The work done by the gravitational force on rock 1 can be calculated using the work-energy theorem. This theorem states that the net work done on an object is equal to the change in its kinetic energy.
What is gravitational force?Gravitational force is the attractive force between two objects that is proportional to their masses and inversely proportional to the square of the distance between them. It is the weakest force in nature and is the reason why objects with mass are attracted to each other. This force was first described by Isaac Newton in his law of universal gravitation, which states that the force between two objects is proportional to the product of their masses and inversely proportional to the square of the distance between them.
Since the rock is launched from rest at a height of h0 and then returns to the same height, its kinetic energy does not change and therefore the net work done on the rock is zero. This means that the work done by the gravitational force on the rock is also zero, since the only force acting on the rock is the gravitational force.
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The dipole moment of the water molecule (H2O) is 6.17x10^-30C.m. Consider a water molecule located at the origin whose dipole moment p points in the +x-direction. A chlorine ion (Cl-), of charge-1.60x10^-19C, is located at x=3.00x10^-9m. Assume that x is much larger than the separation d between the charges in the dipole, so that the approximate expression for the electric field along the dipole axis can be used.
Part A
Find the magnitude of the electric force that the water molecule exerts on the chlorine ion.
Part B
What is the direction of the electric force.
Part C
Is this force attractive or repulsive?
The magnitude of the electric force that the water molecule exerts on the chlorine ion is F = 1.60x10^-19C × 6.17x10^-30C.m / (3.00x10^-9m)^2 = 1.65x10^-48N.
What is magnitude ?
The magnitude of the electric force that the water molecule exerts on the chlorine ion is 1.65x10^-48N.
The direction of the electric force is in the +x direction, away from the chlorine ion.
The force is repulsive
Magnitude is a measure of the size or intensity of something. It is typically used to refer to physical quantities such as mass, force, speed, distance, or energy, but can also refer to abstract concepts like loudness, brightness, or importance. Magnitude is typically expressed on a logarithmic scale, such as the Richter scale for earthquakes or the decibel scale for sound. The magnitude of a physical quantity is often indicated by a unit of measurement, such as kilograms, newtons, miles per hour, or candelas.
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to achieve this vertical leap, with what force did the impala push down on the ground?
The force that the push impala push down on ground is 1941 N and the ratio of this force to the antelope's weight is 4.4.
a)The force that did the impala push down on the ground will be 1941 N.
The acceleration= 7-0/0.21
a= 33.33m/sec^2
The value of force can be calculated by
F= m (a + g)
F= 45( 33.33+9.81)
F= 1941 N
Hence the force that did the impala push down on the ground will be 1941 N.
(b)The ratio of this force to the antelope's weight will be 4.4.
The weight of the antelope=
W= mg
W=45×9.81
Therefore, W=441 N
The ratio of this force to the antelope's weight can be calculated by
F/W=1941/441
F/W= 4.4
Therefore, the ratio of force to the antelope's weight will be 4.4.
What is force?
Force is defined as the product the of mass and acceleration.
Unit of the force= Newton
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Complete question
An impala is an African antelope capable of a remarkable vertical leap. In one recorded leap, a 45 kg impala went into a deep crouch, pushed straight up for 0.21 s, and reached a height of 2.5 m above the ground. To achieve this vertical leap, with what force did the impala push down on the ground? What is the ratio of this force to the antelope's weight?
A 200 ohm resistor is connected to an AC source with peak emf = 10V. What is the peak current through the resistor if the emf frequency is a) 100 Hz b) 100 kHz?
The peak current through 200 ohm resistor for both the cases 50mA.
The number of turns times the size of the coil times the magnetic field's intensity times the angular speed equals peak emf.
The largest amount of current that an output is capable of providing for brief periods of time is known as the peak current. When an electrical device or power source is turned on for the first time, a large initial current known as the peak current flows into the load, starting at zero and increasing until it reaches a peak value.
Formula for the peak current is
peak current=[tex]\frac{peak voltage}{resistance}[/tex]
As in the formula it does not matter whether frequency changes or not.
