On an icy day, you worry about parking your car in your driveway, which has an incline of 12º. Your neighbor's driveway has an incline of 9.0º, and the driveway across the street is at 6.0º. The coefficient of static friction between tire rubber and ice is 0.15. Which driveway(s) will be safe to park in?
Answers
Answer:
Driveway across the street ([tex]\theta = 6^{\circ}[/tex]) is the only choice for a safe parking.
Explanation:
Let suppose that car is represented by a particle, then we proceed to construct its free body diagram and corresponding equations of equilibrium:
[tex]\Sigma F_{x'} = f - W\cdot \sin \theta = 0[/tex] (Eq. 1)
[tex]\Sigma F_{y'} = N-W\cdot \cos \theta = 0[/tex] (Eq. 2)
Where:
[tex]f[/tex] - Static friction force, measured in newtons.
[tex]N[/tex] - Normal force on the car from the ground, measured in newtons.
[tex]W[/tex] - Weight of the car, measured in newtons.
[tex]\theta[/tex] - Driveway inclination, measured in sexagesimal degrees.
By applying definitions of maximum static friction force and weight, we expand the system of equations presented above:
[tex]\mu_{s}\cdot N -m\cdot g\cdot \sin \theta = 0[/tex] (Eq. 1b)
[tex]N - m\cdot g \cdot \cos \theta = 0[/tex] (Eq. 2b)
Where:
[tex]\mu_{s}[/tex] - Static coefficient of friction, dimensionless.
[tex]m[/tex] - Mass of the car, measured in kilograms.
[tex]g[/tex] - Gravitational acceleration, measured in meters per square second.
Then, we substitute normal force and simplify the resulting expression:
[tex]\mu_{s}\cdot m\cdot g \cdot \cos \theta -m\cdot g \cdot \sin \theta = 0[/tex]
[tex]\mu_{s} = \tan \theta[/tex]
[tex]\theta = \tan^{-1}\mu_{s}[/tex] (Eq. 3)
Based on such result, we can conclude that if driveway inclination is greater than value reported, then car shall not be safe in case of parking. Our reference angle is: ([tex]\mu_{s} = 0.15[/tex])
[tex]\theta = \tan^{-1} 0.15[/tex]
[tex]\theta \approx 8.531^{\circ}[/tex]
By direct comparison, we find that driveway across the street ([tex]\theta = 6^{\circ}[/tex]) is the only choice for a safe parking.
Related Questions
Question 5
The head of a hammer is often made of steel. This makes the head heavy, which helps create a strong force for driving nails. Steel is also strong. The
head of a hammer must be strong to resist what force?
Answers
Answer:
the nails
Explanation:
The force of the nail pushing in the opposite direction. The correct option is option D among all the given options.
What is force?A force in physics is an effect that changes the velocity of a mass-moving object, causing it to accelerate from rest, for example. It is a vector quantity since it can be a push or even a pull and always has magnitude and direction.
The head of a hammer is often made of steel. This makes the head heavy, which helps create a strong force for driving nails. Steel is also strong. The head of a hammer must be strong to resist the force of the nail pushing in the opposite direction.
Therefore, the force of the nail pushing in the opposite direction. The correct option is option D.
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Your question is incomplete but most probably your full question was,
The head of a hammer is often made of steel. This makes the head heavy, which helps create a strong force for driving nails. Steel is also strong. The head of a hammer must be strong to resist what force?
A The force of the air resistance on the moving hammer
B The force of the person using the hammer
C The force of gravity pulling down on the hammer
D The force of the nail pushing in the opposite direction
PLEASE HELP ASAP!! IF YOU CAN
Answers
As current increases, the magnetic field strength increases.
a class is performing an experiment to keep an ice cube solid as long as possible. Which students actions could be a source of error in this experiment
A. Maria checked her ice cube every half hour and forgot to reseal the container she put the ice cube in
B. Jody used a different experimental design than Carlos used
C. Carey repeated the experiment with three different ice cubes
D. Jerrie measured the ice cube before it started to melt
Answers
Answer: the answer Is A. Maria checked her ice cube every half hour and forgot to reseal the container she put the ice cube in
Explanation: I just took the test
Answer:
A
Explanation:
APEX:)
When converting from smaller to larger units the decimal point travels right *
Answers
Answer:
False, it travels left.
