Answer:
occasion - a particular event, or the time at which it takes place.
the outer planets are composed of . a. high density metals b. metal and ice c. rock and ice d. argon gas e. ice and gas
The outer planets are composed of c) rock and ice
The four outer planets - Jupiter, Saturn, Uranus, and Neptune - also called Jupiter or giant planets, are large celestial bodies with densities of less than 2 grams per cubic centimeter. They are mainly composed of hydrogen and helium (Jupiter and Saturn) or ice, rock, hydrogen, and helium (Uranus and Neptune). A planet's density depends on its composition. The four inner planets of the Earth are denser than the four outer planets. The inner planets are mostly composed of dense, hard rock. The outer planets are mostly gas, so they have a lower overall density. Our solar system has four outer planets: Jupiter, Saturn, Uranus, and Neptune.
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A pilot needs to know if a plane with clear the tower. The plane will travel 1500 yards before lifting off the ground to travel another 603 yards after which point the plane will be directly over the tower. If the plane had continued on the runway, it is another 600 yards to the control tower, which is 198 feet high.
The statement which best describes how to determine the plane clears the tower is;
Use the Pythagoras Theorem where distance to the tower is a leg of the right triangle & the distance in the air is the hypotenuse. Find the other leg. Convert to feet to compare to the tower height.
What is Pythagoras Theorem?Pythagoras Theorem is a trigonometry equation used to determine the length of one side of a right triangle. The Greek mathematician Pythagoras was the first to develop a geometric proof for the relationship between the sum of the squares of the lengths and the side lengths of a right triangle, even though similar ideas had already been discovered by the Babylonians.
Pythagoras established that the largest of the three squares must have the same area as the combined areas of the other two squares when they are arranged to form a right angle triangle.
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the space shuttle has a mass of 2.0 x 106 kg. at lift off the engines generate an upward thrust of 1.3 x 108 n. what is the acceleration of the shuttle when it is launched?
The acceleration of the space shuttle when it is launched is 6.5 m/s².
What do you mean by acceleration?The rate at which velocity varies with respect to time is referred to as acceleration. Since acceleration has both a magnitude and direction, it is a vector quantity.
To find the acceleration of the space shuttle at lift off, we can use Newton's second law of motion which states that force is equal to mass times acceleration (F=ma).
In this case, the force acting on the shuttle is the upward thrust generated by the engines, which is 1.3 x 108 N.
The mass of the shuttle is 2.0 x 106 kg.
Therefore, the acceleration of the shuttle can be calculated as:
a = F / m
a = (1.3 x 10^8 N) / (2.0 x 10^6 kg)
a = 6.5 m/s²
So, the acceleration of the shuttle when it is launched is 6.5 m/s².
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a charge of 0.08 c moves to the right due to a 4 n force exerted by an electric field. what is the magnitude and direction of the electric field?
The magnitude of the electric field is 50 N/C and the direction is to the right. The electric field is there whether or not a charged object is present in that area.
How is an electric field created?An electric field, or alteration of a space and field in the vicinity of a charged item, is produced. The odd change in the environment would be felt by other charges within this sector.
What transpires in a field of electricity?A charged particle produces electric force in the area around it, which is known as the electric field. Electric fields interact when charged particles were close enough to one another to exert force on one another. Incompatiblely charged particles are drawn to one another. Like-charged particles repel one another.
The magnitude and direction of the electric field can be found using the formula:
F = qE
where F is the force exerted on the charge, q is the charge, and E is the electric field.
Given that the force exerted on the charge is 4 N, and the charge is 0.08 C, we can find the electric field by rearranging the equation to:
E = F/q
The magnitude of electric field is:
E = 4 N / 0.08 C = 50 N/C
To determine the direction of the electric field we can use the given information that the force exerted on the charge is 4 N to the right. The force on a positive charge due to an electric field is in the direction of the field, so the electric field is in the direction of the force, which is to the right.