So, peak current in both cases will be
peak current=[tex]\frac{10}{200}[/tex]
peak current=50mA
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When providing transcutaneous pacing, the appearance of wide QRS complexes and tall, broad T waves after each pacing spike confirms that mechanical capture has been achieved.TrueFalse
The sentence is true. When providing transcutaneous pacing, the appearance of wide QRS complexes and tall, broad T waves after each pacing spike confirms that mechanical capture has been achieved.
Transcutaneous pacing is a method of providing cardiac pacing by delivering electrical impulses through the skin to the heart. When mechanical capture is achieved, it means that the electrical impulse is strong enough to cause the heart muscle to contract.
This is confirmed by the appearance of wide QRS complexes and tall, broad T waves on an electrocardiogram (ECG) after each pacing spike. The QRS complex represents ventricular depolarization, and the T wave represents ventricular repolarization.
Wider QRS complex and taller T waves indicate that the electrical impulse is strong enough to depolarize the entire ventricular muscle, resulting in a stronger mechanical contraction.
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a special electronic sensor is embedded in the seat of a car that takes riders around a circular loop-the-loop ride at an amusement park. the sensor measures the magnitude of the normal force that the seat exerts on a rider. the loop-the-loop ride is in the vertical plane and its radius is 15 m. sitting on the seat before the ride starts, a rider is level and stationary, and the electronic sensor reads 720 n. at the top of the loop, the rider is upside down and moving, and the sensor reads 390 n. what is the speed of the rider at the top of the loop?
In the seat of a vehicle that transports passengers around a circular circle at an amusement park is a specific electronic sensor. The sensor calculates.
What do you mean by electronics?
Definition. To control the flow of electric impulses again for purposes of processing information and system control, electronic devices are necessary. The two most notable examples are transistors and diodes. Integrated circuits are compact packages that may hold numerous electronic devices that are typically small in size.
Why is technology employed today?
Through the usage of personal computers and mobile phones, it improved people's lives and shortened the distances between different countries. It improved discussion and opened up access to languages, some of which depended on translation features, while also facilitating communication between people, communities, and nations.
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If the atomic radius of gold is 0.144 nm, calculate the volume of its unit cell in cubic meters (m^3)
If the atomic radius of gold is 0.144 nm, then the volume of its unit cell in cubic meters is 6.7847 × 10⁻²⁹ m³.
What is atomic radius?A chemical element's atomic radius, which is typically the average or typical distance between the nucleus's centre and the outermost isolated electron, serves as a gauge for the size of its atom. There are numerous non-equivalent definitions of atomic radius because the boundary is not a clearly defined physical entity.
Van der Waals radius, ionic radius, metallic radius, and covalent radius are the four most frequently used definitions of atomic radius. The atomic radius is typically measured in a chemically bonded state because it is difficult to isolate individual atoms to measure their radii separately.
However, theoretical calculations are easier when considering isolated atoms. A variety of definitions result from the dependencies on environment, probe, and state.
Atomic radius of gold (r) = 0.1442nm
= 0.1442 × 10⁻⁹m
Gold is FCC then
FCC unit cell side a = [tex]2\sqrt{2r}[/tex]
Unit of the volume v = a³ = ( [tex]2\sqrt{2r}[/tex] )
Unit cell volume (V) = 16[tex]\sqrt{2\times r^{3}[/tex]
volume of unit cell =6.7847 × 10⁻²⁹ m³
Thus, If the atomic radius of gold is 0.144 nm, then the volume of its unit cell in cubic meters is 6.7847 × 10⁻²⁹ m³.
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a distracted student drops their water bottle. if the bottle is dropped from rest at a height of 1.2 m above the ground, how long will it take to hit the ground?
If the bottle is dropped from rest at a height of 1.2 m above the ground, it will take about 0.49 seconds for the water bottle to hit the ground by using the equation of motion.
