Answer:
The car has approximately 1.42 × 10^6 J of energy when it moves at 101 miles per hour.
Explanation:
First, we need to convert the initial velocity and kinetic energy to SI units:
Initial velocity: 32 miles per hour = 14.3 meters per second (rounded to 2 decimal places)
Kinetic energy: 5 × 10^5 J (given)
Next, we can use the formula for kinetic energy:
KE = (1/2)mv^2
where KE is the kinetic energy, m is the mass of the car, and v is the velocity of the car.
Solving for mass:
m = 2KE/v^2
Substituting the given values:
m = 2(5 × 10^5 J) / (14.3 m/s)^2 ≈ 1569.93 kg (rounded to 2 decimal places)
Now, we can use the same formula to calculate the kinetic energy of the car when it moves at 101 miles per hour (rounded to 2 decimal places):
KE = (1/2)mv^2 = (1/2)(1569.93 kg)(45.06 m/s)^2 ≈ 1.42 × 10^6 J
Therefore, the car has approximately 1.42 × 10^6 J of energy when it moves at 101 miles per hour.
A rocket at rest on the ground with initial mass 20,000 kg, 80% of which is fuel, burns 200kg/s as it flies
directly upwards. The exhaust gas exits the rocket at a relative speed of 1.80 km/s. Find (a) the thrust of
the rocket, (b) how long it takes to exhaust its fuel, and (c) the rocket’s speed at the end of its engine burn.
Assume g is constant and neglect air resistance.
For Part A I got: 360,000 Newtons, Part B: 20 Seconds, Part C 205.658 m/s
Are my answers correct?
3.89 km/s is the rocket's final engine burn speed.
Calculation-The rocket equation can be used to determine the rocket's thrust:
Thrust is calculated as follows: (final mass flow rate minus initial mass flow rate) x (exhaust gas mass flow rate x exhaust gas velocity)
The initial mass flow rate is 16,000 kg/s (0.8 x 20,000 kg).
The final mass flow rate is equal to 20,000 kg - 200 kg/s x t, where t is the engine's burn period.
We obtain the following by substituting the values in the question:
Thrust equals 360,000 N when calculated as (200 kg/s x 1.8 km/s + (20,000 kg - 200 kg/s x t - 16,000 kg) x 1.8 km/s)
(b) The time it takes to exhaust the fuel can be calculated by equating the initial and final masses:20,000 kg - 200 kg/s x t = 0.2 x 20,000 kg
t = 20 seconds.
(c) The rocket equation can be used to determine the rocket's speed at the conclusion of its engine burn:
V is equal to (exhaust velocity) x ln[(initial mass)/(final mass)].
The rocket's final mass, which is what remains after all of its fuel has been consumed, is as follows:
final mass = (mass of rocket) - (mass of fuel)
final mass = 20,000 kg - 16,000 kg
final mass = 4,000 kg
Δv = 1.80 km/s x ln[(20,000 kg) / (4,000 kg)]
Δv = 1.80 km/s x ln(5)
Δv = 3.89 km/s
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Difference between lava and magma.(level is grade 4)
Answer: lava is basically what is outside of the earth's surface. And magma is what's inside the earth's surface.
Explanation:
Scientists use the term magma for molten rock that is underground and lava for molten rock that breaks through the Earth's surface.
Create and describe a scenario in which the forces acting on an object are unbalanced. Explain how you know the forces are unbalanced.
For your scenario, explain how Newton's third law of motion describes the forces involved.
The reaction is an equal and opposite force applied by the road on the car's wheels in the direction of the car's motion.
What is Unbalanced Force?
Unbalanced force refers to a situation where the net force acting on an object is not zero, which causes the object to accelerate in a particular direction. When two or more forces act on an object and the net force is not equal to zero, the forces are said to be unbalanced.
Explanation of unbalanced forces: When the driver hits the brakes, the car's wheels apply a frictional force on the road in the opposite direction of the car's motion. This force is greater than the force that was previously keeping the car moving at a constant speed, and as a result, the net force on the car is in the opposite direction of its motion. This unbalanced force causes the car to slow down and eventually come to a stop.