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uniform circular motion worksheet physics 
The time of motion of the satellite is 1.65 hours.
The speed of the satellite from the center of the Earth is 26,945.35 km/h.
What is the time of motion of the satellite?
The time of motion of the satellite in hours is calculated as follows;
t = ( 99 min / 1 ) x ( 1 hour / 60 min )
t = 1.65 hours
The speed of the satellite from the center of the Earth in km/h is calculated as follows;
v = ( 2πr ) / ( t )
where;
r is the distance of the satellite from the center of the EarthThe position of the satellite above the surface of the Earth = 705 km
The radius of Earth = 6,371 km
The total distance of the satellite from the center of the Earth = 705 km + 6,371 km = 7,076 km
v = ( 2π x 7076 ) / ( 1.65 )
v = 26,945.35 km/h
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For each of the following hypothetical populations, give a plausible sample of size 4.
a. All distances that might result when you throw a football.
b. Page lengths of books published 5 years from now.
c. All possible earthquake-strength measurements (Richter scale) that might be recorded in California during the next year.
d. All possible yields (in grams) from a certain chemical reaction carried out in a laboratory.
a) A distance when you throw a football should be positive, therefore, any 4 numbers r, where r>0 could be a sample. Given that we are seeking for a plausible example, we could
{25,30,35,40}
where the values are in meters. It is not reasonable for a person to throw ball 1000 kilometers for example.
b) page lengths of books published should be positive numbers. With same conclusion as in (a) we could choose
{250,500,750,1000}
where the numbers correspond to the book's page count.. It is not reasonable for a book to have million pages.
c) The Richter scale goes from 0 up to 10, there are no records of anything size more than 10. Therefore, a plausible sample of size 4 could be
{3, 4.2, 5.2, 6}
Any number bigger than 10 would not be reasonable.
d) Depending on certain chemical reaction carried out in a laboratory all possible yields are different. The sample could be
{2,3,4,5}
Where the numbers represent grams.
What is hypothetical populations?
A hypothetical population is a population created by a researcher to study a certain phenomenon or to test a certain hypothesis. Hypothetical populations are often used in computer simulations and mathematical models to study complex systems, such as the spread of a virus or the evolution of a new species. They are also used in the study of population dynamics, to understand how populations change over time.
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when a 0.30 kg mass is suspended from a massless spring, the spring stretches a distance of 2.0 cm. let 2.0 cm be the rest position for the mass-spring system. the mass is then pulled down an additional distance of 1.5 cm and released. calculate the total mechanical energy of the system in si units. spring constant can be found using hooke's law.
The bulk is then released after being dragged down a further 1.5 cm. We'll have 0.284 seconds The period of isolation is now.
In a nutshell, what does distance mean?
The total movement of an object independent of direction is its distance The amount of space that an object has traveled rgardless of where it started or ended is referred to as distance.
What does distance look like in physics?
By combining the two lengths traveled by an automobile the total distance can be determined for instance if the vehicle drives 100 meters north. before making a right turn and heading 300 meters further east. In this instance the vehicle traveled a total of 400 meters.
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1. If the dielectric becomes damaged it can 'break down' like the air does when lightning strikes. What would happen to the charge on the plates?
2. Here are some statements about how an image is produced and processed in a digital camera.
A) Starting in one corner the charge on each square is moved off the CCD.
B) Light enters the camera.
C) That signal can be stored or sent to a computer or other device.
D) The charges on each square are converted into a digital signal.
E) When the light hits a square on the CCD charge is produced.
a. They are in the wrong order. Write the letters for the statements in the correct order.
b. Explain why there is a delay between taking one photograph with a digital camera and taking the next photograph.