To calculate the time it will take for the water bottle to hit the ground, we need to use the equation for motion under constant acceleration, which is the equation t = (2d/g)(1/2) is derived from the kinematic equation of motion, which relates the distance fallen (d), the initial velocity (vo), the final velocity (vf), acceleration (a), and time (t) in the following way: vf2 = 2a*d + vo2
t = (2*d / g)^(1/2)
where t is the time, d is the distance fallen, and g is the acceleration due to gravity (approximately 9.8 m/s2).
Plugging in the given values, we get:
t = (2 * 1.2 m) / 9.8 m/s^2
t = 0.49 s
So it will take about 0.49 seconds for the water bottle to hit the ground if it's dropped from a height of 1.2 meters above the ground.
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Question 10
6.25 pts
A cannon is fired horizontally at 337 m/s off of a 80 meter tall, sheer vertical cliff. How many
seconds
will have elapsed before the cannonball strikes the ground?
Answer: 4 seconds are elapsed before the cannonball strikes the ground.
Explanation:
Height of tower (h) = 80m
Initital velocity in x-dir ([tex]u_{x}[/tex]) = 337m/s
Initial velocity in y-dir ([tex]u_{y}[/tex]) = 0m/s
Time of flight (T)
Gravitational acceleration (g) = 10 m/s
Using second equation of motion,
h = [tex]u_{y}[/tex] + [tex]\frac{1}{2}[/tex]g[tex]t^{2}[/tex]
80 = [tex]\frac{1}{2}[/tex]×10×[tex]T^{2}[/tex]
[tex]T^{2}[/tex] = 16
T = 4s
a car is driven 125 km west and then 75 km southwest. what is the magnitude of the displacement (in km) of the car from the point of origin?
All objects close to the earth are subject to the force of weight. You may determine an object's weight by multiplying its mass by the gravitational acceleration it experiences.
What does physics mean by acceleration?
The rate at which the velocity changes is the precise definition of acceleration. According to the aforementioned equation, the acceleration,, is determined by the ratio of the time it took for the speed to change from to and the difference between both the starting and final speeds,,.
How much of an acceleration is there?
The rate at which velocity changes is called acceleration. The rate at which of velocity in both size and direction provides the amount of the acceleration at every point on a trajectory.
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what is the speed of sound in kilometers per hour?
Answer:
Speed of Sound = 1234.9 kilometers per hour
Explanation:
Depends strongly on temperature and medium; the above answer assumes that the sound wave is propagating through an elastic medium at 20° C (68° F)
a 435n box is sliding down a 40.0 inclined plane. if the acceleration of the box is 0.250 m/s^2 what is the force of friction acting on the bix
W=mg=435NW=mg=435N is the weight of the box. If the box accelerates by 0.250 m/s2, the plane is inclined. much friction is there on the bix
What do you call friction?The force of friction is influenced by outside forces. The two elements that friction depends on are as follows: 1. Regarding the makeup of the contact objects in touch. The two sides that are in touch with one other's depend on each other for friction.
What makes friction popular?In mathematics, the portion or component of the complete item is represented by a fraction.
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A well lagged bar of 100cm has its end maintained at 90°C and 50°C respectively what is the temperature at a point 50cm from the hotter end.
a ladybug is moving at a speed of one centimeter per second. she begins to decelerate at a
rate of -0.25 centimeters per second squared until she comes to rest. how much distance does
the ladybug cover from the moment she begins to decelerate until the moment she comes to
rest?
Ladybug covers distance from the moment she begins to decelerate until she comes to the rest. The deceleration is 0.25m/ s2.
What is Work energy theoram?The net work done on a body is equal to change in kinetic energy of the body. This is called as Work-energy theorem.
Numerically. To find the distance, which Ladybug cover from the moment she begins to decelerate until she comes to the rest, use the formula.
Where, is final velocity, is initial velocity, is acceleration and is displacement. After moving, ladybug comes to the rest, so final velocity, Placing the value of the given initial velocity, , acceleration.
Therefore, Ladybug covers distance from the moment she begins to decelerate until she comes to the rest.
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Compared to their values on Earth, on another planet yourmass would be the same but your weight would be different.
Your bulk and weight would be different on a different planet compared to how they are on Earth.
