A 68 kg skier approaches the foot of a hill with a speed of 15 m>s. The surface of this hill slopes up at 40.0° above the horizontal and has coefficients of static and kinetic friction of 0.75 and 0.25, respectively, with the skis. (a) Use energy conservation to find the maximum height above the foot of the hill that the skier will reach. (b) Will the skier remain at rest once she stops, or will she begin to slide down the hill? Prove your answer.
Answers
Final kinetic energy,Ek2 = 1/2 × m × v2²Ek2 = 1/2 × (68 kg) × (v2)²Ek2 = 34m²/s². The weight of the skier, mg = (68 kg)(9.8 m/s²)mg = 666.4 N. Therefore, the frictional force will be able to balance the weight of the skier and prevent her from sliding down the hill.
(a) Maximum height the skier will reach. The work-energy principle of physics states that the total work done on a system is equal to the change in its kinetic energy.
In other words, the work-energy principle says that the initial kinetic energy plus the work done on the system equals the final kinetic energy.
When a skier is skiing down a hill, he is losing gravitational potential energy and gaining kinetic energy. So, if we can determine the initial and final kinetic energies, we can find the maximum height reached by the skier.
Work done by frictional force, Wfriction = fs×m×g×cosθ×dwhere fs = 0.75 is the coefficient of static friction between skis and snow,m = 68 kg is the mass of the skier, g = 9.8 m/s² is the acceleration due to gravity,θ = 40.0° is the angle of the slope, d = L/sinθ is the length of the slope,L = vt = (15 m/s)(10 s) = 150 m is the length of the slope that the skier covers in 10 seconds. Wfriction = (0.75)(68 kg)(9.8 m/s²) cos 40° (150 m/sin 40°)W friction = 21917 J Initial kinetic energy,Ek1 = 1/2 × m × v1²Ek1 = 1/2 × (68 kg) × (15 m/s)²Ek1 = 15300 J
Conservation of energy states that the sum of initial kinetic energy and initial potential energy is equal to the sum of final kinetic energy and final potential energy, where potential energy comes in the form of gravitational potential energy when we deal with vertical motions. Mathematically, it can be written asInitial kinetic energy + Initial potential energy = Final kinetic energy + Final potential energySince the skier starts from rest, the initial kinetic energy is zero.
Hence, Initial potential energy at the foot of the hill = Final kinetic energy + Final potential energywhere potential energy is given bymgh where m is the mass of the object, g is the acceleration due to gravity, and h is the height of the object above some reference point (usually the ground).
Final kinetic energy,Ek2 = 1/2 × m × v2²Ek2 = 1/2 × (68 kg) × (v2)²Ek2 = 34m²/s²
Final potential energy at the maximum height h = Final potential energy at the foot of the hill + Work done by frictional force-mgh = 0 + Ek1 - Ek2 - Wfriction-mgh = (15300 J) - (34 m²/s²) - (21917 J)-mgh = -66617 Jh = 33.81 mTherefore, the maximum height that the skier will reach is 33.81 m.
(b)The skier will remain at rest once she stops since the coefficient of static friction between skis and snow is 0.75, which is greater than the coefficient of kinetic friction, 0.25.
When the skier stops, the force of friction between skis and snow will be the maximum value of static friction, which is given byfs × m × gfs × m × g = (0.75)(68 kg)(9.8 m/s²)fs × m × g = 477.48 N
The weight of the skier,mg = (68 kg)(9.8 m/s²)mg = 666.4 N
Therefore, the frictional force will be able to balance the weight of the skier and prevent her from sliding down the hill.
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Related Questions
A soccer ball is kicked off a 150 m tall building and lands 30 m away. How long was the ball in the air?
Answers
a. The ball was in the air for 5.53 seconds.
b. The initial velocity of the ball is 54.194 m/s
c. The final velocity of the ball in the y direction is -54.194 m/s
d. The x component of the initial velocity is 50.926 m/s, and the y component is 18.534 m/s.
To solve these questions, we can use the equations of motion for projectile motion. Let's assume the acceleration due to gravity is -9.8 m/\(s^2\) (taking downward as the negative direction).
a. To find the time the ball was in the air, we can use the equation:
Δy = v_iy * t + (1/2) * a_y * \(t^2\)
Where Δy is the vertical displacement, v_iy is the initial vertical velocity, a_y is the vertical acceleration, and t is the time.
