A snowboarder drops from rest into a halfpipe of radius R and slides down its frictionless surface to the bottom
(a) Show that the snowboarder's speed at the bottom of the halfpipe is
v = 2gR (use conservation of energy)
(b) Show that the snowboarder's centripetal acceleration at the bottom is
ac = 2g (Apply the expression for centripetal acceleration)
(c) Show that the normal force on the snowboarder at the bottom of the halfpipe has a magnitude of 3mg (Use Newton's second law of motion)
Answers
A snowboarder drops from rest into a halfpipe of radius R and slides down its frictionless surface to the bottom, the snowboarder's speed is [tex]\mathbf{v = \sqrt{2gR}}[/tex]
The snowboarder's centripetal acceleration at the bottom is [tex]\mathbf{a_c = 2g}[/tex]. The normal force acting on the snowboarder at the bottom of the halfpipe = 3mg
According to the conservation of energy, at any given point of motion, the energy of a system will always be constant.
Using the conservation of energy at rest and also at the bottom of the pipe.
Total potential energy of the person(since its at rest = Total kinetic energy at the bottom of the pipe.[tex]\mathbf{mgR = \dfrac{1}{2}mv^2}[/tex]
The objective is to make the velocity (v) the subject of the formula:
[tex]\mathbf{gR = \dfrac{1}{2}v^2}[/tex]
[tex]\mathbf{2gR = v^2}[/tex]
[tex]\mathbf{v = \sqrt{2gR}}[/tex]
(b)
Using the expression for centripetal acceleration;
[tex]\mathbf{a_c = \dfrac{v^2}{R}}[/tex]
here,
let's replace [tex]\mathbf{v \ \ \ with \ \ \sqrt{2gR}}[/tex];
Then;
[tex]\mathbf{a_c = \dfrac{(\sqrt{2gR})^2}{R}}[/tex]
[tex]\mathbf{a_c =2g}[/tex]
From the image attached below;
Provided that:
n = normal forcew = mg weight of the person[tex]\mathbf{F_c}[/tex] = centripetal forceThen, we can infer that the normal net force acting on the person can be computed as:
[tex]\mathbf{F_c = n -mg}[/tex]By rearrangement;
[tex]\mathbf{n =F_c +mg}[/tex]where;
[tex]\mathbf{F_c = 2 mg}[/tex]∴
n = 2mg + mgn = 3mg
Therefore, we can conclude that the snowboarder's speed, centripetal force, and normal force are proved.
Learn more about centripetal force here:
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Related Questions
If you ran at a rate of 300 m/min for 30 minutes, how far would you have run?
Answers
Answer:
9000 m
Explanation:
I multiplied 300 by 30!
Hope this helps :)
Pls make brainliest :3
And have an amazing day <3
If a car takes a banked curve at less than the ideal speed, friction is needed to keep it from sliding toward the inside of the curve (a real problem on icy mountain roads).
(a)
Calculate the ideal speed in (m/s) to take a 120 m radius curve banked at 15°.
(b)
What is the minimum coefficient of friction needed for a frightened driver to take the same curve at 15.0 km/h?
Answers
Hi there!
(A)
For a banked curve, we know that:
∑F = MgsinФ (force due to gravity)
And:
∑F = mv²/r
The cosine of the centripetal force, mv²/r, is involved in the summation of forces, so:
(mv²/r)cosФ = mgsinФ
Simplify the equation:
(v²/r)cosФ = gsinФ
Divide both sides by cosФ:
(v²/r) = gtanФ
Solve for v:
v = √grtanФ
Plug in given values. g ≈ 9.8 m/s²
v = √(9.8 · 120 · tan(15)) = 17.75 m/s
(b)
Incorporating friction, we now can rewrite the sum of forces. Let's first determine the frictional force acting on the car.
As the horizontal component of the centripetal force is the net force, the vertical component works in the direction of the normal force, so we must include it in the calculation of the frictional force.