The correct option is A.
What do you mean by mass?This was the most basic characteristic of matter and is one of the essential building blocks of physics. The term "mass" refers to a body's total amount of matter. The kilo is the SI unit of mass (kg). A body's bulk remains constant throughout time.
How is mass determined?Scientists frequently use balances to quantify mass. Using an electronic balance or a beam balance, one may directly determine the mass of solids. A liquid's mass may be calculated by measuring its volume and using the density table to determine the liquid's density. The kg is the SI mass unit (Kg).
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The complete question is -
Compared to their values on Earth, on another planet your
(a) mass and weight would both be the same.
(b) mass would be the same but your weight would be different.
(c) weight would be the same but your mass would be different.
What is the exact circumference of a circle with a radius of 17 mm? responses 8.5π mm 8.5 pi, mm 17π mm 17 pi, mm 34π mm 34 pi, mm 68π mm
The circumference of a circle of radius 17 mm is 34π or 34 × 3.14 = 106.76 mm.
What is the circumference?The length of a circular or other curved geometrical object is referred to as its circumference. It is the edge of a surface like this with two dimensions, calculated linear in one dimension. A circle's circumference, which is equivalent to the length of it's own edge measured in linear distance, serves as a measure of length. In order to measure the circumference of a circle in the metric system, a most common units are millimetre, centimeter, and meter, but in the imperial system, the most common units include inch, foot, and yard.
Given :
Radius of circle = 17mm
By using the formula of circumference -
circumference = 2 × π × r
circumference = 2 × π × 17
circumference = 34 π
or 34 × 3.14 = 106.76 mm
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You have a u haul truck, explain why you would use the Ramp on the truck…
if it didn't have a ramp it would be harder to load the truck.
how far from the lens does the pencil need to be for the magnification m to be -1?
For a lens with a negative focal length, the image formed by an object placed at the focal point will be a virtual, inverted image with a magnification of -1. The object needs to be placed at the distance of the negative focal length in front of the lens for the magnification to be -1.
What is magnification?Magnification is the capability to make small objects appear larger. For instance using it to make a microscopic organism observable. Resolution is the capability to differentiate two objects from each other.
Why do lens posses a positive magnification?A concave lens always creates a erect, virtual, and reduced image irrespective of its position. Hence, the magnification is always positive, but less than 1.
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in a pairs figure skating competition, a 65 kg man and his 45 kg female partner stand facing each other on skates on the ice. if they push apart and the woman has a velocity of 1.5 m/s eastward, what is the velocity of her partner? (neglect friction.)
Her partner's final velocity is roughly -1.04 m/s, or 1.04 m/s in the opposite direction from her motion.
How do velocity and speed differ?
Velocity is the pace and direction of an object's movement, whereas speed is the time rate at which an object is travelling along a path. In other words, velocity is a vector, whereas speed is a scalar value.
What is velocity, for instance?
Velocity can be defined as the rate at which something moves in a specific direction. as the speed of a car driving north on a highway or the pace at which a rocket takes off.
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the skaters then rotate around the center of the pole. assume that the friction between skates and ice is negligible. what are (a) the radius of the circle, (b) the angular speed of the skaters, and (c) the kinetic energy of the two-skater system? next, the skaters pull along the pole until they are separated by 1.0 m. what then are (d) their angular speed and (e) the kinetic energy of the sy
Following are the different values asked in the question-
The kinetic energy of the two-skater system is 8.8 102J..
Each skater weighs m = 50 kg.
Two skaters are separated by a distance of d = 3m.
Each skater moves at a velocity of 1.4 meters per second.
The diameter of the circle formed by the separation of two stars. Then, we may determine the angular speed by using this and the relationship between v, r, ω. To get the kinetic energy of the two-skater system, enter the information into the rotating K.E. formula. As you get closer, continue the same process to locate the.
Equations: V = r ω
KE = 1/2 I ω²
Given that both skaters have the same mass and opposite, equal, and accelerating velocities, their total linear momentum is zero. As a result, the system's center of mass stays fixed at the pole's center.