Since the ball was dropped from rest, its initial vertical velocity is 0 m/s, and the vertical displacement is -150 m (negative because it is going downward).
-150 = 0 * t + (1/2) * (-9.8) * \(t^2\)
Simplifying the equation and solving for t, we get:
4.9 * \(t^2\) = 150
\(t^2\) = 150 / 4.9
t ≈ 5.53 seconds
Therefore, the ball was in the air for approximately 5.53 seconds.
b. To find the initial velocity of the ball, we can use the equation:
v_fy = v_iy + a_y * t
Where v_fy is the final vertical velocity.
Since the ball lands 30 m away, its final vertical displacement is 0 m, and the time is 5.53 seconds.
0 = v_iy + (-9.8) * 5.53
Solving for v_iy, we get:
v_iy = 9.8 * 5.53
v_iy ≈ 54.194 m/s
Therefore, the initial velocity of the ball is approximately 54.194 m/s.
c. The final velocity of the ball in the y direction is the same as the initial velocity because the only force acting on it is gravity, which causes a constant acceleration. Therefore, the final velocity in the y direction is approximately -54.194 m/s (negative due to the downward direction).
d. When the ball is kicked off the building at an angle of 20 degrees below the horizontal, we need to find the x and y components of the initial velocity.
The magnitude of the initial velocity (from part b) is 54.194 m/s.
The x component of the initial velocity can be found using:
v_ix = v_i * cos(θ)
Where θ is the angle of 20 degrees below the horizontal.
v_ix = 54.194 * cos(20)
v_ix ≈ 50.926 m/s
The y component of the initial velocity can be found using:
v_iy = v_i * sin(θ)
v_iy = 54.194 * sin(20)
v_iy ≈ 18.534 m/s
Therefore, the x component of the initial velocity is approximately 50.926 m/s, and the y component is approximately 18.534 m/s.
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The question was Incomplete, Find the full content below:
A soccer ball is kicked off a 150 m tall building and lands 30 m away.
a. How long was the ball in the air?
b. What was the initial velocity of the ball?
C. What is the final velocity of the ball in the y direction?
d. Assume the ball has the same speed as you solved for in part b except it is kicked off the building at an angle of 20 degrees below the horizontal. What is the x component of the initial velocity? What is the y component of the initial velocity?
The mass of Jupiter is 4 x 1023 kg. If the mass of the Sun is 2 x 1030 kg and the sun and Jupiter are 7 x 1011 m apart, what is the force of gravity between the two?
Answers
Answer:
the force is 2000
Explanation:
David moves a 350 N bucket with 175 N of force using a pulley. What mechanical advantage does he have when using the pulley?
Answers
Answer:
the mechanical advantage David had when using the pulley is 2.
Explanation:
Given;
load moved by David, L = 350 N
effort applied by David, E = 175 N
The mechanical advantage David had when using the pulley is calculated as;
\(M.A = \frac{Load}{Effort} \\\\M.A = \frac{350}{175} \\\\M.A = 2\)
Therefore, the mechanical advantage David had when using the pulley is 2.
describe free fall and weightlessness ?
Answers
weightlessness is the complete or near complete absense of the sensation of weight.
when in freefall,the only force acting upon your body is the force of gravity a noun contact force.since the gravity cannot be felt without any other opposing forces,you would have no sensation of it.you would feel weightless when in a state of freefall.
base your answer to the question on the information given. a 1,000-kilogram car traveling with a velocity of 20 meters per second decelerates uniformly at -5.0 meters per second^2 until it comes to rest. what is the total distance the car travels as it decelerates to rest?
Answers
Answer:
40 meters
Explanation:
To solve this, we will use the motion formula \(v^{2} =u^{2} +2as\), where v is the final speed, u is the initial speed, a is the acceleration, and s is the distance. We know:
u= 20m/s
a= - 5m/s^2 (note the minus sign because we are decelerating)
v= 0m/s (our final speed will be 0 because we want to come to a stop)
Now plug in these values into the formula:
\(v^{2} =u^{2} +2as\)
\(0^{2} =20^{2} +2(-5)s\)
\(0 =400-10s\)
\(10s=400\)
\(s=40\\\)
What is meant by the term "fixed point"?
