Answers
ANSWER
[tex]35.02m[/tex]EXPLANATION
Parameters given:
Initial velocity, u = 26.2 m/s
When the vase reaches its maximum height, its velocity becomes 0 m/s. That is the final velocity.
We can now apply one of Newton's equations of motion to find the height:
[tex]v^2=u^2-2as[/tex]where a = g = acceleration due to gravity = 9.8 m/s²
Therefore, we have that:
[tex]\begin{gathered} 0=26.2^2-2(9.8)s \\ \Rightarrow19.6s=686.44 \\ s=\frac{686.44}{19.6} \\ s=35.02m \end{gathered}[/tex]That is the height that the vase will reach.
Related Questions
A ball of mass 1.86 kilograms is attached to a cord 1.29 meters long and swung in a vertical circle at a constant speed of 5.27 meters per second. What is the centripetal force acting on the ball? Include units in your answer. What is the tension in the cord when the ball is at the bottom of its path? Include units in your answer. What is the tension in the cord when the ball is at the top of its path? Include units in your answer. All answers must be in 3 significant digits.
Answers
Explanation
Step 1
Draw
so
a)centripetal force:
the centripetal force is given by.
[tex]\begin{gathered} F=ma \\ F=m\frac{v^2}{r} \\ \text{where } \\ F_{C\text{ }}\text{ is the centripetal force} \\ m\text{ is the mass } \\ v\text{ is the velocty } \\ r\text{ is the radius} \end{gathered}[/tex]now, replace
[tex]\begin{gathered} F=m\frac{v^2}{r} \\ F=1.86\text{ kg }\frac{(\text{ 5.27 }\frac{m}{s})^2}{1.29\text{ m}} \\ F=40.044\text{ Newtons} \end{gathered}[/tex]so, the centripetal force is 40.0446 Newtons
b) What is the tension in the cord when the ball is at the bottom of its path?
to find the tension in bottom, we need to add the weigth of the ball,so
[tex]\begin{gathered} \text{weigth}=\text{ mass}\cdot accelofgravity \\ w=mg \end{gathered}[/tex]hence, the tension would be
[tex]\begin{gathered} T_{bottom}=m\frac{v^2}{r}+mg \\ \end{gathered}[/tex]replace
[tex]\begin{gathered} T_{bottom}=m\frac{v^2}{r}+mg \\ T_{bottom}=40.044\text{ N+(1.86 kg}\cdot9.81\text{ }\frac{\text{m}}{s^2}) \\ T_{bottom}=40.044\text{ N+18.2466 N} \\ T_{bottom}=58.291\text{ N} \end{gathered}[/tex]c)What is the tension in the cord when the ball is at the top of its path?
to find the tension in the top we need to subtract the weigth, so
[tex]\begin{gathered} T_{\text{top}}=m\frac{v^2}{r}-mg \\ replace \\ T_{\text{top}}=40.044\text{ N-18.2466 N} \\ T_{\text{top}}=21.79\text{ Newtons} \end{gathered}[/tex]I hope this helps you
Which statement is not true of the reactions on the Sun?A.They are fusion reactions.B.They occur between helium atoms.C.Fast-moving nuclei collide.D.Hydrogen atoms are reacted.
Answers
Answer and explanation:
A correct option is an option (B). Option b is not true of the reaction on the sun because the reactions do not happen in between helium atoms.
All other options (A), (C), and (D) are incorrect because, in sun, the nuclear fusion reaction takes place between hydrogen atoms. Due to the sun's gravitational force and high temperature, the nuclei of helium move vary fast.
Conclusion:
The correct option is option (B).
If a bullet with mass 2.7 grams is fired from a gun with a speed of 202
m/s into a block of wood. If the kinetic energy is transformed to heat,
what is the increase in temperature of the bullet in degrees C,
assuming the specific heat of the bullet is 234 J/kg/C.
Answers
The increase in temperature of the bullet in degrees C is 87.17
Define Specific Heat Capacity?
When a material's temperature rises by 1 K (or 1 °C), or when its mass increases by 1 kg, the specific heat capacity is defined as the amount of heat (J) absorbed per unit mass (kg).
