Answer:
a)[tex]W=0.8J[/tex]
b) [tex]d_t=0.20m[/tex]
c) [tex]\triangle K.E=0.267J[/tex]
Explanation:
From the question we are told that:
Mass of cart 1 [tex]M_1=1.0kg[/tex]
Mass of cart 1 [tex]M_2=0.05kg[/tex]
Force on cart 1 [tex]F_1=4.0N[/tex]
Push Distance of cart 1 [tex]d_1=0.20m[/tex]
Slide Distance of cart 1 [tex]d_1'=0.35m[/tex]
a)
Generally the equation for work-done is mathematically given by
[tex]W=f*d\\W=4*0.20\\W=0.8J \\[/tex]
b)
The systems center of mass moved a net totally of (while being pushed)
Mass 1 =0.20m
Mass 2=0
Therefore
[tex]d_t=d_1+d_2[/tex]
[tex]d_t=0.20+0[/tex]
[tex]d_t=0.20m[/tex]
c)
Since work-done is equal to K.E energy of cart 1
Therefore
[tex]W=1/2mv^2[/tex]
[tex]V_1=\sqrt{\frac{W}{1/2m}}[/tex]
[tex]V_1=\sqrt{\frac{0.8}{1/2(1)}}[/tex]
[tex]V_1=1.264[/tex]
Therefore Kinetic energy before collision is
[tex]K.E_1=1/2mv^2[/tex]
[tex]K.E_1=1/2*1*1.264^2[/tex]
[tex]K.E_1=0.768[/tex]
Generally from the equation for conservation of momentum the Velocity of cart 2 is mathematically given by
[tex]v_2=\frac{m_1V_1}{m_1+m_2}[/tex]
[tex]v_2=\frac{1*1.264}{1+0.5}[/tex]
[tex]V_2=0.842m/s[/tex]
Therefore the final K.E is mathematically given by
[tex]K.E_2=(1/2)(m_1+m_2)V_2^2[/tex]
[tex]K.E_2=1/2*(1.5)(0.842)^2[/tex]
[tex]K.E_2=0.531J[/tex]
Generally the Change in K.E is mathematically given by
[tex]\triangle K.E=K.E_1-K.E_2[/tex]
[tex]\triangle K.E=0.798-0.531[/tex]
[tex]\triangle K.E=0.267J[/tex]
Therefore the will force change the kinetic energy of the system's center of mass by
[tex]\triangle K.E=0.267J[/tex]
(a) The work done by you when you push the cart at a constant force is 0.8 J.
(b) The distance moved by the center mass of the two cart system is 0.23 m.
(c) The change in kinetic energy of the system center of mass is 0.271 J.
Work done by you
The work done by you when you push the cart at a constant force is calculated as follows;
W = Fd
W = 4 x 0.2
W = 0.8 J
Distance moved by the center mass of the two cart systemlet the 0.5 kg mass be the reference mass at zero (0).Xcm = (m₁x₁ + m₂x₂)/(m₁ + m₂)
Xcm = (0.5(0) + 1(0.35)) / (1 + 0.5)
Xcm = (0.35)/(1.5)
Xcm = 0.23 m
Initial velocity of the 1.0 kg massF = ma
a = F/m
a = (4)/1 = 4 m/s²
v² = u² + 2as
v² = 0 + 2(4)(0.2)
v² = 1.6
v = √1.6
v = 1.265 m/s
Final velocity of the massesm₁u₁ + m₂u₂ = v(m₁ + m₂)
1(1.265) + 0 = v(1 + 0.5)
1.265 = 1.5v
v = 0.84 m/s
Change in kinetic energyK.E(initial) = ¹/₂m₁u₁² + ¹/₂m₂u₂²
K.E(initial) = ¹/₂(1)(1.265)² + ¹/₂(0.5)(0) = 0.8 J
K.E(final) = ¹/₂(m₁ + m₂)v²
K.E(final) = ¹/₂(1 + 0.5)(0.84)² = 0.529 J
Δ K.E = 0.8 J - 0.529 J = 0.271 J
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which of the following changes will increase the period of an oscillating spring mass system?
a. an increase in the mass on the spring.
b. an increase in the initial displacement of the spring. c. an increase in the spring constant.
d. more than one of the above.
e. none of the above.
explain your answer.
NO LINKS.
Answer:
a. an increase in the mass on the spring.
Explanation:
An increase in the mass on the spring will increase the period of an oscillating spring mass system.
Mathematically, the period of an oscillating spring mass system is given by the formula;
T = 2π √(m/k)
Where;
T is the period.
m is the mass of the spring.
k is the spring constant.