Answers
Explanation:
A fixed point is a point x such that. f(x) = x . Graphically, these are exactly those points where the graph of f, whose equation.
Answer:
a fix joint is a point x such that.f (x) = x.
Explanation:
Graphically, these are execty those point where the graph of f, whose equation.
What are 3 parts of daltons atomic theory ?
Answers
A uniform electric field of 8 V/m exists between the plates of a parallel plate capacitor. How much work is required to move a 20 mC point charge from the negative plate to the positive plate if the plate separation is 0.050 m
Answers
Hello!
Recall the equation for the force experienced by a charged particle in an electric field:
\(F_E = qE\)
q = Charge of particle (20 mC)
E = Electric field strength (8 V/m)
We also know that 'Work' is equivalent to the following:
\(W = F \cdot d\)
W = Work (J)
F = Force (N)
d = distance (between the plates in this instance, 0.050 m)
If we substitute 'qE' for 'F':
\(W = qEd\)
Plug in the given values and solve.
\(W = (0.02)(8)(0.05) = \boxed{0.08 J}\)
**Since we are pushing a positive particle towards the positive plate, we are increasing its electric potential energy, so WE are doing positive work on the particle.
Tarnish is produced by a redox reaction that occurs when a metal reacts with a nonmetallic compound. the black tarnish on a silver dish might be produced by a reaction between silver and hydrogen sulfide. what occurs during this reaction?
A. A double-replacement reaction takes place
B. An acid-base reaction takes place.
C. silver atoms Gain Electrons from sulfur atoms.
D. Silver atoms louse electrons to sulfur atoms.
Answers
2Ag + H₂S ⇒ Ag₂S + H₂
Ag ⇒ Ag⁺
Silver atoms loose electrons to sulfur atoms.
Answer:
Option D
Explanation:
The reaction is given by
Ag+H_2S—»Ag_2S+H_2In the reaction
silver loses two electrons to sulfur in atoms inorder to attain Ag²+ structure .
As loss of electron is oxidation it's redox reaction
I need helpppp :((((((
Answers
Answer: c. The electric force increases
Explanation:
If the distance between two charged particles decreases, the electric force between them increases.
According to Coulomb's Law, the electric force between two charged particles is directly proportional to the product of their charges and inversely proportional to the square of the distance between them. Mathematically, the equation can be represented as:
F = k * (q1 * q2) / r^2
Where:
F represents the electric force between the particles.
k is the electrostatic constant.
q1 and q2 are the charges of the particles.
r is the distance between the particles.
As the distance (r) between the particles decreases, the denominator of the equation (r^2) becomes smaller, causing the overall electric force (F) to increase. Conversely, if the distance between the charged particles increases, the electric force between them decreases. This inverse relationship between the distance and electric force is a fundamental characteristic of the electrostatic interaction between charged objects.
you wash four loads of dishes with a single type of detergent using cold water in the first load, warm water in the second load, hot water in the third load, and room temperature water that has been neither heated nor cooled, in the fourth load. You then test the effects of the experiment by comparing how clean the dishes were in each load. Identify the control, dependent variable, and independent variable in the experiment.
please help me!?
Answers
Answer:
The water temperature is independent, and the cleanliness of the dishes is dependent.
Explanation:
You can change the independent variable in an experiment, in this case it's the water temperature. The dependent variable is the outcome from the independent variable, in this case being the cleanliness of the dishes. You can't control the cleanliness, but you can control the water temperature.
Hope my explanation isn't too confusing, hope this helps.
Imagine standing outside with an apple in your hand. Toss the apple lightly straight up above your head and catch it as it returns to your hand. Describe how the speed of the apple changes during its "light." This time you throw the apple straight up as hard as you can, and again defily catch it as it returns. How does the flight of the apple this time compare to the lighter toss? What is the same about its flight and what is different: speed? height? time of flight?
Answers
When you toss the apple lightly straight up above your head and catch it as it returns to your hand, the speed of the apple starts at zero when you release it from your hand, then it accelerates until it reaches the highest point, at which point the speed becomes zero again before it starts to decelerate as it falls back to your hand.