This measurement is expressed as J/(kg K) or J/(kg °C).
The heat that is transferred to the bullet as a result of the conversion of kinetic energy to heat is what causes the bullet's temperature to rise.
Q = cm T,
where Q is the energy transferred, c is the substance's specific heat, m is its mass, and T is the temperature change, describes this relationship.
Given,
mass = 2.7 x 10^-3 kg
speed = 202 m/s
C = 234 J/kg/C.
The kinetic energy of the travelling bullet is,
1/2 m(v^2) = 1/2 x 2.7 x 10^-3 x 202 x 202
= 55.08 J
Energy that raises the temperature = 55.08 J
This is equal to mCΔT
Equalising the 2 energies,
55.08 = mCΔT
ΔT = 55.08 / mC
= 55.08 / 2.7 x 10^-3 x 234
= 87.17
Hence, the increase in temperature of the bullet in degrees C is 87.17
To learn more about specific heat capacity from the given link
https://brainly.com/question/21406849
#SPJ1
it would be greatly appreciated if you plug in the numbers according to the format of my worksheet.
Answers
a. List variables
[tex]\begin{gathered} m_{1i}=\text{ 0.015 kg} \\ v_{1i}=\text{ 0.225 m/s} \\ m_{2i}=\text{ 0.03 kg} \\ v_{2i}\text{ =-0.18 m/s} \\ m_{1f}=\text{ 0.015 kg} \\ v_{1f}=-0.315\text{ kg} \\ m_{2f}=\text{ 0.03 kg} \\ v_{2f}\text{ = ?} \end{gathered}[/tex]b. plug into the equation
[tex]\begin{gathered} m_{1i}v_{1i}+m_{2i}v_{2i}=m_{1f}v_{1f}+m_{2f}v_{2f} \\ 0.015\times0.225+0.03\text{ }\times(-0.18)=0.015\times(-0.315)+0.03(v_{2f}) \end{gathered}[/tex]c. solve for missing
[tex]\begin{gathered} v_{2f}=\frac{0.015\times0.225+0.03(-0.18)-0.015\times(-0.315)}{0.03} \\ =0.09\text{ m/s} \end{gathered}[/tex]A spaceship and an asteroid are moving in the same direction away from Earth with speeds of 0.8 c and 0.45 c, respectively. What is the relative speed between the spaceship and the asteroid?
Answers
Answer:
0.35c
Explanation:
The relative speed between the spaceship and the asteroid can be calculated as the difference between their speeds, so it is equal to
Relative speed = 0.8c - 0.45c
relative speed = 0.35c
Therefore, the answer is
0.35c
Good morning I really need some help on this question!
Answers
Sound travels faster in water than air
Here, C is the correct option.
A laboratory cart with a mass of 7 kilograms moves a distance of 0.5 meters in 3 seconds.Calculate the momentum.
Answers
Given that the mass of the cart is m = 7 kg.
The distance is d = 0.5 m.
The time is t = 3 s.
We need to find the momentum, p.
The formula to calculate momentum is
[tex]\begin{gathered} p=mass\times velocity \\ =m\times\frac{d}{t} \end{gathered}[/tex]
Substituting the values, the momentum will be
[tex]\begin{gathered} p=7\times\frac{0.5}{3} \\ =1.167kg\text{ m/s} \end{gathered}[/tex]Thus, the momentum is 1.167 kg m/s.
How do i solve this problem? Hint: The cannonball is being launched vertically upwards, therefore, there is no initial horizontal speed. The given initial speed will also be the initial vertical speed.
Answers
The initial velocity of the ball is given as 36.0 m/s.
The horizontal component of velocity of ball is given as,
[tex]v_x=v\cos \theta[/tex]The ball is projected vertically, therefore, the angle made by ball is 90 degree.
Plug in the known values,
[tex]\begin{gathered} v_x=(36.0m/s)cos90^{\circ} \\ =(36.0\text{ m/s)(0)} \\ =0\text{ m/s} \end{gathered}[/tex]Therefore, the initial horizontal velocity of ball is 0 m/s.