Answer:
Explanation:
A) E) When the light hits a square on the CCD charge is produced
B) A) Starting in one corner the charge on each square is moved off the CCD
C) D) The charges on each square are converted into a digital signal
D) B) Light enters the camera
E) C) That signal can be stored or sent to a computer or other device
b. The delay between taking one photograph with a digital camera and taking the next photograph is due to the time it takes to capture the image and process it into a digital signal. This process includes the capturing of the light entering the camera, the conversion of the charges on each square of the CCD into a digital signal, and the storage or sending of the signal to a computer or other device.
a) For the two vectors A? and B? in the figure (Figure 1) , find the scalar product A? ?B? .
b)Find the magnitude of the vector product A? ×B?
a) The scalar product of A and B is -6.62m2.
b) The vector product of A and B is -8.5k.
Rectangular components of the magnitude of A are:
[tex]\begin{aligned}& A x=3.6 \cos 70 \\& A y=3.6 \sin 70 \\& A=A x^i+A y^j \\& A=3.6 \cos 70 x^i+3.6 \sin 70 x^j \\& A=1.23 x^i+3.38 x^j\end{aligned}[/tex]
Rectangular components of the magnitude of B are:
[tex]\begin{aligned}& B x=-2.4 \cos 30 \\& B y=-2.4 \sin 30 \\& B=B x^i+B y^j \\& B=-2.4 \cos 30 x^i-2.4 \sin 30 x^j \\& B=2.08 x^i-1.20 x^j\end{aligned}[/tex]
a)The scalar product of A.B is
[tex]$$A . B=1.23 *(2.08)+3.38(-1.20)$$$A . B=-6.62 m^2$[/tex]
b)The vector product of A x B is
[tex]\begin{aligned}& A * B=(3.38 * 0+1.20 * 0) i-(1.23 * 0+2.08 * 0) j+(1.23 *-1.20-2.08 * 3.38) k \\& A * B=(-1.476-7.03) k \\& A * B=-8.5 k\end{aligned}[/tex]
What is the scalar product of vectors A and B?The scalar product of two vectors a and b of magnitude |a| and |b| is given as |a||b| cos θ, where θ represents the angle between the vectors a and b taken in the direction of the vectors.
What is a vector product?The Vector Product of two vectors can be defined as the resultant vector perpendicular to both vectors. It is also known as the cross product of two vectors and is often denoted by a x b. The Vector Product of two vectors results in a vector perpendicular to both vectors.
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A rock is thrown from the roof of a building with a velocity v0 at an angle of θ from the horizontal. The building has a height h. You can ignore air resistance. Calculate the magnitude of the velocity of the rock just before it strikes the ground, and show that this speed is independent of angle α.
The magnitude of the final velocity, V, is independent of the angle of θ, and it is equal to the initial velocity, v0
Calculation-If V is the magnitude of the velocity of the rock just before it strikes the ground, then:
Final kinetic energy = initial kinetic energy + potential energy lost
(1/2)mV^2 = (1/2)m(v_0)^2 + mgh
V^2 = (v_0)^2 + 2gh
V = sqrt[(v_0)^2 + 2gh]
The ground, and show that this speed is independent of angle α.This is because the only force acting on the rock is gravity and it acts vertically, so the horizontal component of the velocity doesn't change, and the vertical component is transformed into kinetic energy, which is then conserved.
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include all given digits Mercury Venus Earth Mars Jupiter Saturn Uranus Neptune Distance from the sun (au) 1 NA Orbital Period (years) 1 NA
Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, and Neptune are in order of proximity to the sun. Pluto, which was once thought to be the outermost planet, is now categorized as a dwarf planet.
Pluto is not the only dwarf planet that has been found farther from the Sun. Mercury, Venus, Earth, Mars, Uranus, and Neptune are each 0.39, 0.72, 1, 1.52, 19.18, and 30.06 light-years from the sun, respectively.
Distance is the length difference between the two places.
The distance between each planet from the sun will be given in AU as
Mercury - 0.39 and 0.242
Venus - 0.72 and 0.616
Earth - 1 and 1
Mars - 1.52 and 1.88
Jupiter - 5.20
Uranus - 19.18 and 84.00
Neptune - 30.06 and 165.00
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Answer:
Graph the planet data, shown right, using the regression calculator. When you are done, click “Resize window to fit data.”