Explanation:
Hello.
In this case, we can answer this with an example. If we have 200 g and we want that value in a larger unit, for instance, kilogram, the following conversion is performed since 1 kg equals 1000 g:
[tex]200g*\frac{1kg}{1000kg}=0.200g[/tex]
Whereas we needed to move the decimal point from right to left, which means that it travels left, that is why the statement is false.
Best regards.
Mark is pushing a box down the hall. Mark is using 5N to push the box 20m. How much work is Mark doing?
Answers
Answer:
The answer is 100 JExplanation:
The work done by an object can be found by using the formula
workdone = force × distanceFrom the question
force = 5N
distance = 20m
We have
workdone = 5 × 20
We have the final answer as
100 JHope this helps you
Which of the following is true about the speed of light?
A: it is a constant when the light is traveling in a vacuum
B:it speeds up or slows down depending on the observer
C: it’s slowest in a vacuum
D:it varies depending on the color of the light.
Answers
Answer:
C. it’s slowest in a vacuum
Explanation:
When light propagates through a material, it travels slower than the vacuum speed, c.
Answer:
A
Explanation:
I took the test
PLZZZ
suppose you increase the voltage in the coils of the solenoid of an electromagnet. what happens the the electromagnet?
A. its strength becomes less
B. its strength decreases then increases
C. its strength becomes greater
D. its strength remains the same
Answers
Answer:
Its strength becomes greater
Explanation:
Suppose you increase the voltage in the coils of the solenoid of an electromagnet. the electromagnet strength becomes greater. Hence option C is correct.
What is Electromagnet ?An electromagnet is a type of magnet where an electric current creates the magnetic field. The wire that makes up an electromagnet is often twisted into a coil. A magnetic field is produced by a current flowing through the wire and is focused in the hole in the centre of the coil. When the current is cut off, the magnetic field vanishes. In order to create a stronger magnet, the turns of the wire are frequently twisted around a magnetic core composed of a ferromagnetic or ferrimagnetic material, such as iron.
An electromagnet's key benefit over a permanent magnet is the ability to swiftly alter the magnetic field by adjusting the amount of electric current flowing through the winding. Contrary to a permanent magnet, however
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On a roller coaster when does the car have potential kinetic energy and when is energy transferred?
Answers
Answer: When the roller coaster goes to the top of the tracks there is energy
Explanation: When going up you need energy but going down the energy is being transferred downwards.
A water-balloon launcher with a mass of 2.2 kg is suspended on a wire. It
fires a 0.85 kg balloon to the north at a velocity of 13.0 m/s. What is the
resulting velocity of the launcher if the net force on the launcher is equal to
the reaction force?
A. 5.0 m/s south
B. 33.6 m/s south
C. 5.5 m/s north
D. 6.3 m/s south
Answers
Answer:
5.0 m/s south.
Just did it.
Hope This Helps!
Answer:
5.0 m/s south
Explanation:
A train starts from rest. It acquires a speed of 25 m/s after
20 s. The total
distance is
Answers
Given parameters:
Initial speed of train = 0m/s
Final speed = 25m/s
time = 20s
Unknown:
Total distance covered = ?
Solution:
Speed is a scalar quantity that has magnitude and no direction.
Mathematically;
Speed = [tex]\frac{distance}{time}[/tex]
distance = speed x time
Input the parameters and solve for distance;
Distance = 25 x 20 = 500m
The distance covered is 500m
A gas always spreads out to fill all available space.
True or False
Science Hw
Answers
Answer:
true
Explanation:
i know this im in 6th grade
This is True. Gases spread around freely and take up any available space. For example, there is oxygen. Oxygen is a gas we breathe in and spreads around freely, taking up any space.
For a substance to change from a gas to a liquid, what must happen to its particles?
Answers
You travel 50 meters at an angle of 37° North of East.
a) Calculate the Horizontal component.