The vertical component of velocity of ball is given as,
[tex]v_y=v\sin \theta[/tex]Plug in the known values,
[tex]\begin{gathered} v_y=(36.0m/s)\sin 90^{\circ} \\ =(36.0\text{ m/s)(1)} \\ =36.0\text{ m/s} \end{gathered}[/tex]Therefore, the initial vertical velocity of the ball is 36.0 m/s.
A rectangular container measuring 34 cm ⨯ 38 cm ⨯ 55 cm is filled with water. What is the mass of this volume of water in kilograms and grams?
Answers
We will have the following:
*Kg:
[tex](\frac{1kg}{m^3})(0.34m\ast0.38m\ast0.55m)=0.07106kg/m^3[/tex]*G:
[tex](\frac{1000g}{m^3})(0.34m\ast0.38m\ast0.55m)=71.06g/m^3[/tex]A cyclist is freewheeling (not exerting additional force) down a 7 degree angle hill. The cyclists weight is 75N. What acceleration is the cyclist experiencing? I have to do the following:1. Draw a free body diagram2. Identify Givens and Unknowns3. Identify the Equations4. Set up the equation using the givens and unknowns5. Solve
Answers
The free body diagram in shown below:
From the diagram and the problem we have that:
• The weight and angle of the inclined plane are given.
,• The normal force and the components of the weight are unknown (this implies that the acceleration is unknown too); we also notice that the mass is not given the it is also an unknown.
We know that Newton's second law states that:
[tex]\vec{F}=m\vec{a}[/tex]where F is the resultant force and a is the acceleration. Since this is a vector equation we can decomposed it in two scalar equations (in this case we only need two scalar equations since the forces are coplanar), then we have:
[tex]\begin{gathered} Wx=ma_x \\ N-W_y=ma_y \end{gathered}[/tex]Since we don't expect the cyclist to move in the y direction (otherwise he will surely fall) the equations above would reduce to:
[tex]\begin{gathered} W_x=ma \\ N-W_y=0 \end{gathered}[/tex]From the first equation we can solve the acceleration, to do this we use the triangle to get the x-component of the weight:
[tex]\begin{gathered} W_x=ma \\ W\sin \theta=ma \\ a=\frac{W\sin \theta}{m} \end{gathered}[/tex]Since the weight is given but not the mass we use the fact that the weight is:
[tex]W=mg[/tex]to get the mass, then we have:
[tex]\begin{gathered} m=\frac{W}{g} \\ m=\frac{75}{9.8} \\ m=7.65 \end{gathered}[/tex]hence the mass of the cylcist is 7.65 kg.
Now that we have all the values we need we plug them in the expression for the acceleration:
[tex]\begin{gathered} a=\frac{75\sin 7}{7.65} \\ a=1.19 \end{gathered}[/tex]Therefore the acceleration of the cyclist is 1.19 meters per second per second.
Here are three stress and strain graphs shown on approximately the same scale. Match each graph to one of either copper, glass or rubber. Give reason for your choices, perhaps making reference to the grey circular points
Answers
For the three graphs A,B and C in the graph C we see that the strain is larger for a small value of stress.
This type of graph is for the polymers (rubber).
The graph A has smallest amount of strain for stress in comparison with B.
Upto the grey circle stress and strain are proportional .
Graph A is for Glass and B for Copper.
a block sliding on the ground where uk= 0.193 experiences a 14.7N friction force. what is the mass of the block in kg
Answers
Answer:
F = ma
14.7N = m(0.193)
m = 76.3 kg
when a car driver reached the crest of a hill, she saw the stop light turn red and slammed on the brakes. the car slowed down as it moved to the bottom of the hill. is the KE and PE increasing, decreasing, or staying the same?
Answers
As the brakes are opposing the motion of the car and trying to decrease the velocity of the car while moving down the hill.
Thus, the kinetic energy of the car is decreasing as the car is moving down the hill.
The height of the car is also decreasing with the motion of the car down the hill, thus, the potential energy of the car is also decreasing.