A 3-column table with 8 rows is shown. The first column has entries Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, Neptune. The second column is labeled A (au) with entries 0.39, 0.72, 1, 1.52, blank, blank, 19.18, 30.06. The third column is labeled T with entries 0.242, 0.616, 1, 1.88, blank, blank, 84.0, 165. Jupiter and Saturn are to be interpolated later in the activity.
Explanation: Theres the answer
a particle moves in a straight line at a constant velocity of 30 m/s. what is its displacement between t
The displacement between t=0 and t=5 seconds is 180 m, if the velocity of the particle in a straight line is 30 m/sec.
Velocity is the ratio of displacement and time. It is a vector quantity which has both magnitude and the direction. Main difference between the velocity and the speed is that speed is the ratio of distance and time. distance is irrespective of the direction. Speed is a scalar quantity. The unit of both the velocity and the speed is same, e.g.: m/sec.
Velocity = displacement/time
Displacement = velocity × time
Displacement = 30 × (5-0)
= 180 meters
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a scientist wants to measure the relationship between humidity in the summer and the number of home runs i baseball. Which of the folllowing teastable question about this topic?
Are home run totals in baseball significantly higher in summer months with higher humidity compared to summer months with lower humidity.
What is summer?Summer is a season of warm weather and long days that typically falls between spring and autumn. It is a time of year when people take vacations, enjoy outdoor activities, and soak up the sunshine. During this time of year, the days are longer and the temperatures are higher. During the summer, people often spend more time outdoors, swimming, picnicking, camping,
And participating in other recreational activities. Summer is a great time for barbecues, festivals, and other outdoor activities. The days are often sunny and bright, and the nights are balmy and mild.
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Three 45 ohm lightbulbs and three 75 ohm lightbulbs are connected in series. (a) what is the total resistance of the circuit? (b) what is their resistance if all six are wired in parallel?
a) The total resistance of the circuit in which three 45 ohm lightbulbs and three 75 ohm light bulbs connected in series is 360 ohm.
b) The total resistance of the circuit if all six are wired in parallel is 28.57 ohm.
a) In order to find the series total resistance, we need to add all resistances,
Req = R₁ + R₂ + R₃ + R₄ + R₅ + R₆ = 45 + 45 + 45 + 75 + 75 + 75 = 135+ 225 = 360 ohm
b) Now, since the resistances are in parallel, we need to use the expression below,
1/Req = 1/R₁ + 1/R₂ + 1/R₃ + 1/R₄ + 1/R₅ + 1/R₆
Putting in the values,
1/Req = 1/45 + 1/45 + 1/45 + 1/75 + 1/75 + 1/75
1/Req = 1/0.035
Req = 28.57 ohm
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if you walk 1 mile everyday, and leave your front door at 9am and return at 9:25, what is the displacement
The displacement is zero always because the initial and the final position is same in these cases and displacement is zero when initial and final position are same.
Displacement is defined as the change in position of an object. It is a vector quantity and has a direction and magnitude. It is represented as an arrow that points from the starting position to the final position. For example- If an object moves from A position to B, then the object’s position changes. It is the shortest distance between the initial and final position that is a straight line. A person drives north 6 blocks, turns west, and then drives 6 blocks. The driver then turns south and drives 6 blocks. By this primary information, we can firmly conclude that the The displacement is zero always because the initial and the final position is same in these cases and displacement is zero when initial and final position are same.
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an object is placed in front of a thin lens. an upright image is formed that is one-third the height of the object. if the image is 6.0 cm from the lens, what is the focal length of the lens?
The -6 cm is the focal length of the lens.
What is focal length ?
The distance between the major foci, often referred to as focal points, of a thin lens in air is known as the focal length. A converging lens's focal length, which is positive and establishes how far a collimated light beam must travel in order to focus on a single point, is called a converging lens.
What is height ?