Answers
Answer:
a) x = 39.9 m
Explanation:
To find the components of a vector we can use trigonometric relationships. Since they indicate that the angle is 37º north of east, this angle is measured counterclockwise from the x-axis, therefore using trigonometry.
cos θ = x / d
sin θ = y / d
where the angle is 37º and the distance d = 50 m
x = d cos θ
y = d sim θ
let's calculate
x = 50 cos 37
y = 50 sin 37
x = 39.9 m
y = 30.1 m
Divers at Acapulco dive from a cliff that is 61 m high. If the rocks below the cliff extend outward for 23 m, what is the minimum horizontal velocity a diver must have to clear them?
Answers
Answer:6.5 m/s
Explanation:Look at the image I believe that's the answer
The horizontal velocity of the diver would be 6.522 meters / seconds.
What are the three equations of motion?There are three equations of motion given by Newton
v = u + at
S = ut + 1/2×a×t²
v² - u² = 2×a×s
As given in the problem, Divers at Acapulco dive from a cliff that is 61 m high. If the rocks below the cliff extend outward for 23 m, then we have to find out the minimum horizontal velocity a diver must have to clear them,
By using the second equation of motion in the vertical direction,
s = ut + 0.5at²
61 = 0+ 0.5×(-9.81) ×t²
t² = 61/(0.5×9.81)
= 12.43
t = 3.526 seconds
The horizontal velocity of the diver = 23 meters / 3.526 seconds
=6.522 meters / seconds
Thus, the horizontal velocity of the diver would be 6.522 meters/second.
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6. Which statement best describe the relationship between temperature and thermal energy?
(1 Point)
Temperature is inversely related to thermal energy
Temperature is directly proportional to thermal energy
As temperature foes up, thermal energy goes down
Thermal energy is not related to energy
Answers
Answer:
Temperature is directly proportional to thermal energy.
The v
h.
The velocity of a vehicle reaches 4 m/s in 4 seconds. Is the velocity of the
car uniform? Explain.
Answers
Answer:
The velocity is not uniform
Explanation:
The velocity is not uniform, since the vehicle is increasing its speed to a value of 4 [m/s] in a time of 4 [s], that is, the vehicle is accelerating to increase its velocity, so when there is acceleration the velocity can not be constant or uniform.
Vf = Vo +(a*t)
where:
Vf = final velocity = 4 [m/s]
Vo = initial velocity = 0
a = acceleration [m/s²]
t = time = 4 [s]
a = (4 - 0)/4
a = 1 [m/s²]
A wave has a speed of 23 m/s and a frequency of 13 Hz. What is the wavelength?
Answers
Answer:
1.76923077 meters
Explanation:
wavelength is denoted by the letter lambda it is equal to the speed (v) of a wave in a medium (air , water, light) divided by frequency , equals wavelength . so wavelength = v/f or = 23m/s ÷13hz
No more energy can be removed from matter at
a. its freezing point.
c. absolute zero
b. 0°С.
d. 273 K.
Answers
Which of the following is a characteristic of electromagnetic waves?
A: they are all visible
B: they have a purely particle nature
C: they can travel with or without a medium
D: they cannot travel very fast
Answers
If a boomerhing is thrown 10 m in a straight line and returns
exactly to the spot it was thrown what is its displacement?
Answers
Answer:
0
Explanation:
First of all, what is displacement?
It is the minimum distance covered by a moving object between initial and final position.
Since the boomerang comes back to its original position, the displacement is 0!
Breaking is a result of friction between the brake linings and your foot.
A. True
B. False
Answers
An object is dropped from 20. meters above the moon. The acceleration due to gravity on the moon is 1.62 m/s^2
a. How long does it take for the object to impact the moon?
b. At what speed does it impact the moon?