First, convert 15 km/h to m/s:
15km / h * 1000 m / 1km * 1 h / 3600 sec = 4.167 m/s
Thus:
∑F = mgsinФ - μ(mgcosФ + (mv²/r)sinФ)
mv²/r = mgsinФ - μ(mgcosФ + (mv²/r)sinФ)
Divide all terms by the mass:
v²/r = gsinФ - μ(gcosФ + (v²/r)sinФ)
Solve for μ:
v²/r - gsinФ = - μ(gcosФ + (v²/r)sinФ)
-(v²/r - gsinФ)/(gcosФ + (v²/r)sinФ) = μ
Plug in the given values:
μ = 0.25
Explain how plate tectonics have changed Earth's surface over time. (This is a short writing and I need help. I will mark whoever answers first as Brainliest plus I will give 50 points.)
Answers
Answer:
Plate motions cause mountains to rise where plates push together, or converge, and continents to fracture and oceans to form where plates pull apart, or diverge. The continents are embedded in the plates and drift passively with them, which over millions of years results in significant changes in Earth's geography.
Explanation:
hope it helps ☺️✌️
A speedboat with a mass of 511 kg (including the driver) is tethered to a fixed buoy by a strong 31.5 m cable. The boat's owner loves high speed, but does not really want to go anywhere. So the owner revs up the boat's engine, makes a lot of noise, and runs the boat in circles around the buoy with the cable supplying all the necessary centripetal force. When the tension of the cable is steady at 13300 N, with what force is the boat's engine pushing the boat? Different physics textbooks treat drag force somewhat differently and use different formulas. For the present purpose, take the water's drag force on the boat to be (450 kg/m)×2, where denotes the boat's speed. Ignore any drag force on the cable.
Answers
Answer:
its is 23.09 kb
Explanation:
i did this awsner
An election accelerated through 1 kV possesses de - Broglie wavelength 1. What will be the wavelength of
the same electron, when accelerated through 16kV:
1) 161
2) 41
3) 1/4
4) 116
Answers
Answer:
Correct option is
B
1.7
A
˚
λ=
p
h
=
2mE
h
=
2mqV
h
λ=
2×9.1×10
−31
×1.6×10
−19
×50
6.6×10
−34
=1.72×10
−10
=1.72A
Option B
A horse trainer records the distance a horse travels during three different trials.
What is the horse's average speed in kilometers per minute?
Answers
4.5 + 9.0 + 13.5 = 27km
15 + 30 + 45 = 90min
27 / 90 = 0.3
The horse’s average speed is 0.3km/min
The horse's average speed in kilometers per minute is equal to 0.3 kilometers per minute.
Given the following data:
Time 1 = 15 minutesTime 2 = 30 minutesTime 3 = 45 minutesDistance 1 = 4.5 kilometersDistance 2 = 9.0 kilometersDistance 3 = 13.5 kilometersTo determine the horse's average speed in kilometers per minute:
First of all, we would find the total time and total distance covered:
For total time:
[tex]Total \;time = 15 + 30+45[/tex]
Total time = 90 minutes
For total distance:
[tex]Total \;time = 4.5 + 9.0+13.5[/tex]
Total time = 27 kilometers.
Mathematically, average speed is given by the formula:
[tex]Average\;speed = \frac{Total\;distance}{Total\;time} \\\\Average\;speed = \frac{27}{90}[/tex]
Average speed = 0.3 kilometers per minute.
Read more on average speed here: https://brainly.com/question/17742679
A plane is traveling horizontally at a speed u = 40 m/s at a height h =
100m above ground when it drops a package, as shown in the figure.
How long it takes the dropped package to reach the ground and where?
Answers
Answer:
First get the time in the air from
h = gt2/2 ⇒
t = √(2h/g)
Plug in
h = 100 m
g = 9.8 m/s2
and get t in seconds. Then multiply t by the constant horizontal speed.
x = vt
Plug in
v = 40 m/s
t = ? (result from above)
and get x in meters.
(b)
Vertical speed:
v(t) = v0 + gt
Plug in
v0 = 0
g and t from above
and get v(t) in m/s.