The brakes are applying the frictional force on the car which is converting their energy into heat energy. The thermal energy of the car increases as the car moves down the hill.
Thus, the kinetic energy and potential energy of the car decreases while moving down the hill.
In deep water, a tsunami moves very fast and has a long wavelength and a small amplitude (see A in picture). As it enters shallower water, it slows down, and the wavelength decreases. This causes the wave to become much taller (see B in picture).As waves slow down, they start to bunch together, so they have a shorter wavelength than before. This can also be explained by the wave equation v = f x λ (speed = frequency x wavelength), which shows that, when a wave’s speed decreases, it must have a shorter wavelength than before – slowing down won’t change the wave’s frequency.Having a shorter wavelength means that the waves get higher. You could think of the shortened wave as being ‘squashed’ sideways – the water in the wave has to get higher because there’s not as much room for it within the shorter wavelength. It’s a bit like squeezing a toothpaste tube – all the toothpaste is forced upwards.
Answers
Given:
The wavelength of the wave decreases as it gets closer to the shore.
The speed of the wave decreases as it gets closer to the shore.
The waves get taller as it gets closer to the shore.
To find:
How does a change in velocity cause a change in amplitude?
Explanation:
The amplitude of a wave is described as the distance of the highest point of vibration or the oscillation of the wave from its mean position.
Given that as the velocity of the speed decreases the waves get taller. That is as the velocity decreases the distance of the highest point of vibration of the wave from its equilibrium or mean position increases.
Final answer:
Thus as the velocity of the wave decreases, its amplitude increases.
I have finished most of this question just need help on making sure it’s correct and the last 2
Answers
Given
m: mass
m = 50 kg
KE: kinetic energ
PEg: gravitational potential energy
v: speed
Procedure
Point A
KE = 0
PEg = mgh
PEg = 50 kg * 10 m/s^2 * 100 m
PEg = 50000 J
v = 0 m/s
Point B
h = 60 m
PEg = mgh
PEg = 50 kg * 10 m/s^2 * 60 m
PEg = 30000 J
KE = 20000 J
[tex]\begin{gathered} v=\sqrt[]{\frac{2\cdot KE}{m}} \\ v=\sqrt[]{\frac{2\cdot20000\text{ J}}{50\text{ kg}}} \\ v=\sqrt[]{800\text{ }} \\ v=28.28\text{ m/s} \end{gathered}[/tex]Point C
h = 30 m
PEg = mgh
PEg = 50 kg * 10 m/s^2 * 30 m
PEg = 15000 J
KE = 35000 J
[tex]\begin{gathered} v=\sqrt[]{\frac{2\cdot KE}{m}} \\ v=\sqrt[]{\frac{2\cdot35000\text{ J}}{50\operatorname{kg}}} \\ v=37.41\text{ m/s} \end{gathered}[/tex]Point D
h = 60 m
PEg = mgh
PEg = 50 kg * 10 m/s^2 * 60 m
PEg = 30000 J
KE = 20000 J
[tex]\begin{gathered} v=\sqrt[]{\frac{2\cdot KE}{m}} \\ v=\sqrt[]{\frac{2\cdot20000\text{ J}}{50\text{ kg}}} \\ v=\sqrt[]{800\text{ }} \\ v=28.28\text{ m/s} \end{gathered}[/tex]
Point E
h = 0
PEg = 50 kg * 10 m/s^2 * 0
PEg = 0 J
KE = 50000 J
[tex]\begin{gathered} v=\sqrt[]{\frac{2\cdot KE}{m}} \\ v=\sqrt[]{\frac{2\cdot50000\text{ J}}{50\text{ kg}}} \\ v=44.72\text{ m/s} \end{gathered}[/tex]Which of the following is NOT a requirement for a planet? A. must orbit a star, but is not a star or satellite of another planetB. must be roundC. must clear its orbit of debrisD. must have a moon
Answers
Answer:
D. must have a moon
Explanation:
Scientists say that a planet must orbit a star, must be round, and must be big enough so its gravity clears its orbit of other objects. Therefore, the statement that is not a requirement for a planet is
D. must have a moon
For example, Mercury and Venus are planets with no moons.