However, when you throw the apple straight up as hard as you can, the speed of the apple is faster when you release it from your hand, and it accelerates quickly as it rises. The height of the apple's flight is higher than the lighter toss, and the time of flight is longer.
The same thing about both tosses is that the apple reaches its highest point before it starts to fall back down to your hand. However, the difference is in the speed, height, and time of flight. In the harder toss, the apple travels faster, reaches a greater height, and takes longer to complete its flight.
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a horse is tied with a 2m long rope at a pole. what distance will the horse run around the pole with a rope tightly stretched, if it takes and one a half rounds? also find the displacement of the horse
Answers
Answer: Total distance = 4π meters and the Total Displacement = 0
Explanation: 1.5 rounds around the pole = 1.5 times the circumference of the circle form by the rope.
Circumference of a Circle = 2πr
from the question the radius = 2m, hence the total circumference = 2π*2 = 4π meters.
Displacement which is distance between initial position and final position. When the horse takes one and a half rounds around the pole, it ends up back at the starting point. Hence, the displacement is zero.
a) Calculate the magnitude of displacement of the car in 40 seconds. b) During which part of the journey was the car accelerating? c) Calculate the magnitude of average velocity of the car.
Answers
Answer:
a) 600 meters
b) between 0 and 10 seconds, and between 30 and 40 seconds.
c) the average of the magnitude of the velocity function is 15 m/s
Explanation:
a) In order to find the magnitude of the car's displacement in 40 seconds,we need to find the area under the curve (integral of the depicted velocity function) between 0 and 40 seconds. Since the area is that of a trapezoid, we can calculate it directly from geometry:
\(Area \,\,Trapezoid=(\left[B+b]\,(H/2)\\displacement= \left[(40-0)+(30-10)\right] \,(20/2)=600\,\,m\)
b) The car is accelerating when the velocity is changing, so we see that the velocity is changing (increasing) between 0 and 10 seconds, and we also see the velocity decreasing between 30 and 40 seconds.
Notice that between 10 and 30 seconds the velocity is constant (doesn't change) of magnitude 20 m/s, so in this section of the trip there is NO acceleration.
c) To calculate the average of a function that is changing over time, we do it through calculus, using the formula for average of a function:
\(Average\,of\,f(x)=\frac{1}{b-a} \int\limits^b_a {f(x)} \, dx\)
Notice that the limits of integration for our case are 0 and 40 seconds, and that we have already calculated the area under the velocity function (the integral) in step a), so the average velocity becomes:
\(Avearage=\frac{600\,\,m}{40\,\,s}= 15\,\,\frac{m}s}\)
A parallel beam of light of wavelength 450nm is incident normally on a diffraction grating which has 300lines/mm what is the total number of intensity maxima observed?
Answers
The total number of intensity maxima observed is determined as 15.
Number of intensity maxima observedThe number of intensity maxima observed is calculated as follows;
\(n = \frac{1}{\lambda N}\)
n = (1) / (450 x 10⁻⁹ x 300 x 10³)
n = 7.4
The total number of intensity maxima observed;
nt = 2n + 1
nt = 2(7) + 1
nt = 15
Thus, the total number of intensity maxima observed is determined as 15.
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If you don’t know the answer please please don’t answer, I have to do this for a test and it’s 100 points
Answers
Answer:
I believe that it's C
Explanation:
14. How do speed and velocity differ?
Answers
Answer:
Speed is the time rate at which an object is moving along a path, while velocity is the rate and direction of an object's movement. Put another way, speed is a scalar value, while velocity is a vector.
Explanation:
Calculate the following:
D = 35 m
T = 17 sec
V = ?
Answers
Hope it helps :)
the free expansion of a gas is a process where the total mean energy e remains constant. in connection with this process, the following quantities are of interest.
Answers
The total mean energy of the gas remains constant during free expansion. This means that the total energy of the gas, which includes both kinetic and potential energy of the gas particles, does not change.
