹ N.m²/C²
r = radius of sphere = 8 cm = 0.08 m
Therefore,
[tex]E = \frac{(9\ x\ 10^9\ Nm^2/C^2)(0.502 C)}{(0.08\ m)^2}\\\\[/tex]
E = 5.65 x 10¹⁰ N/C
if A.B=A.C
does this imply that B must be equal to c ?
I need answer with example please
Answers
Answer:
Yes
Explanation:
[tex]Consider\ three\ variables\ a,b\ and\ c.\\If,\\ab=ac\\a*b=a*c\\We\ may\ now\ divide\ the\ LHS\ and\ RHS\ by\ a,\\Hence,\\\frac{a*b}{a} =\frac{a*c}{a}\\Hence,\\b=c[/tex]
[tex]Ex: \\Consider\ a=5, b=6.\\Hence\ if,\\a*b=a*c\\5*6=5*c\\Hence,\\30=5c\\Hence, c=\frac{30}{5}\\c=6\\As\ b\ also\ equals\ to\ 6,\\b=c[/tex]
Dale and Alex push on opposite sides of a couch. Dale pushes to the left with a force of 40 N, while Alex pushes to the right with a force of 32 N. If the
couch has a mass of 28 kg, what is the acceleration of the couch?
A. 2.6 m/s^2 right
B. 2.6 m/s^2 left
C. 0.3 m/s^2 left
D. 0.3 m/s^2 right
Answers
0.3 m/s^2 left will be the acceleration of the couch.
we have given in the statement
force towards left 40 N
force towards right 32 N
net force = 40-32 = 8 N towards left
couch mass = 28 kg
now we will use newtons 2nd law to find acceleration
F=ma, here f is force m is mass a is acceleration
a=F/m
a=8/24
a=0.285 ≅ 0.3 N
An object's rise in velocity rate is referred to as acceleration. It is a vector quantity that is sign-sensitive, and the route shift and body speed variance establish the sign norm. it's unit is m/s^2To know more about acceleration visit : https://brainly.com/question/3046924
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0.3 m/s squared left Answer:
Explanation:
F x T = m (Vf - Vi)
in this equation what does the M stand for
Answers
Answer:
m = mass [kg]
Explanation:
This equation is characteristic of the amount of motion and momentum.
[tex]F*t = m*(v_{f}-v_{i})[/tex]
where:
F = force [N] (units of Newtons)
t = time = [s]
m = mass [kg]
Vf = final velocity [m/s]
Vi = initial velocity [m/s]
Now using the units and placing them in the equation above.
[tex][N]*[s] = [kg]*(m/s-m/s)\\[/tex]
[tex][N]=[kg*m/s^{2} ][/tex]
Now replacing:
[tex][kg*m/s^{2}]*[s]=[kg*m/s][/tex]
The s² is cancelled with the s, therefore.
[tex][kg*m/s]=[kg*m/s][/tex]
Damage to internal organs will present as pain associated with a particular surface area of the body. Why would something like irritation to the diaphragm, which is between the thoracic and abdominal cavities, feel like pain in the shoulder or neck?
Answers
If a mass of an object is 20 kg on earth, so what will be its weight?
Answers
Answer:
200 Newton
Explanation:
Weight is the force with which earth pulls the object.
W = M× g
where m is mass and g is acceleration due to gravity whose value is approximately 10 Newton
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The time taken by a mass projected vertically
upwards to reach the maximum height (with air
resistance not neglected) is 10 sec. The time of
descent of the mass from the same height will be
Answers
Answer:
10s
Explanation:
The time to get to the maximum would be the same as the time to get down to the maximum unless somehow gravity’s changes during the duration it goes up to and from maximum height.
The two ends of an iron rod are maintained at different temperatures. The amount of heat that flows through the rod by conducting DOES NOT depend on
Answers
Answer:
D mass of the iron rod
Explanation:
A) the length of the iron rod.