In Denver, children bring their old jack o lanterns to the top of a tower and compete for accuracy in hitting a target on the ground. suppose that the tower is 9.0m high and that the bullseye is a horizontal distance of 3.5m from the launch point.if the pumpkin is thrown horizontally what is the launch speed needed to hit the ground? (b) If the jack o lantern is given an initial horizontal speed of 3.3m/s, what are the direction and magnitude of its velocity (c) 0.75s later and (d) just before it lands.
Answers
a)
In order to calculate the required horizontal speed, first let's calculate the falling time, using the free-fall formula:
[tex]d=\frac{gt^2}{2}[/tex]For d = 9 and g = 9.8, we have:
[tex]\begin{gathered} 9=4.9t^2 \\ t^2=\frac{9}{4.9} \\ t=1.355\text{ s} \end{gathered}[/tex]Then, let's use this time in the following formula for horizontal distance, so we can calculate the horizontal speed:
[tex]\begin{gathered} \text{distance}=\text{speed}\cdot\text{time} \\ 3.5=\text{speed}\cdot1.355 \\ \text{speed}=\frac{3.5}{1.355}=2.58\text{ m/s} \end{gathered}[/tex]b)
Let's calculate the vertical velocity after 0.75 seconds, using the formula:
[tex]\begin{gathered} V=V_0+a\cdot t \\ V=0+9.8\cdot0.75 \\ V=7.35\text{ m/s} \end{gathered}[/tex]The magnitude can be calculated using the Pythagorean Theorem with the horizontal and vertical velocities:
[tex]\begin{gathered} V^2=7.35^2+3.3^2 \\ V^2=54.0225+10.89 \\ V^2=64.9125 \\ V=8.06\text{ m/s} \end{gathered}[/tex]And the direction is given by the arc tangent of the vertical velocity divided by the horizontal velocity (for this, let's use a negative value of vertical velocity, since it points downwards)
[tex]\theta=\tan ^{-1}(-\frac{7.35}{3.3})=\tan ^{-1}(-2.2272)=-65.82\degree[/tex](d)
To find the vertical velocity, let's use Torricelli's equation:
[tex]\begin{gathered} V^2=V^2_0+2\cdot a\cdot d \\ V^2=0^2+2\cdot9.8\cdot9 \\ V^2=176.4 \\ V=13.28\text{ m/s} \end{gathered}[/tex]Calculating the final speed magnitude and orientation, we have:
[tex]\begin{gathered} V^2=13.28^2+3.3^2 \\ V^2=187.2484 \\ V=13.68\text{ m/s} \\ \\ \theta=\tan ^{-1}(-\frac{13.68}{3.3})=\tan ^{-1}(-4.145)=-76.44\degree \end{gathered}[/tex]lc. A student makes a claim that states the first hill of a roller coaster is always the tallest(Point A) provided there is no mechanical assistance at any point after Point A on the track.Do you accept or reject her claim? Explain your answer. (2 points)
Answers
We accept the claim. This comes from the fact that if there is no mechanical assistance after point A (that is the tallest) then we make sure that the potential energy converts in kinetic energy and that way we make sure that the rollercoaester reaches all the other hills. If the tallest point is not the first one and there's no mechanical assitances then the rollercoester won't reach the hills that are taller than the first one (the kinetic energy won't be enough to reach it).
When an arrow is released from its bow, its energy is transformed from potential energy to kinetic energy. Determine if the statement is correct.
Answers
Let's determine if the statement ''When an arrow is released from its bow, its energy is transformed from potential energy to kinetic energy'' is correct.
Let's first define kinetic and potential energies.
Potential energy is the energy stored in an object due to its position which depends on the relative position of various parts of the system.
Kinetic energy is the energy possesed by an object in motion.
Therefore, before the arrow is released from the bow, it is at rest and the energy is stored.
Hence, it posssess potential energy.