Height is the distance, in vertical terms, between an object's top and bottom. It's called "height" on occasion. Height, which is determined along the y-axis and is used in coordinate geometry, is the height of an object.
The object distance is u = 12 cm
The size of the image is h' = h/3
Where h is the size of the object
a)
the image height if positive because it is upright
b)
The image is a virtual because the image is diminished
c)
The image distance will be negative as the image is virtual
d)
Magnification m = 1/3
image distance = m*u
v = -1/3 *12
v = -4 cm
e)
The thin lens equation is
1/f = 1/u + 1/v
1/f = 1/12 - 1/4
f = -6 cm (lens will be concave)
Therefore, -6 cm is the focal length of the lens.
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While doing an experiment, Tom drops a ball cut of a window 2.3 meters above the ground. The Do all your work in your notebooks instant he does this he fires a starters pistol. Jerry sees the ball hit the ground at the instant he hears the pistols shot. The speed of pistol's sound is 334 m/s -it is constant and wil not change. a. How long did it take for Tom's ball to reach the ground? b. How far away was Jerry standing?
a. The time it takes for the ball to reach the ground is calculated using the equation
t = d/v
Where t is time, d is the distance the ball has to travel, and v is the speed of the sound.
In this case, d = 2.3 meters and v = 334 m/s
Therefore, t = 2.3/334 = 0.0069 seconds.
b. The distance Jerry was standing away from the window is equal to the speed of sound multiplied by the time it took for the ball to reach the ground.
d = vt
Therefore, d = (334 m/s)(0.0069 s) = 2.3 meters.
Therefore, Jerry was standing 2.3 meters away from the window.
two 2.70 cm × 2.70 cm plates that form a parallel-plate capacitor are charged to ± 0.708 nc .
What is the electric field strength inside the capacitor if the spacing between the plates is 1.20 mm? What is potential difference across the capacitor if the spacing between the plates is 1.20 mm? What is the electric field strength inside the capacitor if the spacing between the plates is 2.40 mm? What is the potential difference across the capacitor if the spacing between the plates is 240 mm?
The potential difference = 7.43 V
Electric Field Strength (1.20 mm):
E = (0.708 nC) / (2.70 cm * 2.70 cm * (1.20 * 10^-3 m)) = 6.19 x 10^5 N/C
Potential Difference (1.20 mm):
V = E * d = (6.19 x 10^5 N/C) * (1.20 * 10^-3 m) = 7.43 V
Electric Field Strength (2.40 mm):
E = (0.708 nC) / (2.70 cm * 2.70 cm * (2.40 * 10^-3 m)) = 3.10 x 10^5 N/C
Potential Difference (2.40 mm):
V = E * d = (3.10 x 10^5 N/C) * (2.40 * 10^-3 m) = 7.43 V
What is potential difference?
Potential difference, also known as voltage, is a measure of the electrical potential energy per unit charge between two points in an electric field. It is measured in volts (V).
Therefore, The potential difference = 7.43 V
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two communications satellites in orbit around Earth are 2.52 x 10^5 m apart, and the resulting gravitational force between them is 1.26 x 10^ -16 N. One satellite is three times as massive as the other.
What is the mass of the lighter satellite?
The mass of the lighter satellite is 2.5 x 10^-9 kg.
What is gravitational force?The gravitational force between two objects is given by the equation:
[tex]F = G * (m1 * m2) / r^2[/tex]
Where F is the gravitational force, G is the gravitational constant[tex](6.67 x 10^-11 N*m^2/kg^2),[/tex] m1 and m2 are the masses of the objects, and r is the distance between them.
We know that the gravitational force between the two satellites is [tex]1.26 x 10^-16 N[/tex]. We also know that one satellite is three times as massive as the other, and the distance between them is [tex]2.52 x 10^5 m[/tex]
We can use this information to solve for the mass of the lighter satellite:
F = G * (m1 * m2) / r^2
m2 = 3 * m1
[tex]1.26 x 10^-16 N = (6.67 x 10^-11 Nm^2/kg^2) * (m1 * (3m1)) / (2.52 x 10^5 m)^2[/tex]
m1 = 2.5 x 10^-9 kg
The mass of the lighter satellite is 2.5 x 10^-9 kg.