B) the thermal conductivity of iron.
C) the temperature difference between the ends of the rod.
D) the mass of the iron rod.
E) the duration of the time interval
The amount of heat that will flow through an iron rod whose two ends are maintained at different temperatures would depend on the thermal conductivity of the iron, the temperature difference between the two ends, the length of the iron rod, and the duration of flow of heat.
The thermal conductivity of any material is an indication of the ability of the materials to conduct heat. The higher the thermal conductivity, the higher the amount of heat a material can conduct within a specified period. Hence, the amount of heat that will flow through the iron rod depends on its thermal conductivity.
The temperature difference between two solid materials depends on the amount of heat that will flow across the materials by conduction. The higher the difference, the more the amount of heat that will flow. Hence, the amount of heat that would be conducted depends on the temperature difference between the two ends of the iron rod
The amount of heat that would move my conduction also depends on the distance that would be traveled by the heat. Due to heat loss to the surrounding, the shorter the distance, the more the heat and vice versa. Hence, the amount of heat that will flow through an iron rod depends on the length of the iron rod.
The duration of flow also dictates the amount of heat that will flow between two regions by conduction. The more the duration, the more the heat, provided that other conditions remain constant.
The only option that the amount of heat that would be conducted does not depend on is the mass of the iron rod.
The correct option is D.
the distance between my home to school is 3 km and 240 m. what is the distance in km,m and dm
Answers
Answer:
km = 3.24
m = 3,240
dm = 32,400
Explanation:
km = 1000m
m = 10dm
Explanation:
take a look carefully hope it will help u
A 120V AC signal is available at the wall port. You are required to convert it to a constant DC voltage of 12V for a laptop to operate. What are the three electrical components you will be using to achieve the same? Name the components in order and the function it performs.
Answers
Answer:
The following components shall be used in given order:
1. Step Down Transformer 2. Diode as Rectifier 3. Capacitor
Explanation:
The following components shall be used in given order:
1. Step Down Transformer 2. Diode as Rectifier 3. Capacitor
1.STEP DOWN TRANSFORMER:
The step down transformer is first used to convert the 120 V AC signal into 12 V AC signal. Because the output required is of 12 V.
2.DIODE AS RECTIFIER:
Now, the PN Junction diode is used as a rectifier to convert the 12 V AC signal to 12 V DC signal.
3.CAPACITOR:
Now, the output is in waveforms. So, in order to linearize it in the form of DC current, we use capacitor. The main function of capacitor is to smoothen the signal into a straight line.
A powerful missile reaches a speed of 5 kilometers per second in 10 seconds after its launch. What is the average acceleration of the missile during this period?
A. 0.2 meters/second2
B. 0.4 centimeters/second2
C. 0.5 meters/second2
D. 0.5 kilometers/second2
Answers
Answer:
D option
Explanation:
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Answer:
D. 0.5 km/s2
Explanation:
PLEASE HELP ME!! I NEED ANSWERS ASAP!!!!
Answers
Answer:
I do not know the answer because not all of the information is there.
Explanation:
Answer:
Beep Beep
Explanation:
How much work is done by an applied force to lift a 15-Newton 3Meters and 9.8?
Given=
Unknown=
Formula=
Solution=
Answer=
Answers
The work done by the applied force of 15 Newton to lift the object up 3 meters is 45 J
W = F d
W = Work done
F = Force
d = Distance
F = 15 N
d= 3 m
W = 15 * 3
W = 15 J
Work done is the amount of force required to move an object. It is denoted by W. Its unit is usually Joules.
Therefore, the work done to lift the object is 15 J
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Three people are trying to move a box. Which set of forces will result in a net
force on the box of 20 N to the right?
A.
B.
O C.
O D.