When the arrow is now released from the bow, it is now in motion. Since it is now in motion, the potential energy is now transformed to kinetic energy.
Therefore, the statement ''When an arrow is released from its bow, its energy is transformed from potential energy to kinetic energy'' is correct.
Calculate the answer to the correctnumber of significant digits.1.899+ 0.58
Answers
ANSWER
2.48
EXPLANATION
We have to add like we normally do with whole numbers and put the decimal point in the same place it is in each summand:
The significant digits start with the first digit different from zero, reading from left to right:
This number has 4 significant digits in total: 2, 4, 7 and 9
Note that the numbers added don't have the same number of decimal places. The first one has three decimal places while the second one has two decimal places. This means that we have to round the answer to the second decimal place - which is hte 3rd significant digit. SInce the 4th significant digit is more than 5, we have to add one to the third significant digit:
[tex]2.479\Rightarrow2.48[/tex]Calculate the mass of an object with a weight of 467 N.
Answers
We will have that the mass of the object is:
[tex]\begin{gathered} m=\frac{467N}{9.8m/s^2}\Rightarrow m=\frac{2335}{49}kg \\ \\ \Rightarrow m\approx47.65kg \end{gathered}[/tex]So, the mass of the object is 2335/49 kg, that is approximately 47.65 kg.
What common unit is used to measure sound intensity? Answer here
Answers
Decibel (dB)
Explanation:Sound intensity is the power carried by sound waves per unit area in a perpendicular direction to that area.
The unit of sound intensity is the decibel
A 1 kg mass has a kinetic energy of 1 Joule when its speed isA. 0.45 m/sB. 1.4 m/sC. 1 m/sD. 4.4 m/s
Answers
Kinetic energy = 1/2 x mass x velocity^2
Where:
Kinetic energy = 1 J
mass = 1 kg
Isolate v (speed)
KE = 1/2 m v^2
√(2KE/m) = v
v = √(2KE/m)
Replacing with the values given:
v = √(2*1/1)
v= √2 = 1.4 m/s
Answer: 1.4 m/s (B)
Question 1: Assume that the pendulum of a grandfather clock acts as one of Planck'sresonators. If it carries away an energy of 8.1 x 10-15 eV in a one-quantumchange, what is the frequency of the pendulum? (Note that an energy this smallwould not be measurable. For this reason, we do not notice quantum effects in thelarge-scale world.)
Answers
Given:
Energy = 8.1 x 10⁻¹⁵ eV.
Let's find the frequency of the pendulum.
To find the frequency, apply the formula for the energy of a light quantum:
[tex]E=hf[/tex]Where:
E is the energy
h is Planck's constant = 6.63 x 10⁻³⁴ m² kg/s
f is the frequency.
Where:
1 eV = 1.6 x 10⁻¹⁹ J.
Rewrite the formula for f and solve:
[tex]f=\frac{E}{h}[/tex]Thus, we have:
[tex]f=\frac{8.1\times10^{-15}*(1.6\times10^{-19})}{6.63\times10^{-34}}[/tex]Solving further:
[tex]\begin{gathered} f=\frac{8.1\times10^{-15}*(1.6\times10^{-19})}{6.63\times10^{^{-34}}} \\ \\ \\ f=1.95\text{ Hz.} \end{gathered}[/tex]Therefore, the frequency of the pendulum is 1.95 Hz.
ANSWER:
1.95 Hz
The maximum possible efficiency of a reversible heat engine is 79.46% when the cold temperature is 224.0°C. What is the hot temperature in degrees Celsius?
Answers
We have
A heat engine is 79.46%
TC= 224.0°C
TH=?
we have the next formula
[tex]\eta(\text{\%)}=1-\frac{T_C}{T_H}\times100[/tex]we substitute the values
[tex].7946=1-\frac{224}{T_H}\times100[/tex]then we isolate TH
[tex]\begin{gathered} .07946-1=-\frac{T_C}{T_H}\times1 \\ -0.2054=-\frac{T_C}{T_H}\times1 \\ \frac{T_C}{T_H}\times1=-0.2054 \\ \frac{T_C}{T_H}=\frac{0.2054}{1} \\ \frac{T_H}{T_C}=\frac{1}{0.2054} \\ T_H=4.8685\cdot224 \\ T_H=1090.55\text{ \degree{}C} \end{gathered}[/tex]the hot temperature is 1090.55 degrees Celsius.