They are 3 meters apart, and that distance will remain constant as it is the diameter of the circular motion they will be performing.
Consequently, the circular motion's radius is 1.5m.
Given that both skaters have the same mass and opposite, equal, and accelerating velocities, their total linear momentum is 0
As a result, the system's center of mass stays fixed at the pole's center.
They are 3 meters apart, and that distance will remain constant as it is the diameter of the circular motion they will be performing.
Consequently, the circular motion's radius is radius is 1.5m.
The angular speed of the skaters is
ω = 0.93 rad/s
The two-skater system's moment of inertia is I = (mr2) I = 2 (50) (1.5)2 I = 225 kgm 2.
The two-skater system's kinetic energy is K.E = I2 K.E = (225) (0.93)2 K.E. = 98J.
Step 6: When skaters pull along the pole until they are separated by 1.0 m, determine their angular speed (d)
The radius of the rotating motion would be r f = = 0.5m if the skaters drag the pole till they are separated by.
The two-skater system's M.I would then be
If = 25kgm2 and If = 2 (50) (0.5)2.
I0; = I f W f is the definition of the law of conservation of angular momentum.
As a result, the skaters' angular speed is given by f= If = 2250.93 25 of 8.4 rad/s =
Step 7: Determine the system's kinetic energy when skaters drag the pole until they are separated by 1.0 m. (e)
The two-skater system's kinetic energy is given by K.E = I2 K. E f = (25) (8.4)2 K. E. 8.8 102J.
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Practicals on simple machines
Answer:
1. Pulley System - Pulleys can be used to effectively transfer force, change the direction of a force and/or increase the power of a force. This can be used to teach the students how basic machines can be used to help in everyday life.
2. Lever System - Levers can be used to teach students about how their daily tasks can be made easier using a machine. It also helps illustrate the law of the lever.
3. Wheel and Axle - This machine allows students to learn how a wheel and axle can increase the torque or rotational force on an object thus allowing heavy loads to be moved with less effort.
4. Inclined Plane - This machine teaches students about how even large objects can be moved with a ramp as its sloped shape reduces the force needed to move objects.
5. Screw -The screw allows students to learn how force is transferred from one point to another. It also introduces them to concepts such as rotational force and torque.
An object is acted upon by two forces 3N and 5N inclined at 60 degree to each other. if the object is moved through a distance of 6m by the resultant force, the workdone is
Answer:
48 J
Explanation:
Work Done = Force X Distance moved in a stated direction
Work Done = 3N + 5N X 6m
Work Done = 48 J
Two forces 3N and 5N acting on an object are inclined at 60 degrees to each other. If the resultant force moves the object a distance of 6m, the work done is 35.92 Joules (J).
In physics, work is defined as the transfer of energy that occurs when a force is applied to an object and the object is displaced in the direction of the force. Mathematically, work done is the product of the force applied and the distance moved in the direction of the force.
Work is a scalar quantity and is measured in joules (J) in the International System of Units (SI). When a force is applied to an object and there is no displacement, no work is done. Similarly, if there is displacement but no force acting on the object, no work is done.
Here in the Question,
To find the work done, we need to first find the resultant force.
Using vector addition, we can find the magnitude and direction of the resultant force:
cos(60) = adjacent/hypotenuse
adjacent = cos(60) x 5N = 2.5N
sin(60) = opposite/hypotenuse
opposite = sin(60) x 5N = 4.33N
The horizontal component of the 3N force is 3N cos(60) = 1.5N
The vertical component of the 3N force is 3N sin(60) = 2.6N
The horizontal component of the 5N force is 5N cos(30) = 4.33N
The vertical component of the 5N force is 5N sin(30) = 2.5N
The horizontal component of the resultant force is 4.33N + 1.5N = 5.83N
The vertical component of the resultant force is 2.5N + 2.6N = 5.1N
The magnitude of the resultant force is given by the Pythagorean theorem:
Resultant force = sqrt(5.83^2 + 5.1^2) = 7.59N
The direction of the resultant force is given by:
tan(theta) = opposite/adjacent
theta = tan^-1(5.1/5.83) = 43.1 degrees
The work done is given by:
work = force x distance x cos(theta)
work = 7.59N x 6m x cos(43.1) = 35.92 Joules (J)
Therefore, the work done is 35.92 Joules (J).