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wich the following hasta the most momentum?
A)50 g bullet moving at 200m/s
B)50kg boy running at 8 m/s
C)1000 kg automobile moving at 4m/s
D1,000,000 kg Cruise ship docked in a harbor
Answer for A) momentum = 10 N/s B) momentum = 400 N/s C) momentum = 4000 N/s D) momentum = 0 N/s. Hence, the option C has the most momentum.
To determine which of the given options has the most momentum, we need to calculate the momentum of each object using the formula:
momentum = mass x velocity
A) 50 g bullet moving at 200 m/s:
mass = 50 g = 0.05 kg
velocity = 200 m/s
momentum = 0.05 kg x 200 m/s = 10 N/s
B) 50 kg boy running at 8 m/s:
mass = 50 kg
velocity = 8 m/s
momentum = 50 kg x 8 m/s = 400 N/s
C) 1000 kg automobile moving at 4 m/s:
mass = 1000 kg
velocity = 4 m/s
momentum = 1000 kg x 4 m/s = 4000 N/s
D) 1,000,000 kg Cruise ship docked in a harbor:
mass = 1,000,000 kg
velocity = 0 m/s (since the ship is docked)
momentum = 1,000,000 kg x 0 m/s = 0 N/s
Therefore, option C, the 1000 kg automobile moving at 4 m/s, has the most momentum with a value of 4000 N s. This is because momentum is directly proportional to both mass and velocity. The greater the mass and velocity of an object, the greater its momentum will be.
Option A, the 50 g bullet moving at 200 m/s, has a smaller momentum compared to the others due to its low mass despite having a high velocity.
Option B, the 50 kg boy running at 8 m/s, has a higher momentum than the bullet but lower than the automobile because of its higher mass but lower velocity.
Lastly, option D, the 1,000,000 kg Cruise ship docked in a harbor, has zero momentum since it is not moving (velocity is zero).
The momentum of an object is an important concept in physics that describes the quantity of motion possessed by it. It is determined by the product of mass and velocity, and the object with the highest mass and velocity has the greatest momentum.
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use the bamboo framed bike to describe newton's second law of motion and the relationships that exist between force,mass and acceleration
Answer: The acceleration of an object depends directly upon the net force acting upon the object, and inversely upon the mass of the object. As the force acting upon an object is increased, the acceleration of the object is increased. As the mass of an object is increased, the acceleration of the object is decreased
A 1 kg block is released from the rest from the top of an incline of height h = 1 m (point A) as shown in the figure. The block travels down the incline, passes over a horizontal surface and stops at point C which is x = 1 m from the bottom of the incline (point B). What is the coefficient of kinetic friction between the block and the sliding surface? (The coefficients of kinetic friction between the block and incline and the block and horizontal surface are the same). The incline angle q = 45.
The coefficient of kinetic friction between the block and the surface is 0.5.
What is the coefficient of kinetic friction?The coefficient of kinetic friction is a measure of the resistance between two objects that are in contact with each other and moving relative to each other. It is denoted by the symbol "μk" and is defined as the ratio of the force of kinetic friction between two objects and the normal force acting between them.
Here the block was initially at rest and after travelling some distance it came to rest, therefore change in kinetic energy ∆K=0
Therefore mgh = unghcotx - umgx = 0
where h = 1m, x = 1m
u= 1 / 1+1
= 0.5
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True or false a rare faction is the area of a sound wave where particles are less dense
Answer:
yes
Explanation:
A rare fraction is the area of a sound wave where the particles are less dense because it's moving through the air made of alternating areas of higher and lower density
Calculate the acceleration of a racecar driver who can accelerate from 0 m/s to 90 m/s in 3 seconds.
Answer:30m/s square
Explanation: V-VO = V
T T
\overline{a} = average acceleration
v = final velocity
v_0 = starting velocity
t = elapsed time
=90-0 =30m/s square
3
Write a 16 line poem that describes centripal force utilizing all key concepts and terms. physics pls
A force known as centripetal force causes centripetal acceleration.