(c) It is the same as the initial velocity when released, which is 40 m/s.
(d) The horizontal component is the same as the answer for part (c). The vertical component is the result for part (b), in the downward direction.
HELP PLEASE
......................................................
Answers
8.95 m/s
Mr. Mangan runs 30 m north and 45 m south. What is his total distance
travelled? What is his displacement?
Answers
A soccer ball accelerates as it rolls down a steep hill and then gradually comes to a stop at the bottom. According to Newton's laws which of the following statements could be
true?
Statement 1: While the ball was rolling down the hill the forces acting on it were unbalanced.
Statement 2: The ball was experiencing balanced forces as it rolled down the hill..
Statement 3: Balanced forces acted on the ball once it reached the botto by m of the hill causing it to stop.
O Statement 1 and 2 are both true.
All three statements are true.
Only Statement 1 is true.
Only Statement 3 is true.
0
Answers
Answer:
Statement 1: While the ball was rolling down the hill the forces acting on it were unbalanced.
Explanation:
what would you want individuals and communities to understand to help them avoid negatively affecting climate
Answers
Answer:
ur
Explanation:
mom
A 50 kg boy on ice skates throws a 5 kg ball to the left. If the ball ends up going 20 m/s. How fast is the boy going?
Answers
Answer:
2 m/s
Explanation:
A 50 kg boy on ice skates throws a 5 kg ball to the left. If the ball ends up going 20 m/s. Velocity of boy is 2 m/sec.
What is velocity?When an item is moving, its velocity is the rate at which its direction is changing as seen from a certain point of view and as measured by a specific unit of time.
Uniform motion an object is said to have uniform motion when object cover equal distance in equal interval of time within exact fixed direction. For a body in uniform motion, the magnitude of its velocity remains constant over time.
Given in the question, a 50 kg boy on ice skates throws a 5 kg ball to the left. If the ball ends up going 20 m/s.
Using conservation of momentum, velocity = (20*5)/50 = 2 m/sec.
A 50 kg boy on ice skates throws a 5 kg ball to the left. If the ball ends up going 20 m/s. Velocity of boy is 2 m/sec.
To learn more about velocity refer the link:
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Do you think it wise to make a decision under the influence of an emotion?
Answers
Answer:
no because It can be a disadvantage for us
Answer:
no
Explanation:
nop it isn't wise to make a decision under the influence of emotion because if you act and make decision From influence of emotion you will gonna regret so think before you make decision
What’s the atomic number for magnesium
Answers
Answer:
12
Explanation:
Symbol: Mg
Atomic mass: 24.305 u
Atomic number: 12
Density: 1.738 g/cm³
ball (100 grams) is attached by string (ignorable mass) oflength SOcm and is in a ircular motion: If the ball makes 20 round trips (complete oscillations) along the ircular path in 5 seconds (a) Calculate the time period (T) of the ball in S. units: (b) Calculate the angular velocity (0) of the ball in S lunits: (c) Calculate the linear velocity (v) of the ball in S.I units. (d) Calculate the centripetal force (Fc) on the ball in Newtons (N): Scm (e) Calculate the centrifugal force on the ball in Newtons (N) (0) Are the two forces equal
Answers
Answer:
Hdhjdj
Explanation:
Một chất điểm chuyển động trong mặt phẳng Oxy với phương trình :
{ = 2 + 10
Answers
Answer:
plz write your questions in English
16. If "team A has 3 of its bocce balls closer to the pallino than any of their opponent's balls, who wins the
frame
How many points do they get for that frame?
How many do their opponents get for that frame?
Answers
Answer:
Team A wins the frame with three points. The opposing team gets zero points for the frame.
Explanation:
A 0.15-kg object is projected vertically into the air with a
velocity of 30. m/s. How high above the ground is the
object after 3.3 seconds?