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For the next experiment we will be using an ultrasonic sensor. This works by emitting a sound wave from a speaker and bouncing it off an object. The delay between the sending and retrieval of this sound wave allows us to determine the distance to the object. Assuming a speed of sound of 343 m/s, answer the questions below and show your work: o How far in centimeters does a sound wave travel in 3000 microseconds? o How long in microseconds does it take a sound wave to travel 30 cm?o Truncate your answer to the first decimal place. How long in microseconds does it take for a sound wave generated to bounce and get back from an object 50 cm away?
A) To find the distance a sound wave travels in a certain time, we can use the formula:
distance = speed x time
Given that the speed of sound is 343 m/s and the time is 3000 microseconds, we can calculate the distance as:
distance = 343 m/s x (3000 x 10^-6 s) = 1.029 m
converting this to cm we get:
distance = 1.029 m x 100 cm/m = 102.9 cm
B) To find the time it takes for a sound wave to travel a certain distance, we can use the formula:
time = distance/speed
Given that the distance is 30 cm and the speed of sound is 343 m/s, we can calculate the time as:
time = 30 cm / 343 m/s = 0.00087 s
converting this to microseconds we get:
time = 0.00087 s * 10^6 microseconds/s = 87 microseconds
C) The time it takes for the sound wave to travel to the object and back is twice the time it takes for the sound wave to travel to the object alone. Given that the distance is 50 cm and the speed of sound is 343 m/s, we can calculate the time as:
time = 2 * (50 cm / 343 m/s) = 2 * 0.000146 s = 0.000292 s
converting this to microseconds we get:
time = 0.000292 s * 10^6 microseconds/s = 292 microseconds
So it takes 292 microseconds for a sound wave generated to bounce and gets back from an object 50 cm away.
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how much should a spring of indefinite length be compressed to have a potential energy equivalent to a ball of mass 6 kg raised to a height of 120 m above the ground?
According to the question, 12 m should a spring of indefinite length be compressed to have a potential energy equivalent to a ball of mass 6 kg raised to a height of 120 m above the ground.
How is potential energy defined?Potential energy is the energy of energy stored that depends on how various system elements interact with one another.
Potential Energy of ball = m x g x h
m= 6 kg
g= 10 m/s^2
h= 120 m
PE = 7200 J
Potential Energy of spring = 1/2 x k x d^2
k = 100 N/m
as we know that
Potential Energy of spring = Potential Energy of ball
1/2 x k x d^2 = m x g x h
d = 12 m
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a cheetah can maintain a constant acceleration of 10.0 m/s2 for a time interval of 1.30 seconds. if the cheetah starts from rest, how long will it take the cheetah to move at 25.0 mph?
it will take the cheetah 1.118 seconds to move at 25.0 mph.
What is kinematic equation?Kinematic equations are mathematical equations used in physics to describe the motion of objects. These equations are used to solve problems involving velocity, acceleration, and displacement. The equations rely on the use of Newton's laws of motion, which state that the acceleration of an object is equal to the sum of all the forces acting upon it, divided by its mass.
First let's convert 25.0 mph to m/s:
25 mph = 11.176 m/s
Now we can use the kinematic equation for uniform acceleration:
vf = vi + at
where vf is the final velocity, vi is the initial velocity (which is 0 m/s since the cheetah is starting from rest), a is acceleration (10.0 m/s2), and t is the time interval.
11.176 = 0 + (10.0)(t)
t = 1.118 seconds
Therefore, it will take the cheetah 1.118 seconds to move at 25.0 mph.
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what is the resistance of a 1500 w (120 v ) hair dryer?
The resistance of a 1500 watt (120 volt) hair dryer is 12 ohms.