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Answer:
200 kg
Explanation:
[tex]\sqrt{\frac{(1.26 * 10^{-16})(2.52 * 10^{5})^{2}}{3(6.67 * 10^{-11} } }[/tex]
suppose you are reshelving books in a library. as you lift a book from the floor and place it on the top shelf, two forces act on the book: your upward lifting force and the downward gravity force. hint (a) is the mechanical work done by your lifting force positive, zero, or negative? positive zero negative (b) is the work done by the gravity force positive, zero, or negative? positive zero negative (c) is the sum of the works done by both forces positive, zero, or negative? positive zero negative
The kinetic energy of the book on the floor was zero and the kinetic energy of the book on the top shelf is zero, so no change occurs in the kinetic energy .
What is kinetic energy in simple words?Kinetic energy is the energy an object has because of its motion. If we want to accelerate an object, then we must apply a force. Applying a force requires us to do work.
What is kinetic example?A truck travelling down the road has more kinetic energy than a car travelling at the same speed because the truck's mass is much more than the car's. A river flowing at a certain speed comprises kinetic energy as water has a certain velocity and mass.
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Explain why the line on a heating curve is flat at the melting point and boiling point.
a spring has a force constant of 504.7 n/m. find the potential energy stored in the spring when the spring is a) stretched 4.32 cm from equilibrium. answer in units of j.
The potential energy stored in the spring is 10.9 J.
What is potential energy?Potential energy is the stored energy of an object due to its position or condition. It can be thought of as the energy that an object has because of its location in a gravitational field. Potential energy is stored energy and has the capacity to do work. It is measured relative to a reference point. As an example, when a ball is held at a certain height, it has potential energy because of its position.
The potential energy stored in a spring is:
PE = 1/2 * k * x^2
where k is the force constant (in N/m), and x is the displacement from equilibrium (in m).
In this case, the force constant is 504.7 N/m and the displacement from equilibrium is 4.32 cm, which is 0.0432 m.
Therefore, the potential energy stored in the spring is 10.9 J.
PE = 1/2 * 504.7 N/m * 0.0432 m^2
PE = 10.9 J
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what is the normal force acting on a mountain goat that weighs 900 n and is standing on such a slope?
According to the question the vale of normal force acting is 450 N.
What in science is a force?At this level, calling a force a push or maybe even a pull is entirely appropriate.
We must resolve the mass perpendicular to a inclination in order to calculate the normal force. Consequently, we can write:
N = W CosΘ
= 900 N(Cos 60°)
= 900 N(0.5)
= 450 N
We must add together all the forces acting in conjunction with the inclination in order to calculate the static friction force. We compose:
F = W sinΘ
= 900 N(sin 60°)
= 900 N(0.8660254038)
= 779.42 N
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the unit system used by scientists, which is based on the metric system, is called the .
Answer:
Explanation: The metric system is a system of measurement that uses the meter, liter, and gram as base units of length (distance), capacity (volume), and weight (mass)
si units which are used by scientist to measure
When a light ray in air enters water at 15° from the normal, it
a. sometimes bends towards or away from the normal.
b. always bends toward the normal.
c. always bends away from the normal.
d. does not bend.
(a) light ray sometimes bends towards the normal or away from it.
When a light ray in air enters water at an angle, it bends, the direction of the bending depends on the relative refractive indices of the two materials, and the angle of incidence. Since the refractive index of water is greater than that of air, the light will bend towards the normal.
How would you define refractive index?The refractive index of a material shows how much a pathway of light is bent when it enters certain material. The index of refraction also confines the amount of light that is reflected when reaching the interface.
Who has the highest refractive index?Diamond. Since the speed of light in diamond is the shortest, diamond has the highest refractive index.