If frictional forces and air resistance were acting upon the falling ball in #1 would the kinetic energy of theball just prior to striking the ground be more, less, or equal to the value predicted in #1?
Answers
Given that the ball is falling in two different situations.
Kinetic energy is the energy that an object possesses due to its motion and it is proportional to the square of the velocity of the object.
The frictional force and the air resistance are the forces that will be opposing the motion of the ball. That is these forces act in the opposite direction of the motion of the ball thus reducing the net acceleration acting on the ball.
As the acceleration decreases the final velocity of the ball decreases.
Thus the kinetic energy of the ball just prior to striking the ground will be less than before.
A submarine is stranded on the bottom of the ocean with its hatch 25 m below the surface. In this problem, assume the density of sea water is 1.03 x 10^3 kg/m^3. A) calculate the magnitude of the force in newtons pressing on the hatch from outside by the sea water given it is circular and 0.25m in diameter. The air pressure inside the submarine is 1.00atm (101,325 Pa). B) calculate the magnitude of the force, in newtons needed to open the hatch from the inside
Answers
Given:
The height (depth) of the hatch from the seawater surface is: h = 25 m
The density of seawater is: ρ = 1.03 × 10³ kg/m³
The diameter of the hatch is: d = 0.25 m
The pressure inside the submarine is: Ps = 1 Atm = 101325 Pa
To find:
The magnitude of the force pressing the hatch from the outside by the seawater and the magnitude of force to open the hatch from the inside.
Explanation:
The net pressure on the hatch area is given as:
[tex]P_{net}=\frac{F_{net}}{A}..........(1)[/tex]Here, Pnet is the net pressure on the hatch of area A, and Fnet is the net force acting on the hatch from the outside.
The net pressure Pnet is given as:
[tex]P_{net}=P_{atm}+P_w-P_s[/tex]Here, Patm is the atmospheric pressure above the seawater surface, Pw is the pressure of the water and Ps is the pressure inside the submarine.
The atmospheric pressure Patm of 1 Atm will contribute to the net pressure on the hatch from the outside. The atmospheric pressure Patm will have no effect as it will cancel out with the pressure Ps of equal magnitude as it is in an opposite direction from inside the submarine.
Substituting the values of the atmospheric pressure Patm and the pressure inside the submarine Ps in the above equation, we get:
[tex]\begin{gathered} P_{net}=1\text{ Atm}+P_w-1\text{ Atm} \\ \\ P_{net}=P_w..........(2) \end{gathered}[/tex]Thus the net pressure on the hatch will be the pressure of the seawater only.
Now, the net pressure Pnet can be calculated as:
[tex]P_{net}=h\rho g[/tex]Here, g is the acceleration due to the gravity having a value of 9.8 m/s².
Substituting the values in the above equation, we get:
[tex]\begin{gathered} P_{net}=25\text{ m}\times1.03\times10^3\text{ kg/m}^3\times9.8\text{ m/s}^2 \\ \\ P_{net}=252350\text{ N/m}^2\text{..........\lparen3\rparen} \end{gathered}[/tex]The area of the hatch can e calculated as:
[tex]\begin{gathered} A=\pi r^2 \\ \\ A=\pi\times(\frac{0.25}{2})^2 \\ \\ A=0.0491\text{ m}^2..........(4) \end{gathered}[/tex]Substituting equation (3) and equation (4) in equation (1) and rearranging it, we get:
[tex]\begin{gathered} 252350\text{ N/m}^2=\frac{F_{net}}{0.0491\text{ m}^2} \\ \\ F=252350\text{ N/m}^2\times0.0491\text{ m}^2 \\ \\ F=12390.39\text{ N} \end{gathered}[/tex]A force of 12390.39 Newtons acts on the hatch by the seawater above it. To open the hatch from the inside, an equal magnitude of force is needed to apply from inside the submarine. Thus, a force of 12390 Newtons is required to open the hatch from the inside.