A 46 m
B 53 m
C 110 m
D 150 m
Answers
Answer:
A
Explanation:
y = 30(3.3) - .5(9.8)(3.3^2)
Please answer quick!! if you're right I'll mark you brainliest!
the surface gravity on Jupiter Is 2.4 times the of earth what would your weight be on Jupiter if you weighed 110 pounds on earth
Answers
Answer:
The equation would be 2.4 x 110 which is 264
You would weigh 264 on Jupiter
Explanration:
what is the main features of RCCB?
Answers
Main features of RCCB are:
Both wires phase and neutral are connected through RCCB.Whenever there is any ground fault occurs, then it trips the circuit.The number of current supplies through the line should go back through neutral.These are a very effective type of shock protection.If a car is traveling at 10m/s and then accelerates for 10s at a rate of 0.5m/s^2,what will be final velocity?
Answers
Answer:
[tex]u= 10 \frac{m}{s} \\ t = 10 \: s \\ a = .5 \frac{m}{ {s}^{2} } \\ v = x \\ v = u + at \\ x = 10 + .5 \times 10 \\ x = 10 + 5 \\ x = 15 \frac{m}{s} \\ thank \: you[/tex]
Answer:
15m/s
Explanation:
a=(Vf-Vi)/t
0.5m/s^2=(Vf-10m/s)/10s
when we solve this Vf=15m/s^2
Which term best describes a question that can be tested?
A. Phenomenon
B. Hypothesis
C. Experiment
D. Observation
Answers
Answer:
Hypothesis
Explanation:
because in science a hypothesis is a guess/question that you test. it can be changed many times
Answer:
C) experiment. Is the answer.
hypothesis is the educated guess about what the result of the experiment is before conducting the experiment.
Observation is what you see and record during the experiment.
Two objects, one of mass 17 kg and the other of mass 31 kg approach each other with the lighter one having a speed of 23 m/s. Determine the velocity of the heavier object if the total combined momentum of the objects is zero.
Answers
[tex]\bull\sf m_1=17kg[/tex]
[tex]\bull\sf m_2=31kg[/tex]
[tex]\bull\sf v_1=23m/s[/tex]
[tex]\bull\sf v_2=?[/tex]
According to law of conservation of momentum
[tex]\\ \sf\longmapsto \Delta P=P[/tex]
[tex]\\ \sf\longmapsto m_1v_1=m_2v_2[/tex]
[tex]\\ \sf\longmapsto v_2=\dfrac{m_1v_1}{m_2}[/tex]
[tex]\\ \sf\longmapsto v_2=\dfrac{17(23)}{31}[/tex]
[tex]\\ \sf\longmapsto v_2=\dfrac{391}{31}[/tex]
[tex]\\ \sf\longmapsto v_2=12.6m/s[/tex]
The potential energy U as a function of the position x of an object is given by U (x) = - 400/x, where U is in joules and x is in meters. The object is released from rest at position x = 30 m and is free to move along the x-axis. When the object has moved a distance of 10 m from its initial position, the magnitude of the force associated with this potential energy function is
Answers
Hi there!
We know that:
F = -dU/dx, so:
U = -400/x
dU/dx = 400/x² (Take the derivative)
F = -dU/dx = -400/x²
Finding the force at 10m away from the starting point (30m), means a position of 40m. So:
F = -400/(40²) = -0.25 N
Calculate the potential energy of a 1.5 kg hammer that is located at a height of 2 m
Answers
Answer: 29.43 Joules
Explanation:
PE=mgh
PE=potential energy
M=1.5kg
G=9.81m/s^2
H=2m
PE=29.43J
Answer:
[tex]\boxed {\boxed {\sf 29.4 \ J}}[/tex]
Explanation:
Potential energy is the energy an object possesses due to its position. It is calculated using the following formula:
[tex]PE=mgh[/tex]
The mass of the hammer is 1.5 kilograms and its height is 2 meters. Assuming this is on Earth, the acceleration due to gravity is 9.8 meters per second squared.
m= 1.5 kg g= 9.8 m/s² h= 2 mSubstitute these values into the formula.
[tex]PE= (1.5 \ kg)(9.8 \ m/s^2)(2 \ m)[/tex]
Multiply the numbers together.