What is resistance?Resistance is an opposition or a refusal to accept or comply with something. It is the ability to withstand or overcome something, such as an opposing force or influence. Resistance can also refer to a process of gradual change or transformation over time. Resistance is often seen in the form of protests, civil disobedience, or other forms of dissent. Resistance can also refer to the refusal to accept something as true or valid, such as a political or social ideology.
This can be determined by using Ohm’s Law, which states that voltage (V) is equal to the current (I) multiplied by the resistance (R). Therefore, if the voltage is 120 volts and the wattage is 1500 watts, the resistance can be calculated as follows: R = V/I = 120/1500 = 0.08, or 12 ohms.
It is important to note that the above calculation only applies to a hair dryer that runs on direct current (DC). If the hair dryer is running on alternating current (AC), the resistance may be slightly different. The resistance of an AC-powered hair dryer can be determined by measuring the current and voltage with a multimeter.
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What’s the answers ?
The responses for the parameters of the block-spring system are;
(a) 1161.98
(b) 40.8 J
(c) 6.86 kg
(d) 2,75 m
(e) 25.9 J
(f) 14,9 J
(g) -0,224 m
What is the type of motion of a block spring system?The motion of a block-spring system is a simple harmonic oscillatory motion.
(a) The formula for the total kinetic energy is; K. E = (1/2)·k·x²
Where;
k = The spring constant
x = The diatplacemtent of the spring
The total mechanical energy, E = 40.8 J
The displacement of the spring, x = 0.265 m
Therefore;
40.8 = (1/2)·k·x²
k = 2 × (40.8/0.265²) ≈ 1161.98
The spring constant is about 1161.98 N/m
(b) The kinetic energy of the system at the equilibrium point is the same as the total energy or 40.8 J
(c) Kinetic energy, K.E. = (1/2)·m·v²
m = K.E./((1/2)·v²)
m = 10.8/(1/2×3.45²) ≈ 6.86
The mass is about 6.86 kg
(d) When the displacement is 0.160 m. we get;
What Is The Speed Of The Block When Irs Displacement Is 0.160 m
ω = √(k/m)
v = ω·√(A² - x²)
v = √(1161.98/6.86) × √(0.265² - 0.160²) ≈ 2.75
The velocity when the displacement is 0.160 m. is about 2.75 m/s
(e) The kinetic energy when the displacement is 0.160 m. is therefore;
K.E. = (1/2) × 6.86 × 2.75² ≈ 25.9
The kinetic energy when the displacement is 0.160 m. is about 25.9 J
(e) The total mechanical energy during the motion of the spring, is 40.8 J, we get;
P,E. = E - K,E,
The potential energy in the string when the displacement is 0.160 meters is therefore; P.E. = 40.8 - 25.9 = 14.9
The potential energy is 14.9 J
(g) Energy lost = 11.7 J
0.5 × 6.86 × ((1161.98/6.86) × (0.265² - x²) = 11.7
Solving, we get;
x ≈ -0.224 m
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The aluminum foil on a certain roll has a total area of 18.5m^2 and a mass of 1275-g. Using a density of 2.7g/cm^3 for aluminum, determine the thickness in millimeters of the aluminum foil.
The aluminum foil is 2.5 millimeters thick. For instance, a certain roll measures 18.5 m^2 in size and weighs 1275 g. making use of the 2.7g/cm^3 density of aluminum.
Its density is defined as its mass per unit of volume (also known as specific mass or volumetric mass density). Although density can also be symbolised by the Latin letter D, the most typical mark is (the lower case Greek letter rho). The mathematical definition of density is mass divided by volume. Aluminum foil, usually referred to as aluminium foil in North American English, is a thin metal leaf made of aluminium that has a thickness of less than 0.2 mm (7.9 mils), but micrometres (0.24 mils) are also widely used. It is commonly known as tin foil.
In terms of thickness, 1275/(18.5*104*2.7*10-3) = 2.5mm.
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High-speed stroboscopic photographs show the head of a 220g golf club is traveling at 49.9 m/s just before it struck a a 45.8g gold ball at rest on a tee. After the collision, the club head travels (in the same direction) at 33.9 m/s. Find the speed of the golf ball immediately after impact.