Temperature (T): Although the total mean energy remains constant, the temperature of the gas may change during free expansion. This is because temperature is related to the average kinetic energy of the gas particles, and as the gas expands, the kinetic energy distribution may change, affecting the temperature.Pressure (P): The pressure of the gas can change during free expansion. As the gas expands, the gas particles spread out, resulting in a decrease in the number of collisions with the container walls and a decrease in pressure.
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Find the Force a Watermelon hits the ground with when it is dropped off a roof and has a mass of 18 kg
Answers
Answer:
Explanation:
Weight = Force
Weight = mass x gravity
Weight = 18 kg x 9.81
Weight = 176.58 N
Please give me all formulas of motion that we require to solve numericals..(from ch gravitation class 9)
Answers
Explanation:
F = G*M1 *m2 / r²
g = G *M / R²
v= u+GT.
v² = u²+2gh.
s= ut + 1/2 gt²
W= mg.
pressure = thrust / area.
relative density = density of substance / density of water.
hope it helps you
The diameter of a watermolecule is 0.000000000275 m. How can this number best be expressed in scientific notation
Answers
Answer:
2.75x10⁻¹⁰m
Explanation:
By scientific notation, we have to express 0.000000000275 m in powers.
This can be done by counting the number of zeros after the decimal and the number after 0 which is 2.
from 2 to the decimal point, we have 10 characters
so we express it scientifically as,
= 2.75x10⁻¹⁰m
for easy understanding. i have added an attachment to help you out on how to do this.
A plane travels at a constant speed of 250 m/s as it flies once around a horizontal circle whose radius is 2542m.
a) how long does it take to fly around the circle one ?
b) If the speed were to double, what would happen to the acceleration that the plane experiences ?
c) What is the current value of the acceleration that the plane experiences?
d) if possible, find the net force acting on the plane during this turn. If it’s not possible, what information are we missing?
Answers
A rock is thrown upward with a velocity of 27 meters per second from the top of a 35 meter high cliff on the way back down. When will the Rick be 5 meters from ground level? Round your answer to two decimal places
Answers
Given data
*The given veloicty of the rock is u = 27 m/s
*The given height of the cliff is h = 35 m
*The given height of the Rick from the ground level is s = 5 m
*The value of the acceleration doue to gravity is g = 9.8 m/s^2
The formukla for the time taken by the Rick at 5 meters from the ground level is given as
\(s=h+ut+\frac{1}{2}at^2\)Substitute the known values in the above expression as
\(\begin{gathered} 5=(35)+(27)(t)+\frac{1}{2}(9.8)t^2 \\ 4.9t^2-27t-30=0 \\ t=6.45\text{ s} \end{gathered}\)Hence, the time taken by the Ric at 5 meters above the ground lel is t = 6.45 s
Answer:
6.45 s
Explanation:
df = final position = 5 m a = accel of gravity = -9.81 m/s^2
do = original position = 35 m vo = original velocity = 27m/s
df = do + vot + 1/2 at^2
5 = 35 + 27t - (1/2)9.81t^2
-4.905 t^2+ 27t +30 = 0
Use quadratic formula a = -4.905 b = 27 c = 30
to find t = 6.45 s
(Ignore the negative value found with the Quadratic Formula)
If net force acting on object is 0, then the force is considered to be..
a. balanced
b. equal in direction
c. unbalanced
d. distance/time
Answers
If net force acting on object is 0, then the force is considered to be balanced (option A).
What is net force?A net force refers to the sum of all the forces acting on an object.
The net force can accelerate a mass. Some other force acts on a body either at rest or motion. The net force is a term used in a system when there is a significant number of forces.
Fnet = F₁ + F₂ + F₃.............+ Fn
When the net force of an object is zero (0), this means that the sum of forces acting on the object is balanced. A balanced forces are forces that are opposite in direction and equal in size.
Therefore, a net force of 0 is a balanced force.
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Equation for a particle vibrating in simple harmonic motion is 2y = 8 sin (4πt). Its amplitude and angular frequency is:
(a) 6 cm and 2π rad (b) 4cm and 4π rad (c) 16 cm and 4 Hz (d) 32 m and 2 Hz
Answers
Explanation:
The equation 2y = 8 sin (4πt) is a general equation for a particle vibrating in simple harmonic motion. The amplitude of the oscillations is given by the coefficient of the sine term, which is 8 in this equation. Therefore, the amplitude of the particle vibrating in simple harmonic motion is 8 cm.