[tex]PE=(14.7 \ kg *m/s^2)(2 \ m)[/tex]
[tex]PE=29.4 \ kg*m^2/s^2[/tex]
Convert the units. 1 kilogram meter squared per second squared is equal to 1 Joule. Our answer of 29.4 kg*m²/s² is equal to 29.4 J.
[tex]PE= 29.4 \ J[/tex]
The potential energy of the hammer is 29.4 Joules.
Government has banned the use of plastic bags in some states. Why?
Answers
Answer:
people throw plastic into the oceon
Explanation:
.when people throw plastic into the ocean mother nature gets hurt because of waste if it continues the see we see today will be dirty if all of humanity throwed all of the plastic and waste in the ocean
The three diagrams below show a block of mass m being pulled or pushed at constant acceleration ax along a table with a force P. The coefficient of kinetic friction is k. What is the friction force in each case? Give your answer in terms of the pushing force P, ax, m, and the angle .
Answers
Answer:
Explanation:
1) F = ma
P - Fk = ma
Fk = P - ma
2) F = ma
Pcosθ - Fk = ma
Fk = Pcosθ - ma
3) F = ma
Pcosθ - Fk = ma
Fk = Pcosθ - ma
These results are not very helpful.
If we are allowed to introduce gravity, more useful information comes out
1) Fk = kmg
2) Fk = k(mg + Fsinθ)
3) Fk = k(mg - Fsinθ)
In this exercise we have to use the decomposition of forces in the blocks, so
1) [tex]F_k = P - ma[/tex]
2) [tex]F_k = Pcos\theta - ma[/tex]
3) [tex]F_k = Pcos\theta - ma[/tex]
Thus, observing these blocks and their respective compositions we will find that:
1)
[tex]F = maP - F_k = maF_k = P - ma[/tex]
2)
[tex]F = maPcos\theta - F_k = maF_k = Pcos\theta - ma[/tex]
3)
[tex]F = maPcos\theta - F_k = maF_k = Pcos\theta - ma[/tex]
See more about forces at brainly.com/question/19734564
Random sampling is used by researchers to obtain an).
control group
population of interest
representative sample
experimental sample
Plz help
Answers
Answer:
hey there
the correct answer is option ( B ) population of interest
Explanation
A random sample is a subset of individuals randomly selected by researchers to represent an entire group as a whole. The goal is to get a sample of people that is representative of the larger population.
Explanation:
Hope it helps
Have a nice day : )
An airplane flying upward at 39.6m/s and an angle of 30 degree relative to the horizontal releases a ball when it is 287m above the ground. Calculate the time it takes the ball to hit the ground? Calculate the maximum height of the ball? Calculate the horizontal distance the ball travels from the release point to the ground? Neglect any effects due to air resistance.
Answers
Answer:
Assuming the speed of the plane is 39.6 m/s
vy = 39.6 * sin 30 = 19.8 vertical speed
vx = 39.6 * cos 30 = 34.3 m/s
S = vy t - 1/2 a t^2 to calclulate vertical height
-287 = 19.8 t - 4.9 t^2
4.9 t^2 -19.8 t - 287 = 0
I get t = 9.93 for solving the quadratic for time for ball to hit ground
Horizontal distance = 34.3 m/s * 9.93 s = 341 m
With a vertical speed of 19.9 m/s it takes 19.8 / 9.8 = 2.02 s to reach max height
You can again solve a quadratic or use 19.8 / 2 * 2.02 for time to reach vertical height H = 287 + 20 = 307 m
As a check 307 = 1/2 g t^2 = 4.9 * (9/93 - 2/02)^2 = 307 m max height
After you know how long the ball is in the air there are several ways to calculate the other values.
Suppose an empty grocery cart starts at a rest and rolls downhill in a parking lot. The cart has a maximum speed of 2.2km/s when it hits the side of the store and comes to rest 1.5 min later. If an unbalanced force of 65 N stops the cart, what is the mass of the grocery cart?
Answers
Answer: i dont know
Explanation:
E