Please show your work and use this formula: m1v1+m2v2=m1v1f+m2v2f
Answer:
76.9 m/s
Explanation:
You want the speed of a 45.8 g golf ball after it has been hit by a 220 g club traveling 49.9 m/s, if the club is traveling 33.9 m/s in the same direction after the collision.
MomentumThe conservation of momentum requires ...
m1·v1 +m2·v2 = m1·v1f +m2·v2f
Rearranging this equation, we get ...
m1·(v1 -v1f) = m2·(v2f -v2)
When v2 = 0, we can solve for v2f:
m1(v1 -v1f)/m2 = v2f . . . . . . . divide by m2
ApplicationIn the given scenario, we have ...
m1 = 220 gm2 = 45.8 gv1 = 49.9 m/sv1f = 33.9 m/sThe speed of the driven golf ball will be ...
v2f = (220)(49.9 -33.9)/45.8 ≈ 76.9 . . . m/s
The speed of the golf ball after impact will be 76.9 m/s.
what temperature in celsius would be equal to 100 degrees fahrenheit?
A temperature of 100 degrees Fahrenheit is equivalent to 37.78 degrees Celsius.
The conversion formula between Fahrenheit and Celsius is as follows:
°C = (°F - 32) x (5÷9)
So, to convert 100 degrees Fahrenheit to degrees Celsius, we can plug in 100 for °F and solve for °C:
°C = (100 - 32) x (5÷9) = 68 x (5÷9) = 37.78
It is important to note that the degree unit size (Fahrenheit and Celsius) is not the same, and thus the numerical value of the temperature measured in those scales does not match one to one. The freezing point of water is 32 degrees Fahrenheit (0 degrees Celsius) and the boiling point is 212 degrees Fahrenheit (100 degrees Celsius). This means that 100 degrees Fahrenheit is considered a "hot" temperature, but 37.78 degrees Celsius is considered a "normal" room temperature.
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when a falling meteoroid is at a distance above the earth's surface of 3.30 times the earth's radius, what is its acceleration due to the earth's gravitation?
Answer:
Approximately [tex]0.515\; {\rm m\cdot s^{-2}}[/tex] (assuming that all other forces are negligible).
Explanation:
Look up the following quantities:
Gravitational constant: [tex]G \approx 6.6743 \times 10^{-11}\; {\rm m^{3}\cdot kg^{-1}\cdot s^{-2}}[/tex].Mass of the Earth: [tex]M \approx 5.792 \times 10^{24}\; {\rm kg}[/tex].Radius of the Earth: [tex]R \approx 6.371 \times 10^{6}\; {\rm m}[/tex].At a distance of [tex]r[/tex] from the center of the Earth, the magnitude of the gravitational field strength of the Earth would be:
[tex]\begin{aligned} g &= \frac{G\, M}{r^{2}}\end{aligned}[/tex].
In this question, the asteroid is at [tex]3.30\, R[/tex] above the surface of the Earth. The actual distance between the asteroid and the center of the Earth would be [tex]r = (3.30 + 1)\, R[/tex].
Thus, at the current position of this asteroid, the magnitude of the gravitational field of the Earth would be:
[tex]\begin{aligned} g &= \frac{G\, M}{r^{2}} \\ &= \frac{G\, M}{((3.30 + 1)\, R)^{2}} \\ &\approx \frac{(6.6743 \times 10^{-11}\; {\rm m^{3}\cdot kg^{-1}\cdot s^{-2}})\, (5.792 \times 10^{24}\; {\rm kg})}{((3.30 + 1)\, (6.371 \times 10^{6}\; {\rm m}))^{2}} \\ &\approx 0.515\; {\rm m\cdot s^{-2}}\end{aligned}[/tex].
Assume that the gravitational attraction from the Earth is the only force on this asteroid. Acceleration of the asteroid would be equal to the gravitational field strength: approximately [tex]0.515\; {\rm m\cdot s^{-2}}[/tex].
