Answer:
2454.57
Explanation:
Step 1: Solve
[tex]\frac{(8.86+0.001)}{(3.610)(10^{-3}) }[/tex]
[tex]\frac{8.861}{0.003.61 }[/tex]
2454.57
Therefor the answer to this equation is 2454.57
Robin fired a bullet of mass 100 gm from a gun of mass 5 kg. The bullet leaves the gun with a speed of 400 m/s. After penetrating 4 cm of a plank of 10 cm, the bullet loses one third of its initial velocity.
a. Calculate the backward velocity of the gun?
b. Can the bullet penetrate the plank of the wood completely? Explain mathematically.
please help
(a) The recoil or backward velocity of the gun is 8 m/s.
(b) The bullet cannot penetrate the plank of the wood completely.
The given parameters include;
mass of the bullet, m₁ = 100 g = 0.1 kgmass of the gun, m₂ = 5 kginitial velocity of the bullet, u₁ = 400 m/sthickness of the plank, x = 10 cm(a) The backward or recoil velocity of the gun is calculated by applying the principle of conservation of linear momentum.
let the backward or recoil velocity of the gun = u₂m₁u₁ + m₂u₂ = 0
m₂u₂ = -m₁u₁
[tex]u_2 = -\frac{m_1u_1}{m_2} \\\\u_2 = - \frac{0.1 \times 400}{5} \\\\u_2 = -8 \ m/s[/tex]
Thus, the recoil or backward velocity of the gun is 8 m/s.
(b) determine if the bullet can penetrate the plank of the wood completely
the bullet traveled 4 cm and lost ¹/₃ of u₁the remaining distance to completely penetrate the plank = 6 cmthe final velocity of the bullet at 4 cm, v = 400 - ¹/₃ x 400 m/s = 266.67 m/sthe acceleration of the bullet is calculated as;
v² = u₁² + 2as
2as = v² - u²
[tex]a = \frac{v^2 -u_1^2}{2s} \\\\a = \frac{(266.67)^2 -(400)^2}{2\times 0.04} = -1.111 \times 10^6 \ m/s^2[/tex]
Finally, determine the distance traveled by the bullet when it comes to a complete stop, that is the final velocity = 0
[tex]v_f^2 = v^2 + 2ad\\\\2ad = v_f^2 - v^2\\\\d = \frac{v_f^2 - v^2}{2a} \\\\d = \frac{(0) - (266.67)^2}{2(-1.111\times 10^6)} \\\\d = 0.032 \ m[/tex]
d = 3.2 cm
The total distance traveled by the bullet inside the plank = 4 cm + 3.2 cm = 7.2 cm
Therefore, the bullet cannot penetrate the plank completely.
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A control clinic offers a program that guarantees a weight loss of up to 0.46 kg in one week. Express the weight loss in a ratio of milligrams per second.
Answer:
0.76 mg/s
Explanation:
0.46 kg/week × (1 week / 7 days) × (1 day / 24 hrs) × (1 hr / 3600 s) × (1000 g/kg) × (1000 mg/g) = 0.76 mg/s
A bus is travelling at 10m/s. It accelerates at 2m/s^2 over a distance of 20m. Calculate it's final velocity
Answer:
13.4 m/s
Explanation:
Given:
Δx = 20 m
v₀ = 10 m/s
a = 2 m/s²
Find: v
v² = v₀² + 2aΔx
v² = (10 m/s)² + 2 (2 m/s²) (20 m)
v = 13.4 m/s
An inventive child wants to reach an apple in a tree without climbing the tree. Sitting in a chair connected to a rope that passes over a frictionless pulley, the child pulls on the loose end of the rope with such a force that the spring scale reads 250 N. The child’s true weight is 320 N, and the chair weighs 160 N. (a) Show that the acceleration of the system is upward and find its magnitude. (b) Find the force the child exerts on the chair.
Answer:
(a) 0.42 m/s²
(b) 83 N
Explanation:
Assuming g = 10 m/s².
Draw free body diagrams for the child and the chair.
There are three forces on the child:
Tension force T pulling up,
Weight force Mg pulling down,
and normal force N pushing up.
There are three forces on the chair:
Tension force T pulling up,
Weight force mg pulling down,
and normal force N pushing down.
Sum of forces on the child in the y direction:
∑F = ma
T + N − Mg = Ma
Sum of forces on the chair in the y direction:
∑F = ma
T − N − mg = ma
Add the equations together to find the acceleration.
2T − Mg − mg = Ma + ma
a = (2T − Mg − mg) / (M + m)
a = g (2T − Mg − mg) / (Mg + mg)
a = (10 m/s²) (2 × 250 N − 320 N − 160 N) / (320 N + 160 N)
a = 0.42 m/s²
Plug into either equation to find the normal force.