What exactly is centripetal force?An object must experience a force directed towards the centre of the circle in order to travel evenly in a circle, because all things moving in uniform circular motion accelerate towards the centre. Its motion is caused by centripetal force. Gravity creates centripetal force in the event of orbiting satellites such as the moon orbiting the earth or the earth orbiting the sun. As athletes spin a huge ball on a chain, such as in the Olympic hammer throw, they generate centripetal force, which is then transmitted through the chain.
Newton's second law states that force and acceleration are connected by the formula F=ma. We already have formulas that express the centripetal acceleration relationships, so we can easily tweak them to demonstrate the relationships.
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how much pressure is applied to the ground by a 90 kg man who is standing on square stilts that measures 0.04 m on each edge?
Answer units in Pa.
What is this pressure in pounds per square inch?
Answer in units Ib/in^2
The pressure applied by the man to the ground is 551812.5 Pa or 5.06 psi.
What exactly are pressure and its unit?Force applied per unit area is what is referred to as pressure. It can be calculated mathematically using P=FA, where F is the force acting perpendicular to surface area A. The pascal (Pa), or one newton per square metre (N/m 2), is the common unit of pressure.
The following formula can be used to determine how much pressure the man is exerting on the ground:
Pressure = Force / Area
where Area is the portion of the stilts that are in touch with the ground and Force is the man's weight.
Weight equals mass multiplied by gravitational acceleration yields the man's weight.
Weight = 90 kg * 9.81 m/s²
Weight = 882.9 N
The area of each stilt is:
Area = length * width
Area = 0.04 m * 0.04 m
Area = 0.0016 m²
As a result, the man is exerting the following pressure on the ground:
Pressure = Force / Area
Pressure = 882.9 N / 0.0016 m²
Pressure = 551812.5 Pa
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Draw the trajectory of the shuttlecock before it was smashed by the player and right after it went down on the other side of the net. You can use arrow line to indicate its direction.
The trajectory of the shuttlecock before it was smashed by the player and right after it went down on the other side of the net is shown in the attachment.
What is the trajectory of a projectile?The trajectory of a projectile is the path that an object takes through the air when it is thrown, and launched into the air.
The trajectory of a projectile is affected by several factors including the initial velocity of the object, the angle at which it was launched, the air resistance, and the gravitational pull of the earth.
In the absence of air resistance, the trajectory of a projectile would follow a parabolic path. However, in the presence of air resistance, the trajectory of the projectile will be affected by the forces of air resistance, and the path will deviate from a perfect parabolic shape.
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Carla, who has a mass of 51-kg, hits the 32-kg punching bag with a force of 2,071 N. What is the force that the punching bag applies to Carla?
Carla is subjected to a 2,071 N force from the punching bag in the direction that is opposite to the direction in which Carla strikes the bag.
StepsFor every action, there is an equal and opposite response, states Newton's third rule of motion.
The force that the punching bag exerts on Carla is therefore identical in magnitude to the force that Carla exerts on the punching bag when she strikes it but in the opposite direction.
Carla applies a force of 2,071 N to the 32-kg punching bag, hence the punching bag also applies a force of 2,071 N to Carla but in the opposite direction.
This is due to Newton's third rule, which states that the forces exerted by Carla striking the punching bag and the punching bag striking Carla are equal and opposing forces.
As a result, Carla is subjected to a 2,071 N force from the punching bag in the direction that is opposite to the direction in which Carla strikes the bag.
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a bungee jumper who is about to jump has her energy stored entirely as gravitational potential energy. After jumping she bounces up and down on the elastic bungee cord. what has happened to her initial gravitational potential energy when she reaches the bottom of this motion the first time after she jumps?
A. Most of her initial energy has been converted to kinetic energy.
B. Most of her initial energy has been converted to potential energy stored in the bungee cord.
C. Most of her initial energy has been depleted due to friction and air resistance.
D. Most of her initial energy has been converted back to gravitational potential energy.
Answer: D. Most of her initial energy has been converted back to gravitational potential energy. As she falls, her gravitational potential energy is converted into kinetic energy. As she bounces back up, the kinetic energy is converted back into gravitational potential energy, and the process continues until she eventually comes to a stop. Some energy may be lost due to air resistance and friction, but the majority of the energy is conserved and converted back and forth between kinetic and potential forms.
A ball is tossed up into the air and falls back down to the ground as it moves from point A to point E as seen in the picture below. When will the ball's potential energy be decreasing and its kinetic energy increasing?
Answer:
Energy = Potential Energy + Kinetic Energy
E = M g h + 1/2 M v^2
On the way up h (height) is increasing and the velocity v is decreasing.
Between C and E the given conditions hold
A 50.0-g
meter stick is balanced at its midpoint ( 50.0 cm
). Then, mass 1=0.200 kg
and mass 2=0.300 kg
are hung with light string from points at 1=20.0 cm
and 2=70.0 cm,
respectively, as shown in the figure. Define the counterclockwise direction to be positive.
Calculate the torque 0,1
acting on the meter stick due to 1,
the torque 0,2
due to 2,
the torque 0,stick
due to the weight of the meter stick, and the torque 0,pivot
due to the pivot, all about an axis pointing out of the screen at the 0.00-cm
point.
The torque 0,1 acting on the meter stick due to 1 is 3.92Nm.
The torque 0,2 acting on the meter stick due to 1 is 20.94Nm.
The torque 0,stick due to weight of meter stick is 2.45Nm.
The torque 0,pivot acting due to pivot is 0.
What is torque?The rotating equivalent of force is torque. The moment of force is another name for it (also abbreviated to moment). It illustrates how a force can cause a change in the body's rotational motion.
The definition of torque is the product of the force's perpendicular component's magnitude and the force's line of action's separation from the point being measured. Torque can also be understood in terms of the law of conservation of energy.
Using the formula:
τ= r × F
where,
τ is the torque,
F is the force and,
r is the distance of the line of action of a force from the point around which torque is being determined.
Substituting the values and solving for torque:
The torque 0,1 acting on the meter stick due to 1 is 3.92Nm.
The torque 0,2 acting on the meter stick due to 1 is 20.94Nm.
The torque 0,stick due to weight of meter stick is 2.45Nm.
The torque 0,pivot acting due to pivot is 0.
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How many kilocalories of heat does an expenditure of 477 kJ produce?
A magnetic field is the area around a magnet where it's force can be felt. Magnetic fields are invisible. How did part 1 of the Procedure and Data section provide evidence that magnetic fields exist?
Part 1
1. Tape one magnet to a smooth, flat surface. Place the other magnet on that surface 10 cm away, oriented so that its north pole is facing the south pole of the other magnet. Slowly push the free magnet toward the magnet that it taped down.
The Procedure and Data section provides evidence that magnetic fields exist by demonstrating the force exerted by a magnetic field on a nearby object. In this experiment, two magnets are used, and one magnet is taped down on a smooth.
What are magnets ?A magnet is an object that produces a magnetic field, which is a force that can attract or repel certain materials, such as iron, nickel, and cobalt. Magnets have two poles, called the north pole and the south pole, which are opposite in nature and attract each other, while like poles repel each other. This property of magnets is used in various applications, such as electric motors, generators, magnetic storage devices, and compasses. Magnets can be either natural, such as lodestone, or artificial, such as magnets made from iron, nickel, cobalt, or other magnetic materials.
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Attachment has the question, Thankyou
The magnitude of the car's centripetal acceleration will be equal to the magnitude of its tangential acceleration 12.5 seconds after starting.
Centripetal vs tangential accelerationThe centripetal acceleration, ac, of an object moving in a circular path of radius r and tangential speed v is given by:
ac = v^2/r
The tangential acceleration, at, is given by:
at = a
where a is the constant tangential acceleration.
Let's assume that the car starts at rest at the edge of the track, so its initial tangential speed, v0, is zero. Then the tangential speed of the car at time t is:
v = v0 + at = at
The time t when the magnitudes of ac and at are equal can be found by setting ac = at and solving for t:
ac = at
v^2/r = a
(at)^2/r = a
t = sqrt(ar/at)
Substituting r = 125 m and a = 1.5 m/s^2:
t = sqrt((1.5 m/s^2)(125 m)/(1.5 m/s^2)) = 12.5 s
Therefore, the magnitude of the car's centripetal acceleration will be equal to the magnitude of its tangential acceleration 12.5 seconds after starting.
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If the earth revolve around the sun, why we see the same stars every night in the same position.?
The stars are not fixed but they are just constantly moving. We see them in the same position every night because they seem to be very small to us and also due to the earth's revolution.
If you factor out the daily motion of the stars across the sky due to the earth's rotation, you end up with a pattern of stars that seems to never change. The stars seem so fixed that ancient sky-gazers mentally connected the stars into figures called constellations that we can still make out today. But in reality, the stars are constantly moving every time. They are just so far away that the eye without any instrument cannot see their movement. But sensitive instruments can detect their movement.
2. A person with a mass of 50 kg is driving her car at a velocity of 15m / s . The car is involved in a small collision, and the airbag is deployed. The airbag provides a stopping force of 1200 N. The person's final velocity is 0m / s . How long does it take for the person to be stopped by the airbag ?
Answer:
It takes approximately 0.625 seconds for the person to be stopped by the airbag.
Explanation:
We can use the formula for average acceleration to solve this problem:
a = (v_f - v_i) / t
where:
a = average acceleration
v_f = final velocity (0 m/s)
v_i = initial velocity (15 m/s)
t = time
We know that the airbag provides a stopping force of 1200 N, which is equal to the net force on the person-car system. We can use Newton's second law of motion to find the acceleration of the person:
F_net = ma
where:
F_net = net force (1200 N)
m = mass of person (50 kg)
a = acceleration
Solving for a, we get:
a = F_net / m
a = 1200 N / 50 kg
a = 24 m/s^2
Now we can substitute the values of a, v_f, and v_i into the formula for average acceleration and solve for t:
a = (v_f - v_i) / t
24 m/s^2 = (0 m/s - 15 m/s) / t
t = -15 m/s / 24 m/s^2
t = 0.625 s
Therefore, it takes approximately 0.625 seconds for the person to be stopped by the airbag.
The left-right reversal of an object is called (a) lateral inversion
(b) lateral reflection
(c) parallel inversion
(d) parallel reflection
The left-right reversal of an object is called as : (a) lateral inversion
What is meant by lateral inversion?Apparent reversal of mirror image's left and right when it is compared with the object is called as lateral inversion. Lateral means sideways. In plane mirror, each point on image is as far behind the mirror plane as the corresponding point on object is in front.
The phenomenon where left appears as the right and vice versa in a mirror is known as lateral Inversion.
Lateral inversion is the side ways reversal of image's left and right when compared to that of the object and lateral inversion is observed in images formed by plane mirror.
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The engines on an airplane cause the airplane to accelerate down the runway. The acceleration is 7.00 ft/s/s. How far does the airplane go in a time of 27 sec?
The distance travelled by the plane in 27 seconds, given that the acceleration of the plane is 7.00 ft/s/, is 2551.5 ft
How do i determine the distance travelled by the plane?The distance travelled by the plane in 27 seconds can be obtained as illustrated below:
Acceleration of plane (a) = 7.00 m/s/sInitial velocity of plane (u) = 0 ft/sTime taken (t) = 27 secondsDistance travelled by the plane (s) =?s = ut + 1/2at²
s = (0 × 27) + (1/2 × 7 × 27²)
s = 0 + (3.5 × 729)
s = 0 + 2551.5
s = 2551.5 ft
From the calculation made above, we can conclude that the distance travelled is 2551.5 ft
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Which is true about the bioelectrical impedance body composition test?
O The amount of fat will be miscalculated if the person is dehydrated.
O It uses electrodes to measure body fat in relation to lean body mass.
O It can be used to determine the location of fat in the body.
O The amount of water in the body does not affect the test.
Answer:
measures body composition based on the rate at which an electrical current travels through the body
Explanation:
Refer to the standard normal distribution. Find a z value such that the probability of obtaining a larger z value is:
a) 0.05.
b) 0.025.
c) 0.20
Answer:
Explanation:
a) To find a z value such that the probability of obtaining a larger z value is 0.05, we need to find the z value such that the area to the right of it is 0.05. Using a standard normal distribution table or calculator, we find that z = 1.645.
b) To find a z value such that the probability of obtaining a larger z value is 0.025, we need to find the z value such that the area to the right of it is 0.025. Using a standard normal distribution table or calculator, we find that z = 1.96.
c) To find a z value such that the probability of obtaining a larger z value is 0.20, we need to find the z value such that the area to the right of it is 0.20. This is equivalent to finding the z value such that the area to the left of it is 0.80. Using a standard normal distribution table or calculator, we find that z = 0.84 (rounded to two decimal places).
I need this today 15 points.
The entire distance that an object travels in a given amount of time is the definition of average speed for that object. Therefore, her average speed for the entire trip was 1.49 m/s.
What is the average speed of entire trip?
It is calculated by dividing the total distance something travels by the total amount of time it spends traveling.
average speed = total distance / total time
Now, let's find the total time. The time it takes to go from A to B is:
time = distance / speed = d / 2.3
The time it takes to go from B to A is:
time = distance / speed = d / 1.1
total time = d / 2.3 + d / 1.1
total time = (d * 1.1 + d * 2.3) / (2.3 * 1.1)
total time = (3.4d) / 2.53
Now, we can find the average speed:
average speed = 2d / [(3.4d) / 2.53]
average speed = (2 * 2.53) / 3.4
average sped = 1.49 m/s (rounded to two decimal places).
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A scale used to weigh fish consists of a spring hung from a support. The spring's equilibrium length is 10.0 cm. When a 4.0 kg fish is suspended from the end of the spring, it stretches to a length of 12.0 cm.
What is the spring constant k for this spring?
If an 8.0 kg fish is suspended from the spring, what will be the length of the spring?
.
Answer:
We can use Hooke's Law to find the spring constant k:
F = kx
where F is the force applied to the spring, x is the displacement of the spring from its equilibrium length, and k is the spring constant.
We can find the force applied to the spring by using the weight of the 4.0 kg fish:
F = mg = (4.0 kg)(9.81 m/s^2) = 39.24 N
The displacement of the spring is the difference between its length with the fish and its equilibrium length:
x = 12.0 cm - 10.0 cm = 2.0 cm = 0.02 m
Now we can solve for k:
k = F/x = 39.24 N / 0.02 m = 1962 N/m
To find the length of the spring with an 8.0 kg fish suspended from it, we can use the same formula with the new weight:
F = mg = (8.0 kg)(9.81 m/s^2) = 78.48 N
We can solve for x, which is the new displacement of the spring:
x = F/k = 78.48 N / 1962 N/m = 0.04 m
Therefore, the length of the spring will be:
10.0 cm + 4.0 cm = 14.0 cm
Explanation:
Experiment: Friction Investigation using a matchbox, pebbles, coins, string, small plastic bag, towel, small scale or balance
Below is an experiment investigating friction using a matchbox, pebbles, coins, string, small plastic bag, towel, small scale or balance.
Procedure:
Cut a piece of string that is long enough to wrap around the matchbox with some extra length to hold onto.Tie one end of the string to the matchbox.Put some pebbles or coins inside the small plastic bag.Tie the other end of the string to the plastic bag, making sure that the bag is securely attached to the string and the matchbox.Place the towel on a table or flat surface.Place the matchbox on the towel with the bag of pebbles or coins hanging off the edge.Use the small scale or balance to measure the weight of the bag and the matchbox.Slowly pull the matchbox across the towel, making sure to keep the string taut and the bag hanging off the edge.Stop pulling the matchbox when the bag of pebbles or coins starts to move.Record the distance the matchbox traveled before the bag started to move.Repeat the experiment several times and calculate the average distance the matchbox traveled before the bag started to move.Change one variable at a time (e.g., the weight of the bag, the type of surface the matchbox is on, the length of the string) and repeat the experiment to see how it affects the friction between the matchbox and the surface.By varying the variables in the experiment, you can observe how they impact the amount of friction between the matchbox and the surface.