Answers
Answer:
a. Approximately 3.21 seconds
b. Approximately 5.196 m/s
Explanation:
a. The height from which the object is dropped = 20 meters
The location of the occurrence = The moon
The acceleration due to gravity on the moon = 1.62 m/s²
The time it took the object to to impact the moon is given by the equation of free fall as follows;
h = 1/2·a·t²
Where;
h =The height from which the object is allowed to freely fall = 20 meters
a = The acceleration due to gravity on the moon = 1.62 m/s²
t = The time of motion of the object
Substituting the values, gives;
20 = 1/2 × 1.62 × t²
t² = 20/(1.2 × 1.62) ≈ 10.23 s²
t = √ 10.23 ≈ 3.21 s
The time in motion of the object before impact, t = 3.21 seconds
b. The final speed, v is given from the equation for speed under free fall, which is presented as follows;
v = u + a·t
Where
u = The initial vertical velocity = 0
Substituting the values gives;
v = 0 + 1.62 × 3.21 ≈ 5.196 m/s
The final speed, v with which the object impacts the moon ≈ 5.196 m/s
Can someone explain which of Newton’s Law is demonstrated in part 1 and which is demonstrated in part 2? (Picture)
Answers
Answer:
Every action has an equal and opposite reaction. If the student doesn't push, nothing moves, is one student pushes, both move which is an example of newtons third law.
Explanation:
If the distance of an object is determined from the relation: d = a X + b Y Where: (d) is the distance covered by the body. (a) is a physical quantity which has a dimensions (L T^-1). (b) Is a physical quantity which has a dimensions (L T^-2). So: *
The dimension formula of (X) is T and that of (Y) is T^2.
The dimension formula of (X) is T and that of (Y) is T^-2
The dimension formula of (X) is T^-1 and that of (Y) is T^2.
The dimension formula of (X) is T^-1 and that of (Y) is T^-2.
Answers
Answer:
The dimension formula of X is T and that of Y is T^2
Explanation:
d = aX + bY is ACTAULLY [tex]S = V_{i} t + \frac{1}{2} a t^{2}[/tex]
so v = LT^-1
t = T
numerics do not have any dimensional formula so ignore [tex]\frac{1}{2}[/tex]
a = LT^-2
t = T^2
So answer for x is T and y T^2
HEY CAN ANYONE PLS ANSWER DIS!!!!!!!!
Answers
Answer:
Distillation
Explanation:
Answer:
distillation is correct
Explanation:
hope it helps
You toss an apple across the room to a friend. Which of the following
statements is true about the apple at the top of its trajectory?
Answers
I believe the answer is C, but im not sure.
Explanation:
Answer:
its vertical component of its velocity is zero
Explanation:
A driver in a 500 kg car going 20 m/s sees a large box in the middle of the road 100 meters away. How much net force is required to get the car to stop without hitting the box?
WILL GIVE BRAINLY AND 50 POINTS
Answers
Answer:
620
Explanation:
Answer:
100
correct me if I am wrong
An escaped convict runs 1.70 km due East of the prison. He then runs due North to a friend's house. If the magnitude of the convict's total displacement vector is 2.50 km, what is the direction of his total displacement vector with respect to due East?
Answers
Answer:
The right approach will be "47° north of east".
Explanation:
The given values are:
East of prison
= 1.70 km
Displacement vector
= 2.50 km
Now,
The direction will be:
⇒ [tex]Cos \ \theta =\frac{1.7}{2.5}[/tex]
⇒ [tex]=0.68[/tex]
⇒ [tex]\theta=47.16^{\circ}[/tex]
i,e., [tex]\theta = 47^{\circ}[/tex] (north of east)
The direction of his total displacement vector with respect to due East is 1.83km
Resultant vectorGiven the following parameters
Distance ran through east = 1.70km
displacement = 2.50km
Required
Total displacement vector with respect to due north
Using the expression below;
d = √x² + y²
2.5² = 1.7² + y²
y² = 2.5² - 1.7²
y² = 3.36
y = 1.83km
Hence the direction of his total displacement vector with respect to due East is 1.83km
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PHYSICAL SCIENCE, PLEASE HELP!
Which items are matter?
Answers
Answer:
Mobile phone & battery.
What is the density of a 15 g object that has a volume of 6 cm??
Answers
Answer:
2.5 g/cm³
Explanation:
To find density, divide the mass by the volume. In this case, 15 grams divided by 6 cm³ equals 2500 kg/m³, or simplified, 2.5 g/cm³. Hope it helps! To type ³, turn on Num Lock and then press Alt+0179. Have a good day!