T + N − Mg = Ma
250 N + N − 320 N = (320 N / 10 m/s²) (0.42 m/s²)
N = 83 N
How much work is done in moving a body of mass 1.0 kg from an elevation of 2 m to
an elevation of
Answer:
The work done is -176.4 J.
Explanation:
Given that,
Mass = 1.0 kg
An elevation of 2 m to an elevation of 20 m.
Suppose, Find the work done by the gravitational field of the earth?
We need to calculate the force
Using formula of force
[tex]F=mg[/tex]
Put the value into the formula
[tex]F=1.0\times9.8[/tex]
[tex]F=9.8\ N[/tex]
We need to calculate the displacement
Using formula of displacement
[tex]Displacement = s_{2}-s_{1}[/tex]
[tex]s=20-2=18\ m[/tex]
The direction of displacement is upward.
Since gravitational force is downwards and displacement is upwards,
Then the angle is 180°.
We need to calculate the work done
Using formula of work
[tex]W=f\cdos s\cos\theta[/tex]
[tex]W=9.8\times18\cos180[/tex]
[tex]W=-176.4\ J[/tex]
Hence, The work done is -176.4 J.
convert as indicated step by step 1)1 sec into day 2) 1 week into sec (3) 50cm into meter
Answer:
1) 1,157*10⁻⁵ day; 2) 604800 sec.; 3) 0.5 m.
Explanation:
1) 1 second into one day:
one day consists of 24 hours, it means 24*3600=86400 seconds. Then 1 second is 1/86400 day or 1,157*10⁻⁵ day.
2) 1 week into seconds:
1 day consists of 3600*24=86400 seconds, then the week is 7*86400=604800 seconds.
3) 50 cm into meter:
100 cm is one meter, then 50 cm is 0.5 meter.
PS. note, there is not the only way to perform conversion.
write two ways to be protected from the energy crisis?
Please Help
A skydiver jumps out of a hovering helicopter, so there is no forward velocity. Use this information to answer questions. Ignore wind resistance for this exercise.
What is the skydiver's velocity after one second? Show your work and include direction.
Answer:
I suppose that by forward velocity the question refers to horizontal velocity
Since the acceleration due to gravity is 10 m/s2.The object gains an increase of 10 m/s in speed per second.In after one second its speed will be 10M/S
The direction will be downward i.e vertical
A particular celestial body orbits at a particular speed. For every two orbits it makes, another celestial body orbits three times. This orbital resonance would correspond to which musical interval?
Answer:
Explanation:
frequency of first body f₁ = 2 / T where T is time taken by it for making two orbits
frequency of second body f₂ = 3 / T
ration of two frequency
f₁ / f₂ = 2 / 3
This ratio is called perfect fifth in musical interval .
a boy looks at the reflection of his digital watch in a plane mirror and thinks the time is 10:11. what is the correct time?
Answer:
11:10 will be the time. reflection causes the object to be flipped when you see its image at the mirror
Describe manipulated Variable
A stone is dropped from the same height at Terai and at the top of the
mountain. Where does it fall faster? Why?
Answer:
It will fall at the same speed in both locations
Explanation:
When an object is falling, it is accelerated to the same degree irrespective of the height from which it is falling.
All objects on the earth's surface experience an acceleration due to gravity. This acceleration due to gravity is the same for all objects irrespective of their height or mass.
Hence for a stone dropped from the same height as Terai and the top of a mountain, the acceleration due to gravity is the same in both cases hence they will fall at the same speed.
What is the Opportunity Cost in textbooks from going from point A to B?
Answer:
60.00
Explanation:
you welcome
A ship sets out to sail to a point 123 km due north. An unexpected storm blows the ship to a point 112 km due east of its starting point. (a) How far and (b) in what direction (as an angle from due east, where north of east is a positive angle) must it now sail to reach its original destination
Answer:
Explanation:
We shall represent the point of destination and point of new starting point in vector form .
i and j will represent east and north .
point of destination = 123 j
starting point = 112 i
distance between the two
D = 123 j - 112 i
magnitude of D = √ ( 123² + 112² )
= 166.35 km
Direction of D
Tanθ = - 123 / 112
= - 1.09
θ = 132.54 degree from east in positive angle .
Clois what is the weight of a body in the earth, if its weig is 5Nin moon?
Explanation:
because the moon has less mass than earth, the force due to gravity at the lunar surface is only about 1/6 that on earthso,the weight of a body on earth is 6×5N =30N
According to Hooke's law
(a) stress x strain = constant
(b) stress / strain = constant
(c) strain / stress = constant
(d) stress = strain
Answer:
According to Hook's law, we know,
strain/stress =Constant
Explanation: So, the ratio between stress and strain is always constant.