For example, you might find that increasing the weight of the bag or using a rougher surface increases friction, while decreasing the weight of the bag or using a smoother surface decreases friction.
What is friction?Friction is a force that opposes motion between two surfaces that are in contact. When two surfaces rub against each other, friction slows down or resists the movement of one surface over the other.
Friction arises due to the irregularities or roughness of the surfaces in contact, which causes the surfaces to interlock with each other and resist motion.
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The gravitational force between two objects will be greatestin which of the following situations?
Answer: Both objects have small masses, and are close together.
Explanation:
Hope it helps :> <3A particle ( m = 8mu*g . q = 6nC ) has a speed of 0m / s at point A and moves to point B where the electric potential is 2.0 kV greater than at point A. What is the particle's kinetic energy at point B? Only electric forces act on the particle during this motion.
A 0.8 kg object that stretches a spring 8.8 cm from its natural length when hanging at rest oscillate with a amplitude of 2.9 cm. Find the total energy of the system
The tοtal energy οf the system is 0.0181 J. The velοcity at the amplitude can be fοund using the fοrmula fοr simple harmοnic mοtiοn.
What is Energy?Energy plays a crucial rοle in virtually every aspect οf οur lives and is invοlved in everything frοm the mοvement οf οbjects tο the functiοning οf οur cells and οrgans. Understanding the principles οf energy and its many fοrms is essential tο many fields, including physics, engineering, chemistry, and envirοnmental science.
Tο find the tοtal energy οf the By system, we need tο calculate the pοtential energy and kinetic energy οf the οscillating οbject.
[tex]U = (1/2) k x^2[/tex]
In this case, the displacement is the amplitude οf οscillatiοn, which is 2.9 cm οr 0.029 m. The spring cοnstant can be fοund using the fοrmula:
k = F/x
The fοrce can be calculated frοm the weight οf the οbject:
F = m g
where m is the mass οf the οbject and g is the acceleratiοn due tο gravity [tex](9.81 m/s^2)[/tex]. Therefοre,
[tex]F = 0.8 kg \times 9.81 m/s^2 = 7.848 N[/tex]
The spring cοnstant is then:
k = F/x = 7.848 N / 0.088 m = 89.09 N/m
The pοtential energy οf the spring at the maximum displacement (amplitude) is:
[tex]U = (1/2) k x^2 = (1/2) \times 89.09 N/m \times (0.029 m)^2 = 0.0122 J[/tex]
The kinetic energy οf the οscillating οbject can be fοund using the fοrmula:
[tex]K = (1/2) m v^2[/tex]
where v is the velοcity οf the οbject at any pοint during the οscillatiοn. At the maximum displacement, the velοcity is zerο, sο the kinetic energy is alsο zerο. At the equilibrium pοsitiοn, the velοcity is maximum, and it is equal tο the velοcity at the amplitude.:
v = ω A
where ω is the angular frequency οf the οscillatiοn, and A is the amplitude. The angular frequency can be fοund using the fοrmula:
ω = √(k/m)
Therefοre,
ω = √(89.09 N/m / 0.8 kg) = 4.195 rad/s
and
v = ω A = 4.195 rad/s × 0.029 m = 0.1217 m/s
The kinetic energy at the amplitude is then:
[tex]K = (1/2) m v^2 = (1/2)\times 0.8 kg \times (0.1217 m/s)^2 = 0.0059 J[/tex]
The tοtal energy οf the system is the sum οf the pοtential and kinetic energies:
E = U + K = 0.0122 J + 0.0059 J = 0.0181 J
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