Final answer:
The magnitude of force pressing the hatch from the outside by the seawater is 12390.39 Newtons.
The magnitude of force required to open the hatch from inside the submarine is 12390.39 Newtons.
(A) The magnitude of the force in newtons pressing on the hatch from outside by the seawater given it is circular and 0.25 m in diameter is 1.24 × 10 ⁴ N.
(B) The force applied needed to open the hatch from the inside is 1.24 × 10 ⁴ N.
What is force?In the body, force is the result of either a push or a pull. The three main categories of forces are friction, nuclear, and gravitational. For instance, when a hand strikes a wall, the hand puts force on the wall and the wall also exerts a force on the hand. Newton was given a variety of laws to help him understand force.
Given :
The density of seawater, ρ = 1.03 x 10³ kg / m³ ,
The height of the hatch of the submarine, h= 25 m,
The gravitational acceleration, g = 9.8 m / s² ,
The radius of the hatch, r = 0.25 m
Calculate the area of the hatch by the formula given below,
A = π × r² = π × (0.125 m)² [r = d / 2]
A = 4.9 x 10 ⁻² m²
(A) Calculate the force of the water by the following formula,
[tex]P = F / A[/tex]
F = P × A (P = ρ × g × h)
F = ρ × g × h × A
Substitute the values,
F = 1.03 x 10³ kg / m³ × 9.8 m / s² × 25 m × 4.9 x 10 ⁻² m²
F = 12365.15 N or 1.24 × 10 ⁴ N
(B) The force needed to open the hatch = The Force applied by water on the hatch.
Therefore, the magnitude of the force in newtons pressing on the hatch from outside by the seawater given it is circular and 0.25 m in diameter is 1.24 × 10 ⁴ N, and the force applied needed to open the hatch from the inside is 1.24 × 10 ⁴ N.
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A tractor travels at a constant speed of 6m/s. Find the power supplied by the engine if it can supply a maximum force of 467 kN.
Answers
speed = v = 6m/s
Force = 467 kn = 467000N
Power = Work/ time
Work = Force x distance
Speed = distance / time
Isolating Distance:
Distance = Speed * time
P =[ Force * (speed * time ) ] / time
P = Force * speed
Replacing:
P = 467000 N * 6 m/s = 2,802,000 W
An airplane covers a straight-line distance of 8.13 km in 33.5 s, during which time it has a constant forward acceleration of 4.6 m/s2.1. what is the speed at the first begining of 33.5 s.2.what is the speed at the end of the 33.5 s.
Answers
Given data
*The given distance is s = 8.13 km = 8130 m
*The given time is t = 33.5 s
*The given acceleration is a = 4.6 m/s^2
(1)
The formula for the speed at the first beginning of 33.5 seconds is given as
[tex]s=ut+\frac{1}{2}at^2[/tex]Substitute the known values in the above expression as
[tex]\begin{gathered} 8130=u(33.5)+\frac{1}{2}(4.6)(33.5)^2 \\ u=165.6\text{ m/s} \end{gathered}[/tex]Hence, the speed at the first beginning of 33.5 s is u = 165.6 m/s
(2)
The formula for the speed at the end of the 33.5 s is given as
[tex]v=u+at[/tex]Substitute the known values in the above expression as
[tex]\begin{gathered} v=(165.6)+(4.6)(33.5)_{} \\ =319.7\text{ m/s} \end{gathered}[/tex]Hence, the speed at the end of the 33.5 s is v = 319.7 m/s
Which option gives an object's volume in SI units?O A. 2,6 m3OB. 4.3 kgOC. 3.4 LD. 5.5 K
Answers
ANSWER:
A. 2.6 m^3
STEP-BY-STEP EXPLANATION:
The volume of an object is given by the cube of its length.
In SI the unit for length is the meter, therefore, in the case of volume it would be cubic meters.
This means that the correct answer is: A. 2.6 m^3