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Determine the volume of concrete needed to construct the curb.Express your answer to three significant figures and include the appropriate units.V3 mm
The volume of concrete needed to construct the curb comes out to be 73.2 Vmm³.
Volume is an amount of space that occupies. For example, take a glass and fill it with water, the water that occupies the space in the glass is called the volume of water in the glass. Same for concrete, take a box of length (1m), breadth,(1m) depth(1m) and fill it with concrete. Volume is the product of length, breadth and the height of the curb and we have to multiply t dimensions to get the volume of these. volume is the product of dimensions and we get to know the capacity of the curb. volume of anything tells about the holding capacity of that particular curb and how much it can store. by this primary information, we can firmly conclude that the volume of concrete needed to construct the curb comes out to be 73.2 Vmm³.
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A 3.0 kilogram object is placed on a frictionless track at point a and released from rest. (assume the gravitational potential energy of the system to be zero at point c).
At point A, there is 90J of potential energy.
At point B, there is 60J of kinetic energy.
Point G must be the trajectory's furthest point.
The definition of gravitational potential energyThe force that a body gets when it is far from the earth can be described as the power of pulling toward this center of the earth. The due to gravity increases with increasing distance. Its mathematical formula is.
m : mass
g : gravity
h : height
Calculation
If we want to know the potential energy at the starting point (point A) then we only have to use the equation Ep:
Ep = mgh
m =3kg
g = 10m/s²
h = 3m
Ep = 3kg*10m/s²*3m
Ep = 90J
Now if we want to know the kinetic energy at point B, we must make an
energy balance
Ea = Eb
90J = Ec + Epb
90J = Ec + 3kg*10m/s²*1m
Ec = 60J
The farthest point of the trajectory must not exceed a height of 3m, and this is point G.
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a subway train starts from rest and accelerates at 5 ft/s2 until it reaches a speed of 38 ft/s. it then coasts for 1200 ft, maintaining the maximum speed. it then slows down into the station at -4 ft/s2 before coming to a stop. how long did it take the subway train to move from one station to the next? what is the total distance between stations? (48.7 s, 1525 ft)
The train takes 48.7 seconds to move from one station to other, and distance between these two stations is 1525 ft.
Initial speed of the train, u = 0 (start from rest)
Acceleration of the train = 5 ft/s²
Deceleration of the train = -4 ft/s²
Maximum speed of the train, v = 38 ft/s
Time taken by the train to reach that constant speed, t₁ = 38/5 = 7.6 sec
Distance covered by the train during accelerated motion, d₁ = ut + 0.5at²
d₁ = 0 × 7.6 + 0.5 × 5 × 7.6²
d₁ = 144.4 ft
Time taken by the train to cover 1200 ft distance at constant speed, t₂ = 1200/38 = 31.6 sec
Time taken by the train to completely stop, t₃ = (38-0)/4 = 9.5 sec
Distance travelled during the decelerated motion, d₃ = ut + 0.5at²
d₃ = 38 × 9.5 + 0.5 × (-4) × 9.5²
d₃ = 180.5 ft
Total time taken during the entire journey, T = t₁ + t₂ + t₃
T = 7.6 + 31.6 + 9.5 = 48.7 sec
Total distance travelled during entire journey, D = d₁+d₂+d₃
D = 144.4 + 1200 + 180.5 = 1524.9 ≈ 1525
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: A mass m is oscillating with amplitude A at the end of a vertical spring of spring constant k. Part (a) The mass is increased by a factor of four. What is true about the period? Choose the best answer. MultipleChoice : 1) The period increases by a factor of four. 2) The period doubles. 3) The period is halved. 4) The period decreases by a factor of four. Part (b) The mass is increased by a factor of four, keeping A and k constant. What is true about the total mechanical energy? Choose the best answer. Multiple Choice : 1) The energy increases by a factor of four. 2) The energy doubles. 3) The energy remains unchanged. 