The angular frequency is given by the coefficient of the variable t, which is 4π in this equation. Therefore, the angular frequency of the particle vibrating in simple harmonic motion is 4π rad/s.
Therefore, the answer is (b) 4 cm and 4π rad.
why is it more difficult to start moving a heavy carton from rest than it is to keep pushing it with constant velocity?
Answers
It is more difficult to start moving a heavy carton from rest than it is to keep pushing it with constant velocity because of static friction.
Static friction refers to the resistance encountered when attempting to initiate the movement of two objects that are in contact with each other but not currently in motion relative to each other. When an object is at rest, the force of static friction acts in the opposite direction to any force applied to it.
In this case, the force applied to the carton is the force needed to start moving it from rest. The force of static friction is greater than the force applied to the carton, making it difficult to start moving the carton from rest.
Once the carton is moving with constant velocity, the force of static friction is no longer acting on it. The only force acting on the carton is the force that is applied to keep it moving at a constant velocity. This force is equal to the force of kinetic friction which is less than the force of static friction.
To summarize, the initial effort required to overcome the static friction between a heavy carton and its resting position is greater compared to the continuous force needed to maintain its constant velocity. The force of static friction is greater than the force applied to the carton, making it difficult to start moving the carton from rest.
Once the carton is moving with constant velocity, the force of static friction is no longer acting on it, and the only force acting on the carton is the force that is applied to keep it moving at a constant velocity.
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A force F is exerted on a 5 kg block to move it across a rough surface, as shown above. Themagnitude of the force is initially 5 N, and the block moves at a coristant velocity. While the block ismoving, the force is instantaneously increased to 12 N. How much kinetic energy does the block now gain as it moves a distance of 2m.
Answers
Given that the mass of the block is m = 5 kg
The total force is F = 5+12 = 17 N
The displacement of the block is d = 2 m
We have to find the gain in kinetic energy.
The gain in kinetic energy is given by the formula
\(\begin{gathered} \Delta K\mathrm{}E\text{. = work done} \\ =F\times d \end{gathered}\)Substituting the values, the gain in kinetic energy will be
\(\begin{gathered} \Delta K.E.=17\times2 \\ =34\text{ J} \end{gathered}\)Thus, the gain in kinetic energy is 34 J
What are some sources of error in a refraction lab using pins and a glass block?
Answers
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Capacitor electric field [8 pts.] A fully charged parallel-plate capacitor with a plate separation of 12.5 mm and a capacitance of 10 uF stores 8 m) of energy. Find the electric field strength inside the capacitor. (A) 42 V/m (B) 320 V/m (C) 1250 V/m (D) 2260 V/m (E) 3200 V/m << +8 (F) 4200 V/m
Answers
We know that the energy stored in a parallel-plate capacitor can be expressed as:$$E=\frac{1}{2}CV^2$$where E is the energy in joules (J), C is the capacitance in farads (F), and V is the voltage across the plates in volts (V).Now we can find the electric field inside the capacitor.
Let E be the electric field strength, d be the plate separation, and A be the area of each plate. The capacitance C can be expressed as:
\($$C=\frac{\epsilon_0A}{d}$$\)
where ε0 is the permittivity of free space, which is approximately equal to 8.85 x 10-12 F/m.
Therefore, we have:
\($$C=\frac{\epsilon_0A}{d}$$\)
Rearranging this equation gives:
\($$A=\frac{Cd}{\epsilon_0}$$$$A=\frac{(10×10^{-6})×(12.5×10^{-3})}{8.85×10^{-12}}=1.418×10^{-2}m^2$$\)
Now we can find the electric field inside the capacitor. The potential difference V between the plates can be found using the energy stored in the capacitor. Therefore, we have:
\($$V=\sqrt{\frac{2E}{C}}$$$$V=\sqrt{\frac{2×(8×10^{-3})}{10×10^{-6}}}=\sqrt{16}=4V$$\)
The electric field strength E inside the capacitor can be expressed as:\($$E=\frac{V}{d}=\frac{4}{12.5×10^{-3}}=320V/m$$\)
Therefore, the answer is (B) 320 V/m.
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