So, if stress is increased, then strain changes in that way so that this ratio always remains constant.
You are hiking in a canyon and you notice an echo. You decide to let out a yell and notice it took 2 seconds before you heard the echo of your yell. How far away is the canyon wall that reflected your yell
Answer:
d = 343 m
Explanation:
Given that,
You notice that an echo took 2 seconds before you heard the echo of your yell.
We need to find that how far away is the canyon wall that reflected your yell. It means we need to find the distance.
The distance covered by an object is given by :
d = v × t
v is speed of sound in air, v = 343 m/s
The sound took 1 s to reach the wall and 1 s back to you.
It means that,
d = 343 × 1
d = 343 m
So, canyon will reflect your yell at a distance of 343 m
please answer
during a journey, a car travels at 40 km in 2.5 hours, next 62 km in 3 hours, then took a break for 30 minutes, again travelled the last 120 km in 3.2 hours. calculate the average speed of the car during the journey.
average speed of the car is 23.9 km/h
A group of air particles in a balloon are spread far apart and moving rapidly around inside the balloon. The balloon is placed in a refrigerator for 30 minutes. What would you expect to happen to the appearance of the balloon? Explain your answer in terms of particle movement and their change in temperature. The balloon is removed from the refrigerator and placed on the kitchen counter. What would you expect to happen to the appearance of the balloon? Explain your answer in terms of particle movement and their change in temperature.
Answer:
1) The balloon will shrink
2) The balloon will grow bigger and regain its shape
Explanation:
By the kinetic theory of gases, we have;
[tex]v_{rms} = \sqrt{\dfrac{3 \cdot R \cdot T}{MW} }[/tex]
[tex]P = \dfrac{n \cdot MW \cdot vrms^2}{3 \cdot V}[/tex]
Where;
[tex]v_{rms}[/tex] = RMS Speed
R = The universal gas constant
T = The temperature
MW = The Molecular weight
n = The number of moles
V = The volume
P = The pressure
1) When the balloon is placed in the refrigerator for minutes, the temperature inside the balloon will drop and RMS speed will reduce, however due to the elastic wall of the balloon, the pressure will remain the same therefore the volume will reduce and the balloon will shrink
2) When the balloon is placed on the kitchen counter, the temperature inside the balloon will rise leading to the increase in the RMS speed which will raise the pressure effect on the wall of the balloon as the balloon is made of elastic material, as the pressure rises, the wall expands to keep the pressure constant and the volume occupied by the air particles will increase, the balloon will grow bigger and regain its shape.
The wavelength of a radio wave varies inversely as its frequency. A wave with a frequency of 1800 kilohertz has a length of 200 meters. What is the length of a wave with a frequency of 360 kilohertz?
Answer:
1000meters
Explanation:
Let the wavelength of the radio wave be W and it's frequency be f. If the wavelength of a radio wave varies inversely as its frequency, then W∝1/f
W = k/f where k is the constant of proportionality.
k = Wf
If a wave with a frequency of 1800 kilohertz has a length of 200 meters, then k = 1800×200
k = 360,000kHzm
To get the length of a wave with a frequency of 360 kilohertz, we will substitute the value of k and f = 360kHz into the initial formula i.e
W = k/f
W = 360,000/360
W = 1000meters
Hence the length of a wave with a frequency of 360 kilohertz is 1000meters
Students are going to conduct an experiment to study the effect of a net force applied to an object on the object’s motion. In each trial of the experiment, the students will apply a net force on the object. They also need to take two other measurements. What are the other quantities they should measure in each trial of the experiment?(1 point) velocity and time mass and acceleration mass and velocity acceleration and time
Answer:
A. velocity and time
Explanation:
A force can be define as an agent which has the capacity to change the state of an object. It can either increase the velocity of a body, change its direction of motion or cause a moving object to come to rest.
From Newton's second law of motion;
F = ma
where F is the force on the object, m is the mass of the object and a is the acceleration of the object. The unit of force is kgm/[tex]s^{2}[/tex] or Newtons.
a = [tex]\frac{change in velocity}{change in time}[/tex]
In the given question, apart from the mass of the object which is constant, the students should take the measurements of the velocity and time in each trial so as to calculate the required acceleration.
Answer:
mass and acceleration!
Explanation:
Because i am in class just like you and got it wrong because i didn't choose my first answer:(
Question 5
Calculate the kinetic energy of a car (m - 800 kg) moving at 15 m/s. Write your answer to the nearest whole number in the blank space
provided. Only write the numerical value of the answer without units. Do not leave any space in between numbers.
Answer: Joules
Answer:
90,000Explanation:
[tex]m =800kg\\v = 15\\\\K.E = \frac{1}{2}mv^2\\ K.E= \frac{1}{2} \times 800\times 15^2\\= 400 \times 225\\= 90000 joules\\= 90 kilojoules[/tex]
Two 110 kg bumper cars are moving toward each other in opposite directions. Car A is moving at 8 m/s and Car Z at −10 m/s when they collide head–on. If the resulting velocity of Car A after the collision is −10 m/s, what is the velocity of Car Z after the collision? 10 m/s −8 m/s 8 m/s 10 m/s-
Answer:
it will be 8ms-1
Explanation:
MaUa+MbUb=MaVa+MbVb
Which statement describes one feature of Rutherford's model of the atom?
O The atom is mostly empty space.
O The atom cannot be divided into smaller particles.
O Electron clouds are regions where electrons are likely to be found.
O The electrons are located within the positive material of the nucleus.
Answer:
The atom is mostly empty space.
Explanation:
Ernest Rutherford in the year 1911 developed a model of an atom. In his model the atom was shown that the atom is mostly empty spaces composed of negative electrons which orbits round a positive nucleus just like planets revolving round the sun.
Rutherford came up with this model by performing experiments in 1909 which involves the scattering of alpha particles on a thin gold foil. From this experiments he came up with his model.
Answer:
A!
Explanation:
The atom is mostly empty space.
lab safety test Safety goggles and an apron must be worn when handling chemicals labeled corrosive because they:________.
Answer: React with the skin
Explanation:
lab safety test Safety goggles and an apron must be worn when handling chemicals labeled corrosive because they React with the skin
010) Identify the true statement. Group of answer choices The height of waves is determined by wind strength and fetch. Wave base is the lowest sea surface elevation attained during the passage of a wave. Waves have no effect on the seafloor near the shoreline. Waves speed up as they enter shallower water.'
Answer:
The height of the wave is determined by the wind strength and fetch.
Explanation:
The height of the wave is determined by the wind strength and fetch.
The more the strength and the more the fetch size the more will be the height of the wave.
Remember as the wave approaches the coast its wavelength decreases and the wave height increases, whereas when the wave goes away from the coast its wavelength increases and height decreases.
What did Bohr's model of the atom include that Rutherford's model did not have?
a nucleus
energy levels
electron clouds
smaller particles
Answer:
The correct option is energy levels
Explanation:
Rutherford's model of an atom suggests that an atom has a tiny positively charged central mass (now called the nucleus) which is surrounded by electrons (negatively charged) in a cloud-like manner.
Bohr's model went a bit further than the Rutherford's model in describing an atom by suggesting that the electrons which surrounds in the nucleus travel in fixed circular orbits. This description by Bohr was able to describe the energy levels of orbitals which assumes that smallest orbitals have the lowest energy while the largest orbitals have the highest energy.
Answer:
energy levels
hope this helped!
Explanation:
Find the acceleration of a body moving with uniform velocity
Answer:
The derivative of a constant term is always 0. So the acceleration of the body would be zero. Hence, the acceleration of a body moving with uniform velocity will always be zero.
If a force of 1250 N acts on an area of 25 metres squared, what will be the pressure acting on the surface? Show your working as well.
Answer: 50 Pa
Explanation:
Pressure = Force/Area
Pressure = N/m^2
Pressure = 1250/25
Pressure = 50
Pressure = 50 Pa
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Answer:
50 pascal
Explanation:
Force=1250N
Area=25m^2 [ pressure=force/area]
P=F/A
1250/25=50
predict the reading of the spring balance when the wooden block is pulled on the sandpaper. Explain your answer.
Answer:
* if the spring force is greater than the maximum of the static friction force,
Fe = m (a + μ_k g)
* If the elastic force is less than or equal to the static friction force, the result is with static friction coefficient
Fe =μ_s m g
Explanation:
For this exercise we must apply Newton's second law to the system
X axis
Fe -fr = m a
Fe = m a + fr
Y axis
N-W = 0
N = W = mg
the roe force is given by
fr = μ N
fr = μ mg
we substitute
Fe = m a + μ m g
Ee = m (a + μ g)
Let's analyze the solution. We have several possibilities
* if the spring force is greater than the maximum of the static friction force, the system acquires an acceleration and the result is with the kinetic friction coefficient
Fe = m (a + μ_k g)
* If the elastic force is less than or equal to the static friction force, the result is with static friction coefficient
Fe =μ_s m g