4) The energy is halved. 5) The energy decreases by a factor of four. Part (c) The mass is increased by a factor of four, keeping A and k constant. What is true about the maximum speed? Choose the best answer. MultipleChoice: 1) The maximum speed increases by a factor of four. 2) The maximum speed doubles. 3) The maximum speed is halved. 4) The maximum speed decreases by a factor of four. 5) The maximum speed remains unchanged. Part (d) The amplitude is doubled, keeping mass and k constant. What is true about the period? Choose the best answer. Multiple Choice : 1) The period increases by a factor of four. 2) The period doubles. 3) The period remains unchanged. 4) The period is halved. 5) The period decreases by a factor of four. Part (e) The amplitude is doubled, keeping mass and k constant. What is true about the total mechanical energy? Choose the best answer. Multiple Choice : 1) The energy doubles. 2) The energy is halved. 3) The energy increases by a factor of four. 4) The energy decreases by a factor of four. 5) The energy remains unchanged. Part (f) The amplitude is doubled, keeping mass and k constant. What is true about the maximum speed? Choose the best answer. MultipleChoice: 1) The maximum speed increases by a factor of four. 2) The maximum speed is halved. 3) The maximum speed doubles. 4) The maximum speed decreases by a factor of four. 5) The maximum speed remains unchanged.
Previous question
Part (a) The period of oscillation is given by the formula: T = 2π × [tex]\sqrt{(m/k)}[/tex]
Since the mass is increased by a factor of four, the period will change as follows: T' = 2π × [tex]\sqrt{(4m/k)}[/tex] = 2π × 2 × [tex]\sqrt{(m/k)}[/tex] = 4π × [tex]\sqrt{(m/k)}[/tex] = 2 × T
The period doubles. So, the answer is 2) The period doubles.
Part (b) The total mechanical energy of the system is given by the formula: E = 1/2 × kA² + 1/2 × mv²
What is total mechanical energy?Since amplitude A and spring constant k are constant, the only change in energy is due to the change in mass. If the mass is increased by a factor of four, the total mechanical energy will change as follows:
E' = 1/2 × kA² + 1/2 × 4mv² = kA² + 2mv² = 2(1/2 × kA² + 1/2 × mv²) = 2E
The energy doubles. So, the answer is 2) The energy doubles.
Part (b) The mass is increased by a factor of four, keeping A and k constant. The total mechanical energy will increase by a factor of four. So, the answer is 1) The energy increases by a factor of four.
Part (c) The mass is increased by a factor of four, keeping A and k constant. The maximum speed will decrease by a factor of four. So, the answer is 4) The maximum speed decreases by a factor of four.
Part (d) The amplitude is doubled, keeping mass and k constant. The period will remain unchanged. So, the answer is 3) The period remains unchanged.
Part (e) The amplitude is doubled, keeping mass and k constant. The total mechanical energy will increase by a factor of four. So, the answer is 3) The energy increases by a factor of four.
Part (f) The amplitude is doubled, keeping mass and k constant. The maximum speed will double. So, the answer is 3) The maximum speed doubles.
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A bowling ball has a mass of 25 kg and a velocity of 20 m/s. A marble has a
mass of 5 kg and a velocity of 50 m/s. Which has greater momentum?
The momentum of the bowling ball is 500kgm/s and that of the marble is 250kgm/s. Therefore, the momentum of bowling ball is greater than that of marble.
What is Momentum?Momentum is the product of the mass and velocity of an object. It is a quantity of motion of an object. It is a vector quantity because it possess both the magnitude and the direction. The SI unit of momentum is kgm/s.
p = m × v
where, p = momentum of the object,
m = mass of the object,
v = velocity of the object.
The momentum of the bowling ball with a mass of 25kg and a velocity of 20m/s is:
p = 25 × 20 = 500kgm/s
The momentum of the marble with a mass of 5kg and velocity of 50m/s is:
p = 5 × 50 = 250kgm/s.
Therefore, the momentum of the bowling ball is more than the momentum of the marble.
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