Hence, the mass of a spring is directly proportional to the period of oscillation of the spring.
This ultimately implies that, as the mass of the spring increases, the period of oscillation will increase. Similarly, the period of oscillation will decrease with an increase in the spring constant i.e there exist an inverse relationship between the period and spring constant.
During launches, rockets often discard unneeded parts. A certain rocket starts from rest on the launch pad and accelerates upward at a steady 3.45m/s2 . When it is 230m above the launch pad, it discards a used fuel canister by simply disconnecting it. Once it is disconnected, the only force acting on the canister is gravity (air resistance can be ignored).
1- How high is the rocket when the canister hits the launch pad, assuming that the rocket does not change its acceleration?
2- What total distance did the canister travel between its release and its crash onto the launch pad?
Answer:
Explanation:
Time elapsed to reach the height of 230 m be t
s = ut + 1/2 at²
230 = .5 x 3.45 t²
t = 11.55 s
velocity at height of 230 m
v = u + at
= 0 + 3.45 x 11.55 = 39.84 m/s
This velocity will be attained by canister .
time to reach zero velocity at the top position t
v = u - gt
0 = 39.84 - 9.8 t
t = 4.06 s
height travelled by canister during this 4.06 s
v² = u² - 2gH
0 = 39.84² - 2 X 9.8 H
H = 80.98 M
Total height attained by canister = 80.98 + 230 = 310.98 m
Time of fall by canister t
s = 1/2 gt²
310.98 = .5 x 9.8 t²
t = 7.97 s
Total time taken by canister to reach the ground after its release from rocket
= 4.06 + 7.97 = 12.03 s
Distance travelled by rocket in 12.03 s
s = ut + 1/2 a t²
= 39.84 x 12.03 + .5 x 3.45 x 12.03²
= 479.27 + 249.64
= 728.91 m
height of rocket required = 230 + 728.91
= 958.91 m
2 )
Distance travelled by canister between its release and fall on the ground
= 80.98 + 80.98 + 230
= 391.96 m.
A sign which weighs 38.3 N is supported symmetrically by two cables which make an angle of 1.0 degrees with the horziontal. A single cable will pull upward on the sign with a force of how may Newtons?
The single cable will pull upward on the sign with a force of 38.3 N.
What is single cable?Single cable is a type of cable that is composed of a single electrical conductor. It is most commonly used in low voltage applications such as wiring for computers and domestic appliances. Single cable is typically insulated with rubber, PVC or other insulating materials. The insulator protects the conductor from short circuits and other electrical hazards.
This is because the sign is supported symmetrically by two cables, which means that the total downward force on the sign is equal to the total upward force. Since the two cables make an angle of 1.0 degrees with the horizontal, the total downward force on the sign is equal to the combined weight of the sign (38.3 N) and the two cables pulling down on it. Therefore, the single cable must pull up with a force of 38.3 N in order to keep the sign in equilibrium.
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Q12. How big is a Moon? How big is a Mars? What is therefore the weight of the person from Q11 on the Moon? What is the person's weight on Mars?
Answer:
The moon is 1,079.4 mi.
Mars is 2,106.1 mi
Multiply your weight by the moon's gravity relative to earth's, which is 0.165. Solve the equation. In the example, you would obtain the product 22.28 lbs. So a person weighing 135 pounds on Earth would weigh just over 22 pounds on the moon
Being that Mars has a gravitational force of 3.711m/s2, we multiply the object's mass by this quanitity to calculate an object's weight on mars. So an object or person on Mars would weigh 37.83% its weight on earth.
Explanation:
~Hope this helps
If 12 coulombs of electric charge pass a point in 4.0
seconds, the current is
A) 8.0 amperes
B) 16 amperes
C) 3.0 amperes
D) 48 amperes
Answer:
AS
Explanation:
Ruby was training for a race at the high school track. She took her dog walked 2250 meters in 15 minutes. Calculate the average speed
Answer:
Average speed [tex]= 2.5[/tex] meter per second
Explanation:
Given
The total distance walked [tex]= 2250[/tex] meters
The total time taken to walk [tex]2250[/tex] meters is [tex]15[/tex] minutes
In one minute there are [tex]60[/tex] seconds
As we know Average speed is equal to total distance travelled divided by total time taken
Hence,
Average speed
[tex]\frac{2250}{15*60} \\2.5[/tex]meter per second
A 62.3 kg base runner begins his slide into second base while moving at a speed of 4.49 m/s. He slides so that his speed is zero just as he reaches the base. The acceleration of gravity is 9.8 m/s². What is the magnitude of the mechanical energy lost due to friction acting on the run- ner?
Answer:
628 J
Explanation:
ME = PE + KE
PE = mgh = 0, because h = 0
KEi (initial KE) = 1/2mv² = 1/2(62.3 kg)(4.49 m/s)² = 628 J
KEf (final KE) = 0, because v-final = 0
All the initial ME, which is all KE, converts to thermal E due to friction
the valu
In an experiment the value of thickness of a
wire was found to be 1.54, 1.53, 1.44, 1.54, 1.56
and 1.45 in successive measurements. Then the
percentage error is
(1) 28%
(2).09 %
(3) 9%
(4) 2.8%
Answer:
[tex]\% Error = 2.6\%[/tex]
Explanation:
Given
[tex]x: 1.54, 1.53, 1.44, 1.54, 1.56, 1.45[/tex]
Required
Determine the percentage error
First, we calculate the mean
[tex]\bar x = \frac{\sum x}{n}[/tex]
This gives:
[tex]\bar x = \frac{1.54+ 1.53+ 1.44+ 1.54+ 1.56+ 1.45}{6}[/tex]
[tex]\bar x = \frac{9.06}{6}[/tex]
[tex]\bar x = 1.51[/tex]
Next, calculate the mean absolute error (E)
[tex]|E| = \sqrt{\frac{1}{6}\sum(x - \bar x)^2}[/tex]
This gives:
[tex]|E| = \sqrt{\frac{1}{6}*[(1.54 - 1.51)^2 +(1.53- 1.51)^2 +.... +(1.45- 1.51)^2]}[/tex]
[tex]|E| = \sqrt{\frac{1}{6}*0.0132}[/tex]
[tex]|E| = \sqrt{0.0022}[/tex]
[tex]|E| = 0.04[/tex]
Next, calculate the relative error (R)
[tex]R = \frac{|E|}{\bar x}[/tex]
[tex]R = \frac{0.04}{1.51}[/tex]
[tex]R = 0.026[/tex]
Lastly, the percentage error is calculated as:
[tex]\% Error = R * 100\%[/tex]
[tex]\% Error = 0.026 * 100\%[/tex]
[tex]\% Error = 2.6\%[/tex]
Tritium, the 3H atom, consists of a nucleus of one proton and two neutrons with a single electron. It is unstable and decays via beta emission to singly ionized helium, 3 He , consisting of a nucleus of two protons and one neutron with a single electron. This decay takes place instantaneously and thus there occurs a sudden doubling of the Coulomb interaction between the atomic electron and the nucleus. If the tritium atom is in its ground state when it decays, determine the probability that the 3He atom is in its ground state immediately after the decay.
Required:
Determine the probability that the 3H^+ atom is in its ground state immediately after decay.
Answer: hello your question is poorly written attached below is the complete question
P( ³₂He₊ ) at ground state = 1
Explanation:
Determine the probability that the 3He atom is in its ground state after decay
From the attached solution the coulomb interaction of ( ³₂He) is double that of H³ . given that coulomb interaction is attractive ( -ve ) this will make the product to become more stable hence the product ( ³₂He₊ ) will be gotten at the ground state
i.e. P( ³₂He₊ ) at ground state = 1
attached below is a detailed solution
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Which has more momentum, a 0.5kg toy car moving a 5 m/s or a 1000kg real car that is
parked?
Answer:
The toy car. An object that isn't moving has no momentum
Explanation:
Which model below describes the processes of Gamma radiation?
A
B.
C.
D.
Answer:
C
Explanation:
Which statement can be made about the amplitude of any transverse wave?
It is the length from the midpoint to the crest.
It is half the length from the midpoint to the trough.
It is the length of the wavelength.
It is half the length of the wavelength.
Answer:
A) It is the length from the midpoint to the crest.
Explanation:
The correct statement about the amplitude of any transverse wave is: It is the length from the midpoint to the crest. The correct option is A.
What is a transverse wave?A transverse wave is a type of wave in which the displacement of the medium is perpendicular to the direction of wave propagation.
Examples of transverse waves include light waves and water waves in which the surface of the water oscillates up and down while the wave moves horizontally.
The properties of a transverse wave include:
Amplitude: The maximum displacement of the medium from its rest position. This represents the intensity or strength of the wave.
Wavelength: The distance between two adjacent points in the wave that are in phase with each other, for example, between two consecutive crests or troughs. It is typically represented by the symbol λ.
Frequency: The number of complete wave cycles that pass a point in a given amount of time, usually measured in hertz (Hz). The frequency is inversely proportional to the wavelength and is represented by the symbol f.
Period: The time taken for one complete wave cycle to pass a given point, usually represented by the symbol T. The period is directly proportional to the wavelength and inversely proportional to the frequency.
Speed: The speed at which the wave propagates through the medium, usually represented by the symbol v. The speed is directly proportional to the frequency and wavelength.
These properties are related to each other by the wave equation:
v = fλ,
Where v = the speed of the wave,
f = the frequency,
and λ = the wavelength.
Therefore, The correct statement about the amplitude of any transverse wave is A. It is the length from the midpoint to the crest.
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Why is Dimension important in Physics?
Explanation:
Dimensions help understand how physical amounts are related to their dependence on basic or fundamental volumes, i.e. how the body's dimensions rely on mass, time, length and temperature.
Understanding dimensions is of utmost importance as it helps us in studying the nature of physical quantities mathematically. The basic concept of dimensions is that we can add or subtract only those quantities which have same dimensions. Also, two physical quantities are equal if they have same dimensions.
A ruler partially hangs over the end of a bench. It is supported at one end and made to vibrate at the other end in an attempt to display simple harmonic motion. If the ruler has an amplitude of 0.22 cm and makes twelve complete vibrations in 0.12 seconds, how far does the end of the ruler travel in 4.7 seconds?
What is another way to describe the vector 100 m/s down
Answer:
Describe how one-dimensional vector quantities are added or subtracted.
Hi, can anyone help me with this question I have?
Assume a tornado is in the vicinity of your neighborhood. Which would
be the most useful information to determine your safety - speed or
velocity? Explain your answer.
Answer:
speed
Explanation:
you need to move fast so the tornado can't reach you
what change do you need to make when comparing objects going upward against gravity versus downward with gravity?
A. Different amount of time in motion
B. Different length of displacement
C. Different sign + or - on the acceleration
D. Different changes to velocity
If an object is working against gravity, that means gravity must have the opposite sign of the object (this is why we see objects slow down at their peak height and return to us if we throw them in the air!). If the object is working with gravity, though, they must both be moving in the same direction, therefore gravitational acceleration would be the same sign as the velocity (positive or negative depending on how you define your axes).
Therefore, your answer should be C. Different sign + or - on the acceleration.
I hope this helps!
Explained Kepler's laws, satellites motion and weightlessness
30. How do you make a conclusion?
Which are dangerous places to put a flammable substance? Check all that apply.
near a flame
on a scale
near a ruler
in a sink
near a hot plate
Answer:
near a flame and a hot plate
Explanation:
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Which has more momentum, a 0.5kg toy car moving a 5 m/s or a 1000kg real car that is
parked?
Answer:
The toy car
Explanation:
the real car is parked so yeah but maybe in some way technically the real car has more "momentum"
A lawnmower is pushed with a force of 72 Newtons at an angle of 40 degrees from the horizontal. How much work is done to the mower if it moves 740 meters?
The work done to the mower is the product of force and the distance covered by the object which is equal to 40,811 Joules.
What is Work done?Work done can be defined as the product of external force and the distance over which the force is being applied. Work is done on an object when a force is applied to an object and the object is moved through a particular distance.
From this we can see that:
X-Component:
cos(θ) = x/F
Then,
X= F cos(θ).…..(1)
Now putting the values of F and θ in equation (1) we get,
X = 72 N × cos(40)
X = 72 N × 0.766
X= 55.15 N this is the x-component force
The work done to the mower is:
W = F × d
W = 55.15 × 740
W = 40,811 Joules
The work done to the mower is 40811 Joules.
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I need help i don’t want to go to summer school
Ball A with a mass of 0.280kg makes an elastic head-on collision with ball B initially at rest. After collision, ball B moves off with half the original speed of ball A. Is the momentum conserved in the collision? Why?
The mass of ball B and the final velocity of ball A can complement the conservation of linear momentum. The answer is yes.
What is Momentum ?Momentum can simply be defined as the product of mass and velocity. It is a vector quantity.
Given that ball A with a mass of 0.280kg makes an elastic head-on collision with ball B initially at rest. After collision, ball B moves off with half the original speed of ball A.
In an elastic head-on collision, momentum is mostly always conserved. That is, the sum of the momentum before collision will be equal to the sum of the momentum after collision.
Mathematically, MaUa = MaVa + MbVb
Is the momentum conserved in the collision?
The answer is yes!
Why?
Because we need to consider the mass of the ball B and the final velocity of the ball A.
Therefore, In consideration of the mass of the ball B and the final velocity of the ball A, we can say that the momentum is conserved.
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While skiing in Jackson, Wyoming, your friend Ben (of mass 63.2 kg) started his de- scent down the bunny run, 11.5 m above the bottom of the run. If he started at rest and converted all of his gravitational potential energy into kinetic energy, what is Ben's kinetic energy at the bottom of the bunny run? Use g = 9.8 m/s² Answer in units of J.- answer :7100J part 2 of 2 What is his final velocity? Answer in units of m/s.
Answer:
12.3 m/s
Explanation:
To calculate the final velocity of Ben, we can use the equation KE = 1/2mv^2, where KE is the kinetic energy and m is the mass of Ben. Inserting the given values, we get:
7100 = 1/2 (63.2 kg) v^2
Therefore, v^2 = 7100/31.6
v = √(7100/31.6)
v = 12.3 m/s
when a resistor is connected to a battery, current flows through the resistor. If the voltage of the battery is doubled, the current will be?
Resistors limits the current/amps but keep the voltage the same.
What happens if you connect the resistor to the battery?You don't want to attach them together with a wire since there would be too much current loose through, such that the battery heats up till it blows or something.
Current is directly corresponding to voltage; a doubling of the voltage will double the current. But the current is also inversely comparable to the resistance; a doubling of the resistance will halve the current.
So we can conclude that Resistance residue is the same, but power becomes four times i.e. multiplication. If the current is I and the voltage is V,
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Two protons are held a distance d apart. The electrostatic force and the gravitational force that one proton exerts on the other are Fe and Fg, respectively. Which of the following correctly compares the magnitude and direction of these forces?
Fe > Fg, opposite direction
a. Fe > Fg, same direction
b. Fe < Fg opposite direction
c. Fe < Fg same direction
Answer:
Explanation:
charge on each proton = 1.6 x 10⁻¹⁹ C
mass of proton = 1.67 x 10⁻²⁷ kg
Electrostatic force of repulsion Fe = 9 x 10⁹ x ( 1.6 x 10⁻¹⁹ )² / d²
= 23.04 x 10⁻²⁹ / d²
Gravitational force of attraction = G Mm / d²
M = m = 1.67 x 10⁻²⁷ kg
Gravitational force of attraction Fg = 6.67 x 10⁻¹¹ x ( 1.67 x 10⁻²⁷ )² / d²
= 18.60 x 10⁻⁻⁶⁵ / d²
So Fg is far less than Fe and former is attractive , later is repulsive .
Fe > Fg, opposite direction , is the answer .
Someone please help me with this question
How are mass and weight different?
Answer:
The mass is the amount of matter in something. Weight is mass times gravitational field strength and so also includes gravity. Mass is measured in grams (g) and weight is measured in Newtons (N)
Which increases the rate of soil formation?
A. mixed layers
B. more precipitation
C. cooler temperatures
D. very hard parent material
Answer:
a
Explanation:
Answer: b. more precipitation
Explanation:
An electron accelerates through a 12.5 V potential difference, starting from rest, and then collides with a hydrogen atom, exciting the atom to the highest energy level allowed. List all the possible quantum-jump transitions by which the excited atom could emit a photon and the wavelength (in nm) of each.
Answer:
Explanation:
An electron accelerates through a 12.5 V potential difference, starting from rest, so it will acquire kinetic energy of 12.5 eV .
In hydrogen atom energy of n th orbit in terms of eV is given as follows
En = -13.6 / n² eV
Total energy of 1 st orbit E₁ = - 13.6 eV
Total energy of 2 st orbit E₂ = - 13.6 eV / 2² = - 3.4 eV
Total energy of 3 st orbit E₃ = - 13.6 eV / 3² = - 1.5 eV
Total energy of 4 st orbit E₄ = - 13.6 eV / 4² = - 0.85 eV
E₄ - E₁ = 13.6 - 0.85 = 12.75 eV
E₃ - E₁ = 13.6 - 1.5 = 12.10 eV
E₂ - E₁ = 13.6 - 3.4 = 10.2 eV .
The electron has energy of 12,5 eV so it can excite electron from E₁ to E₃ . .
Jump possible = E₃ to E₂ , E₂ to E₁ and E₃ to E₁
Energy of E₃ to E₂ = 3.4 - 1.5 eV = 1.9 eV
wavelength = 1237 / 1.9 nm = 651 nm
E₃ - E₁ = 13.6 - 1.5 = 12.10 eV
wavelength = 1237 / 12.10 nm = 102.23 nm
E₂ - E₁ = 13.6 - 3.4 = 10.2 eV
wavelength = 1237 / 10.2 nm = 121.27 nm
wavelength of photon possible are 651 nm , 121.27 nm , 102.23 nm .