18 N
55 N
55 N
6 N
← PREVIOUS
1₂
28 N
16 N 17 N
0
10 N
17 N
$
16 N
-
20 N
6 N
Correct answer is A
Answers
Answer:
A
Explanation:
18-28=10
10+10=20
20N to the right
The world record for a woman running a marathon is approximately 2.25 hours. If a marathon's distance is 26.2 miles (42164.81 meters) and it is run
in a southeast direction, what is the velocity?
60 mph southeast
0.09 mph southeast
Omph southeast
11.6 mph southeast
Answers
Answer:
11.6mph South East
Explanation:
Given parameters:
Time = 2.25hrs
Displacement = 26.2miles south east
Unknown:
Velocity = ?
Solution:
Velocity is the displacement divided by the time taken. It is a vector quantity with both magnitude and direction.
Now;
Velocity = [tex]\frac{displacement}{time taken}[/tex]
Velocity = [tex]\frac{26.2}{2.25}[/tex] = 11.6mph South East
Answer:
11.6mph south east.
The subjective perception of the frequency of sound is called ?
Answers
Answer: The subjective perception of the frequency of sound is called a Pitch
Explanation: Because the Pitch has a lowest and highest of a sound fundamental
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10. The Earth's radius is about 6370 km. An object that has a mass of 20 kg is taken to a
height of 160 km above the Earth's surface. How much does the object weigh at this
height?
Answers
Answer:
Weight:
P =m·g₁ = 20·9.55 = 191 H
Explanation:
Given:
R = 6 370 км = 6 370·10³ m
m = 20 kg
h = 160 km = 160·10³ m
g = 9.8 m/s²
____________________
P - ?
Acceleration of free fall at the Earth's surface:
g = G*M / R² (1)
Acceleration of free fall at height h:
g₁ = G*M / (R + h) ² (2)
Divide (1) by (2):
g / g₁ = ((R + h) / R)²
g / g₁ = ( 1 + h / R)² = ( 1 + 160 / 6 370)² ≈ 1.026
g₁ = g / 1.026 = 9.8 / 1.026 ≈ 9.55 m/s²
Weight:
P =m·g₁ = 20·9.55 = 191 H
HELP right awayyy !!!
Answers
Answer:
Question 4 is actually Acceleration
which of the following could be cause of a irregular systolic reading
1. The one-way valves are not working
2 Blood is not flowing properly from the veins to the heart
3 Carbon dioxide and oxygen are mixing in the blood
4. The left ventricle is having difficulty contracting
Answers
Suppose, that you are measuring the length of a wood block and the edge of your block appears to be lined up exactly with a millimeter mark. How would you express the estimate part of a millimeter when you record the block’s length?
Answers
When taking the measurement, the estimate part of a millimeter when recording the block’s length can be expressed as ± 0.5 mm.
What are measurements?Measurements are the processes by which the attributes and properties of a given object or substance is quantified.
There are two types of measurements that can be obtained from any given object and they are:
quantitative measurementsqualitative measurementsQuantitative measurements measures the properties of objects in terms of numbers. Some examples of quantitative measurements are length, temperature, time, mass, etc.
Qualitative measurements describe the non-numerical features of objects such as color, texture, etc.
The measurement of length of a block of wood is a quantitative measurement.
The uncertainty or estimate of a measurement is half plus or minus the smallest division in the measurement.
The uncertainty or estimate of the millimeter block = ¹/₂ * 1 mm
The uncertainty or estimate of the millimeter block = ±0.5 mm
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Which of the following will increase if the voltage in a circuit is increased?
Check all that apply
A.Magnetic force
B. Resistance
C. Current
D. Heat produced by the circuit
Answers
Answer:
D i think (apologies if incorrect)
PLZZZ I will give brainliest. A ball that contains mechanical energy is rolled across the floor. You notice the ball is slowing down. If the ball started with 20 units of energy, explain how much energy would there be when the ball comes to a complete stop? How can you tell?
Answers
Answer: because of friction it will stop rolling completly
Explanation: