Explanation:
It is given that, An astronaut is in equilibrium when he is positioned 140 km from the center of asteroid X and 481 km from the center of asteroid Y, along the straight line joining the centers of the asteroids. We need to find the ratio of their masses.
As they are in equilibrium, the force of gravity due to each other is same. So,
[tex]\dfrac{Gm_xM}{r^2}=\dfrac{Gm_yM}{r^2}\\\\\dfrac{m_x}{r_x^2}=\dfrac{m_y}{r_y^2}\\\\\dfrac{m_x}{r_x^2}=\dfrac{m_y}{r_y^2}\\\\\dfrac{m_x}{m_y}=(\dfrac{r_x^2}{r_y^2})\\\\\dfrac{m_x}{m_y}=(\dfrac{140^2}{481^2})\\\\\dfrac{m_x}{m_y}=0.0847[/tex]
So, the ratio of masses X/Y is 0.0847
if two point charges are separated by 1.5 cm and have charge values of 2.0 and -4.0, respectively, what is the value of the mutual force between them
Complete question:
if two point charges are separated by 1.5 cm and have charge values of +2.0 and -4.0 μC, respectively, what is the value of the mutual force between them.
Answer:
The mutual force between the two point charges is 319.64 N
Explanation:
Given;
distance between the two point charges, r = 1.5 cm = 1.5 x 10⁻² m
value of the charges, q₁ and q₂ = 2 μC and - μ4 C
Apply Coulomb's law;
[tex]F = \frac{k|q_1||q_2|}{r^2}[/tex]
where;
F is the force of attraction between the two charges
|q₁| and |q₂| are the magnitude of the two charges
r is the distance between the two charges
k is Coulomb's constant = 8.99 x 10⁹ Nm²/C²
[tex]F = \frac{k|q_1||q_2|}{r^2} \\\\F = \frac{8.99*10^9 *4*10^{-6}*2*10^{-6}}{(1.5*10^{-2})^2} \\\\F = 319.64 \ N[/tex]
Therefore, the mutual force between the two point charges is 319.64 N
Determine the position in the oscillation where an object in simple harmonic motion: (Be very specific, and give some reasoning to your answer.) has the greatest speed has the greatest acceleration experiences the greatest restoring force experiences zero restoring force g
Answer:
Explanation:
The greatest speed is attained at middle point or equilibrium point or where displacement from equilibrium point is zero .
When the object remains at one of the extreme point it experiences greatest acceleration but at that point velocity is zero . Due to acceleration , its velocity goes on increasing till it come to equilibrium point . At this point acceleration becomes zero . After that its velocity starts decreasing because of negative acceleration . Hence at middle point velocity is maximum .
The greatest acceleration is attained at maximum displacement or at one of the two extreme end .
Greatest restoring force too will be at position where acceleration is maximum because acceleration is produced by restoring force .
Restoring force is proportional to displacement or extension against restoring force . So it will be maximum when displacement is maximum .
Zero restoring force exists at equilibrium position or middle point or at point where displacement is zero . It is so because acceleration at that point is zero .
A typical electric oven has two separate heating elements: one on top and one on the bottom. The bottom element is used for baking while the top element is used to broil foods. When only the bottom element is active and glowing red hot, what heat transfer mechanisms carry most of the heat to the food in the oven?
Answer:
Convection and Radiation mechanisms carry most of the heat
Explanation:
This is because Convection proceeds strongy as heated air rises from the hot element while Radiation is also strong, although the material of the cooking pots will how effective it is.
Which of the following explains why metallic bonding only occurs between
metallic atoms?
A. Metallic atoms are less likely to give their electrons to nonmetallic
atoms
B. Electrical conductivity is higher in metallic atoms, which means
they are more likely to attract free electrons.
C. Metallic atoms are highly reactive and do not tend to form bonds
with other atoms.
D. Metallic atoms have valence shells that are mostly empty, which
means these atoms are more likely to give up electrons and allow
them to move freely.
Answer:
D. Metallic atoms have valence shells that are mostly empty, which
means these atoms are more likely to give up electrons and allow
them to move freely.
Explanation:
Metals usually contain very few electrons in their valence shells hence they easily give up these few valence electrons to yield metal cations.
In the metallic bond, metal cations are held together by electrostatic attraction between the metal ions and a sea of mobile electrons.
Since metals give up their electrons easily, it is very easy for them to participate in metallic bonding. They give up their electrons easily because their valence shells are mostly empty, metal valence shells usually contain only a few electrons.
Rank the six combinations of electric charges on the basis of the electric force acting on q1. Define forces pointing to the right as positive and forces pointing to the left as negative. Rank positive forces as larger than negative forces.
1. q1=+1nC
q2=-1nC
q3 =-1nC
2. q1= -1nC
+ q2 = + 1nC
q3= +1nC
3. q1= +1nC
q2= +1nC
q3= +1nC
4. q1= +1nC
q2= + 1nC
q3= -1nC
5. q1= -1nC
q2= - 1nC
q3= -1nC
6. q1=+1nC
q2=-1nC
q3 =+1nC
Answer:
Plss see attached file
Explanation:
At what temperature will water begin to boil and turn to steam?
212 degrees Celsius
100 degrees Fahrenheit
212 kelvins
100 degrees Celsius
Answer:
100 degrees Celsius
Explanation:
Water starts to boil at 100 degrees celcius or 212 degrees fahrenheit.
At 100 degrees Celsius water begin to boil and turns to steam.
What are the boiling point and melting point of water?The melting point for water is 0 degrees C (32 degrees F). The boiling point of water varies with atmospheric pressure. At lower pressure or higher altitudes, the boiling point is lower. At sea level, pure water boils at 212 °F (100°C).
Is boiling water always 212?If the temperature is much above 212°F, the water will boil. That means that it won't just evaporate from the surface but will form vapor bubbles, which then grow, inside the liquid itself. If the water has very few dust flecks etc.
Learn more about a boiling point here https://brainly.com/question/40140
#SPJ2
An object has an acceleration of 6.0 m/s/s. If the net force was doubled and the mass was one-third the original value, then the new acceleration would be _____ m/s/s.
Hahahahaha. Okay.
So basically , force is equal to mass into acceleration.
F=ma
so when F=ma , we get acceleration=6m/s/s
Force is doubled.
Mass is 1/3 times original.
2F=1/3ma
Now , we rearrange , and we get 6F=ma
So , now for 6 times the original force , we get 6 times the initial acceleration.
So new acceleration = 6*6= 36m/s/s
A skater spins at 3rev/s when she stretches her arms outward. If she keeps her fists on her chest she can spin at 4.5rev/s and her body inertia is 3kg.m2. What is her body inertia when she stretches her arms outward?
Answer:
Body inertia I = 4.5 kg/m^2
Explanation:
Here, we want to calculate the body inertia when the arms are stretched outwards.
We know from the question that angular momentum is conserved
Thus;
I * 3 = 4.5 * 3
I = 4.5 kg/m^2
A body's current radiation rate is 30% higher than it was an hour ago. Calculate the percentage by which your temperature increased.
Answer:
6.8%
Explanation:
According to Stefan-Boltzmann law, radiation is directly proportional with temperature raised to the fourth power:
P ∝ T⁴
Writing a proportion:
P₁ / P₂ = T₁⁴ / T₂⁴
1.3P / P = (T₁ / T₂)⁴
T₁ / T₂ = ∜1.3
T₁ = 1.068 T₂
The temperature increased by 6.8%.
A motor is designed to operate on 117 V and draws a current of 12.3 A when it first starts up. At its normal operating speed, the motor draws a current of 3.38 A. Obtain (a) the resistance of the armature coil, (b) the back emf developed at normal speed, and (c) the current drawn by the motor at one-third normal speed
Answer:
a) using
R=V/I =117/12.3
R=9.5 ohms
b)
E=V-I*R =117-3.38*9.5
E=84.8Volts
c)
at (1/3)rd of normal speed ,back emf is (1/3) of its maximum
value
E=(1/3)*84.8=28.3Volts
Current drawn
I=V-Eback/R =117-28.3/9.5
I=9.33A
Explanation:
The resistance is = 9.5 ohms
The back emf developed at normal speed is = 84.90 volts
The current drawn at one-third normal speed =9.33 A.
To calculate the resistance of the armature coil this formula is used;
V = IR
make R the subject of formula,
R = V/I
where R = resistance
V = voltage
I = Current
R = 117/12.3
R = 9.5 ohms
To calculate the back emf developed at normal speed, this formula is used;
E = V + Ir ( for normal emf)
But for back emf which is the difference between the supplied voltage and the loss from the current through the resistance, this formula is used;
E = V - Ir
where V = 117v
I = 3.38
r = 9.5
E = 117 - ( 3.38 × 9.5)
= 117 - 32.11
= 84.90 volts
To calculate the current drawn at one-third normal speed;
1/3 of Emf = 1/3 × 84.90
= 28.3volts
Therefore current (I) = V - E/ R
= 117- 28.3/9.5
= 88.7/9.5
= 9.33 A
Learn more about current here:
https://brainly.com/question/24858512
Two protons are released from rest, with only the electrostatic force acting. Which of the following statements must be true about them as they move apart? (There could be more than one correct choice.)a. Their electrical potential energy keeps decreasing.b. Their acceleration keeps decreasing.c. Their kinetic energy keeps increasing.d. Their kinetic energy keeps decreasing.e. Their electric potential energy keeps increasing.
Answer:
Explanation:
correct options
a ) Their electrical potential energy keeps decreasing
Actually as they move apart , their electrical potential energy decreases due to increase of distance between them and kinetic energy increases
so a ) option is correct
b ) Their acceleration keeps decreasing
As they move apart , their mutual force of repulsion decreases due to increase of distance between them so the acceleration decreases .
c ) c. Their kinetic energy keeps increasing
Their kinetic energy increases because their electrical potential energy decreases . Conservation of energy law will apply .
The moving apart should be true statements:
a. The electrical potential energy should be reduced.
b. The acceleration should be reduced.
c. The kinetic energy should be increased.
True statements related to moving apart:At the time when the moving part, there is the reduction of the electric potential energy because there is a rise in the distance due to which the increment of the kinetic energy. The reduction of the mutual force of repulsion because of increment in the distance due to this the acceleration should be reduced. There is the increase in the kinetic energy due to the reduction of the electrical potential energy. here the law of conversation of energy should be applied.
Learn more about energy here: https://brainly.com/question/10658188
How much work is required to carry an electron from positive terminal of 12Volt battery to negative terminal?
Answer:
Explanation:
Work required = q x V
where q is charge on electron and V is potential difference
= 1.6 x 10⁻¹⁹ x 12
= 19.2 x 10⁻¹⁹ J
Consider an electromagnetic wave where the electric field of an electromagnetic wave is oscillating along the z-axis and the magnetic field is oscillating along the x-axis.
In what directions is it possible that the wave is traveling?
A. The-z direction.
B. The ty direction
C. The +x direction.
D. The -y direction
E. The -x direction.
F. The +z direction.
Answer:
The wave will be travelling in the y-axis
Explanation:
An e-m wave has a spatially varying electric field that is always associated with a magnetic field that changes over time and vice versa. The electric field and the magnetic field oscillates perpendicularly to each other, and together form a wave that travels in a perpendicular direction to the magnetic and the electric field in space. The movement of the e-m wave through space is usually away from the source where it is generated. So, if the electric field travels in the z-axis, and the magnetic field travels through along the x-axis, then the e-m wave generated will travel in the y-axis direction.
Do the math: How many seconds would it take an echo sounder’s ping to make the trip from a ship to the Challenger Deep (10,994 meters) and back? Recall that depth in meters = ½ (1500 m/sec × Echo travel time in seconds). Round your answer to two decimal places.
Answer:
14.66secsExplanation:
Given the formula for calculating the depth in metres expressed as
depth in meters = ½ (1500 m/sec × Echo travel time in seconds)
Given depth of the challenger = 10, 994 meters, we will substitute this given value into the formula given to calculate the time take for the echo to travel.
10, 994 = depth in meters = ½ * 1500 m/sec × Echo travel time in seconds
10,994 = 750 * Echo travel time in seconds
Dividing both sides by 750;
Echo travel time in seconds = 10,994 /750
Echo travel time in seconds ≈ 14.66secs (to two decimal places)
Therefore, it would take an echo sounder’s ping 14.66secs to make the trip from a ship to the Challenger Deep and back
"A power of 200 kW is delivered by power lines with 48,000 V difference between them. Calculate the current, in amps, in these lines."
Answer:
9.6×10⁹ A
Explanation:
From the question above,
P = VI.................... Equation 1
Where P = Electric power, V = Voltage, I = current.
make I the subject of the equation
I = P/V............. Equation 2
Given: P = 200 kW = 200×10³ W, V = 48000 V.
Substitute these vales into equation 2
I = 200×10³×48000
I = 9.6×10⁹ A.
Hence the current in the line is 9.6×10⁹ A.
An electromagnetic standing wave in air of frequency 750 MHz is set up between two conducting planes 80.0 cm apart. At how many positions between the planes could a point charge be placed at rest so that it would remain at rest?
Answer:
The positions the point charge will be placed at rest and still remain at rest are 20 cm, 40 cm, and 60 cm between the ends.
Explanation:
Given;
distance between the conducting planes, d = 80 cm
frequency of the electromagnetic wave, f = 750 MHz
speed of light, c = 3 x 10⁸ m/s²
Determine the wavelength
λ = C/f
where;
λ is the wavelength
C is the speed of light
f is the frequency
λ = C/f
λ = (3 x 10⁸) / (750 x 10⁶)
λ = 0.4 m = 40 cm
One complete cycle = one wavelength = 40 cm
half of the wavelength ( λ / 2) = 20 cm
one wavelength + half wavelength (3λ / 2) = 60 cm
The positions of the wave at zero amplitude (between 0 and 80 cm) = 20 cm, 40 cm, 60 cm
Thus, the positions the point charge will be placed at rest and still remain at rest are 20 cm, 40 cm, and 60 cm between the ends.
A body of mass 2.5kg is raised 4.0m above the ground.Calculate the potential energy if g=10m/s squared
Answer:
100 joulesExplanation:
[tex]mass = 2.5kg\\height = 4.0\\Acceleration \: due \:to\:gravity = 10m/s^2\\\\P.E = mgh\\P.E = 2.5kg\times10\times4\\\\Potential \: Energy = 100 joules[/tex]
The potential energy if g = 10m/s² is 98 J
What is Potential Energy ?Potential energy is the energy held by an object because of its position relative to other objects, stresses within itself, its electric charge, or other factors.
Formula for potential energy :
P.E. = mgh
m = mass (kg)g = gravity (m/s²)h = height/distance (m)Given :
The book is held from the ground of a distance = 4.0 m,
so
h = 4.0 m
we know that the book weighs,
2.5 kg
so
m = 2.5 kg.
Now we just put it in the formula ;
PE = (2.5kg) × (9.8 m/s²) × ( 4.0 m)
P E = 98 J
Therefore, The potential energy if g = 10m/s² is 98 J
Learn more about Potential Energy here ;
https://brainly.com/question/24284560
#SPJ2
As a wheel turns, the angle through which it has turned varies with time as β(t)=Ct + Bt3 where C=0.400rad/s and B=0.0120rad/s3. Calculate the angular velocity w(t) as a function of time.
Answer:
ω(t) = 0.4 + 0.036 t²
Explanation:
The angular displacement of the disk is given as the function of time:
β(t) = Ct + B t³
where,
C = 0.4 rad/s
B = 0.012 rad/s³
Therefore,
β(t) = 0.4 t + 0.012 t³
Now, for angular velocity ω(t), we must take derivative of angular displacement with respect to t:
ω(t) = dβ/dt = (d/dt)(0.4 t + 0.012 t³)
ω(t) = 0.4 + 0.036 t²
two resistors of resistance 10 ohm's and 20 ohm's are connected in parallel to a batery of e.m.f 12V. Calculate the current passing through the 20hm's resister
Calculate the power of the eye in D when viewing an object 5.70 m away. (Assume the lens-to-retina distance is 2.00 cm. Enter your answer to at least one decimal place.)
Answer:
Power=50.17dioptre
Power=50.17D
Explanation:
P=1/f = 1/d₀ + 1/d₁
Where d₀ = the eye's lens and the object distance= 5.70m=
d₁= the eye's lens and the image distance= 0.02m
f= focal length of the lense of the eye
We know that the object can be viewed clearly by the person ,then image and lens of the eye's distance needs to be equal with the retinal and the eye lens distance and this distance is given as 0.02m
Therefore, we can calculate the power using above formula
P= 1/5.70 + 1/0.02
Power=50.17dioptre
Therefore, the power the eye's is using to see the object from distance is 5.70D
A piece of electronic equipment that is surrounded by packing material is dropped so that it hits the ground with a speed of 4 m/s. After impact, the equipment experiences an acceleration of a = 2kx, where k is a constant and x is the compression of the packing material. If the packing material experiences a maximum compression of 20 mm, determine the maximum acceleration of the equipment.
Answer:
Maximum acceleration is 800m/s^2
Explanation:
See attached file
g a conductor consists of an infinite number of adjacent wires, each infinitely long. If there are n wires per unit length, what is the magnitude of B~
Answer:
B=uonI/2
Explanation:
See attached file
A person standing 180m from the foot of a high building claps hi
hand and hears the echo 0.03minutes later. What is the speed
sound in air at that temperature?
A) 331m/s
B) 240m/s C) 200m/s D) 300m/s
Answer:
C) 200 m/s
Explanation:
The sound travels a total distance of 360 m in 0.03 minutes.
v = (360 m) / (0.03 min × 60 s/min)
v = 200 m/s
Scientists studying an anomalous magnetic field find that it is inducing a circular electric field in a plane perpendicular to the magnetic field. The electric field strength is 4.0 mV/m at a point 1.5 m away from the center of the circle. At what rate is the magnetic field changing?
Answer:
The rate at which the magnetic field changes is [tex]\frac{\Delta B }{\Delta t } = - 5.33*10^{-3} \ T/ s[/tex]
Explanation:
From the question we are told that
The electric field strength is [tex]E = 4.0 mV/m = 4.0 *10^{-3} V/m[/tex]
The radius of the circular region where the electric field is induced is
[tex]d = 1.5 \ m[/tex]
Generally the induced electric field is mathematically represented as
[tex]E = - \frac{r}{2} * \frac{\Delta B }{\Delta t }[/tex]
The negative sign show that the induced electric field is acting in opposite direction to the change in magnetic field
Where [tex]\frac{\Delta B }{\Delta t }[/tex] is the change in magnetic field
So
[tex]\frac{\Delta B }{\Delta t } = - \frac{2 * E }{r}[/tex]
substituting values
[tex]\frac{\Delta B }{\Delta t } = - \frac{2 * 4.0 *10^{-3}}{ 1.5 }[/tex]
[tex]\frac{\Delta B }{\Delta t } = - 5.33*10^{-3} \ T/ s[/tex]
An inductor is connected to a 18 kHz oscillator. The peak current is 70 mA when the rms voltage is 5.4 V What is the value of the inductance L
Answer:
The value of the inductance is 0.955 mH
Explanation:
Given;
frequency of the oscillator, f = 18 kHz = 18,000 Hz
the peak current, I₀ = 70 mA = 0.07 A
the root mean square voltage, [tex]V_{rms}[/tex] = 5.4 V
The root mean square current is given as;
[tex]I_{rms}= \frac{I_o}{\sqrt{2} }[/tex]
[tex]I_{rms} = \frac{0.07}{\sqrt{2} } \\\\I_{rms} = 0.05 \ A[/tex]
Inductive reactance is given by;
[tex]X_L =\frac{V_{rms}}{I_{rms}} \\\\X_L = \frac{5.4}{0.05} \\\\X_L = 108 \ ohms[/tex]
Inductance is given by;
[tex]L = \frac{X_L}{2\pi f} \\\\L = \frac{108}{2\pi *18,000} \\\\L = 9.55 *10^{-4} \ H[/tex]
L = 0.955 mH
Therefore, the value of the inductance is 0.955 mH
The value of the inductance (L) for this oscillating circuit is equal to [tex]9.55 \times 10^{-4}[/tex] Henry.
Given the following data:
Oscillator frequency = 18 kHzPeak current = 70 mARms Voltage = 5.4 VTo determine the value of the inductance (L):
First of all, we would find the root mean square (rms) current by using the formula:
[tex]I_{rms} = \frac{I_o}{\sqrt{2} }\\\\I_{rms} = \frac{70 \times 10^{-3}}{1.4142} \\\\I_{rms} = 0.050 \;A[/tex]
Next, we would calculate the inductive reactance of the oscillator by using the formula:
[tex]X_L = \frac{V_{rms}}{I_{rms}} \\\\X_L = \frac{5.4}{0.050} \\\\X_L = 108 \; Ohms[/tex]
Now, we can solve for the value of the inductance (L):
[tex]L = \frac{X_L}{2\pi f}[/tex]
Where:
L is the inductance.f is the frequency.[tex]X_L[/tex] is the inductive reactance.Substituting the parameters into the formula, we have;
[tex]L = \frac{108}{2 \times 3.142 \times 18 \times 10^3} \\\\L = \frac{108}{113112}[/tex]
L = [tex]9.55 \times 10^{-4}[/tex] Henry.
Read more: https://brainly.com/question/12530980
1.5 kg of air within a piston-cylinder assembly executes a Carnot power cycle with maximum and minimum temperatures of 800 K and 300 K, respectively. The heat transfer from the air during the isothermal compression is 80 kJ. At the end of the isothermal compression, the volume is 0.2 m3. Determine the volume at the beginning of the isothermal compression, in m3. Assume the ideal gas model for air and neglect kinetic and potential energy effects.
Answer:
Explanation:
Carton cycle consists of four thermodynamic processes . The first is isothermal expansion at higher temperature , then adiabatic expansion which lowers the temperature of gas . The third process is isothermal compression at lower temperature and the last process is adiabatic compression which increases the temperature of the gas to its original temperature .
So the given process of isothermal compression must have been done at the temperature of 300K , keeping the temperature constant .
Work done on gas at isothermal compression is equal to heat transfer .
work done on gas = 80 x 10³ J
work done on gas = n RT ln v₁ / v₂
n is number of moles v₁ and v₂ are initial and final volume
molecular weight of gas = 28.97 g
1.5 kg = 1500 / 28.97 moles
= 51.77 moles
work done on gas = n RT ln v₁ / v₂
Putting the values in the equation above
80 x 10³ = 51.78 x 8.31 x 300 x ln v₁ / .2
ln v₁ / .2 = .62
v₁ / .2 = 1.8589
v₁ = 0.37 m³
Two objects are in all respects identical except for the fact that one was coated with a substance that is an excellent reflector of light while the other was coated with a substance that is a perfect absorber of light. You place both objects at the same distance from a powerful light source so they both receive the same amount of energy U from the light. The linear momentum these objects will receive is such that:
Answer:
absorbent p = S / c
reflective p = 2S/c
Explanation:
The moment of radiation on a surface is
p = U / c
where U is the energy and c is the speed of light.
In the case of a fully absorbent object, the energy is completely absorbed. The energy carried by the light is given by the Poynting vector.
p = S / c
in the case of a completely reflective surface the energy must be absorbed and remitted, therefore there is a 2-fold change in the process
p = 2S/c
A stone with a mass m is dropped from an airplane that has a horizontal velocity v at a height h above a lake. If air resistance is neglected, the horizontal distance R from the point on the lake directly below the point of release to the point where the stone strikes the water is given by which formula? R=v(2h/g)2 None of these are correct. R = 2mv sqrt(2h/g) R = v sqrt(2h/g) R=(1/2)gt2
Answer:
R = v √(2h / g)
Explanation:
This exercise can be solved using the concepts of science, projectile launching
let's calculate the time it takes to get to the water
y = y₀ +[tex]v_{oy}[/tex] t - ½ g t²
as the stone is skipped the vertical speed is zero
y = y₀ - ½ g t²
for y=0
t = √ (2y₀ / g)
the horizontal distance it covers in this time is
R = v₀ₓ t
R = v₀ₓ √(2 y₀ / g)
let's call the horizontal velocity as v and the height is h
R = v √(2h / g)
A 4g bullet, travelling at 589m/s embeds itself in a 2.3kg block of wood that is initially at rest, and together they travel at the same velocity. Calculate the percentage of the kinetic energy that is left in the system after collision to that before.
Answer:
The percentage of the kinetic energy that is left in the system after collision to that before is 0.174 %
Explanation:
Given;
mass of bullet, m₁ = 4g = 0.004kg
initial velocity of bullet, u₁ = 589 m/s
mass of block of wood, m₂ = 2.3 kg
initial velocity of the block of wood, u₂ = 0
let the final velocity of the system after collision = v
Apply the principle of conservation of linear momentum
m₁u₁ + m₂u₂ = v(m₁+m₂)
0.004(589) + 2.3(0) = v(0.004 + 2.3)
2.356 = 2.304v
v = 2.356 / 2.304
v = 1.0226 m/s
Initial kinetic energy of the system
K.E₁ = ¹/₂m₁u₁² + ¹/₂m₂u₂²
K.E₁ = ¹/₂(0.004)(589)² = 693.842 J
Final kinetic energy of the system
K.E₂ = ¹/₂v²(m₁ + m₂)
K.E₂ = ¹/₂ x 1.0226² x (0.004 + 2.3)
K.E₂ = 1.209 J
The kinetic energy left in the system = final kinetic energy of the system
The percentage of the kinetic energy that is left in the system after collision to that before = (K.E₂ / K.E₁) x 100%
= (1.209 / 693.842) x 100%
= 0.174 %
Therefore, the percentage of the kinetic energy that is left in the system after collision to that before is 0.174 %
A student builds a rocket-propelled cart for a science project. Its acceleration is not quite high enough to win a prize, so he uses a larger rocket engine that provides 39% more thrust, although doing so increases the mass of the cart by 13%. By what percentage does the cart's acceleration increase?
Answer:
Explanation:
a = F / m
where a is acceleration , F is thrust and m is mass
taking log and differentiating
da / a = dF / F - dm / m
(da / a)x 100 = (dF / F)x100 - (dm / m) x100
percentage increase in a = percentage increase in F - percentage increase in m
= percentage increase in acceleration a = 39 - 13 = 26 %
required increase = 26 %.