You can improve how you handle stress and difficulties (adversity) in your life by using a variety of stress management techniques. You may lead a more well-balanced existence by controlling your stress.
What are the importance of managing stress?You put your complete well-being at danger if you're under a lot of stress every day. Your mental balance and physical health both suffer from stress. Your capacity for clear thinking, successful functioning, and enjoyment of life is reduced. You could feel helpless in combating stress. There won't ever be more hours in the day, the bills won't stop rolling in, and your obligations to your job and family will always be demanding. Stress is a natural, spontaneous reaction to a stressful situation on the body, mind, and emotions. Everyone's life entails it as a normal aspect. Stress can spur growth, activity, and change when it is used constructively. Long-term, negative stress, though, might lower your level of well-being.Though it may not seem like it, you actually have a lot more control. Achieving effective stress management enables you to release the grip that stress has on your life and improves your ability to be happier, healthier, and more effective. The ultimate objective is a well-balanced existence with time for work, relationships, relaxation, and fun—as well as the resilience to hold up under stress and face obstacles head-on. However, there is no one approach to stress management that works for everyone. Discovering what works best for you through experimentation is crucial. You can do it with the aid of the stress-reduction advice that follows.To know more about Stress Management, visit:
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When using their brakes,
cars disengage the engine so that it no longer
provides any forward force.
A(n) 2006.1 kg car is coasting along a level
road at 31.5 m/s. A constant braking force
is applied, such that the car is stopped in a
distance of 62.1 m.
What is the magnitude of the braking force?
Answer in units of N.
The magnitude of the braking force is 0
What is acceleration?
velocity changes with time at an accelerating rate in both speed and direction. In the case of simple harmonic motion, the spring's elastic force serves as the restoring force. The application of Hooke's law, F = - kx, allowed for its discovery. Here, k is the spring constant and x is the spring's deformation (change of its length from equilibrium position).
We can see that this force is variable and dependent on the mass-spring system's x displacement. The minus sign indicates that the force's direction is the opposite of the displacement, and as a result, the force causes the mass of the back to return to its equilibrium position.
As with any force, restoring force can be calculated using Newton's second law, F = ma, where m is the body's mass and an is its acceleration.
Now we can write:
The body's displacement x is zero when it reaches equilibrium. Acceleration is therefore 0.
By the way, when the amplitude of the this mass-spring system reaches its maximum, the acceleration will be at its maximum value. The mass-spring pendulum swings in the opposite direction at these points. We refer to those as inflection points.
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the speed of light in a material is what is the critical angle of light ray at the interface between material and vacuum
This problem indicates that the speed of light in a material medium is 0.5 10⁸ m / s, they ask to find the critical angle between the material and the vacuum.
Let's find the refractive index of the material
n = c / v
n = 3 10⁸ / 0.5 10⁸
n = 6
When the material passes from one medium to another, it must comply with the law of refraction.
n₁ sin θ = n₂ sin θ₂
for the angle criticize the angles tea2 = 90
t = sin⁻¹n₂/ n₁
The vacuum replacement index is n₂ = 1
t = sin⁻¹ (1/6)
t = 9.59º
Therefore, the angle of refractive index will be 9.59°.
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[NOTE: THIS IS AN INCOMPLETE QUESTION. THE COMPLETE QUESTION IS: The speed of light in a material is 0.50 c. what is the critical angle of a light ray at the interface between the material and a vacuum?]
4. A 1.5 m tall man is standing 2m away from the concave lens (remember f is negative) of a peephole with a focal length of 3.0 cm. a) What is the distance to the image in centimeters? b) What is the magnification of the image in meters?
Here,
Size of object = 1.5 m;
Object distance (u) = - 2m = -200cm
focal length (f) = - 3.0 cm
Image distance (v) = ?
Using lens formula
[tex]\begin{gathered} \frac{1}{f}=\text{ }\frac{1}{v}-\frac{1}{u}; \\ \frac{1}{-3}=\frac{1}{v}-\frac{1}{-200}; \\ \frac{1}{-3}=\text{ }\frac{1}{v}\text{ +}\frac{1}{200} \\ \frac{1}{v}=\text{ -}\frac{1}{3}-\frac{1}{200}=-\text{ }\frac{203}{600} \\ v=\text{ - }\frac{600}{203}=\text{ -2.96 cm} \end{gathered}[/tex]Now magnification is given by
[tex]Magnification=\text{ }\frac{v}{u}=\text{ }\frac{2.96}{200}=0.0148[/tex]Final answer is :-
Image distance = - 2.96 cm & magnification = 0.0148
a motorcycle traveling 100m/s drives off a horizontal ramp and lands a horizontal distance of 40m away from the edge of the ramp, what is the height of the ramp?
We will have the following:
First, we determine the time it takes for the motorcycle to traverse the 40 m:
[tex]40m=(100m/s)t\Rightarrow t=0.4s[/tex]Now, we will use the time to determine the height of the ramp:
[tex]\begin{gathered} d=(0m/s)(0.4s)+\frac{(9.8m/s^2)(0.4s)^2}{2}\Rightarrow d=\frac{98}{125}m \\ \\ \Rightarrow d=0.784m \end{gathered}[/tex]So, the ramp was located 0.784 meters in height.
Which factor will increase the resistance of a conductor?
Length is directly proportional to resistance. When length increases resistance increases and vice versa.
Cross sectional area is inversely proportional to resistance. When cross sectional area of a conductor increases resistance decreases and vice versa.
Different materials have different resistances.
Temperature is directly proportional to resistance. When temperature increases resistance increases and vice versa.
Two students in bumper cars want to prove conservation of momentum. They collide their bumper cars. The first bumper car has a mass of 120 kg and was moving with a velocity of 4 m/s before the collision and with a velocity of −2 m/s after the collision. The second bumper car has a mass of 90 kg and was moving at a velocity of −5 m/s before the collision. To prove conservation of momentum, what must the velocity of the second bumper car be after the collision?
A. 1.0 m/s
B. 2.7 m/s
C. 3.0 m/s
D. 2.3 m/s
The velocity of the second bumper car will be 3 m/s after the collision.
Given parameters:
Mass of the first bumper car; m = 120 kg.
Mass of the second bumper car; M = 90 kg.
Before collision velocity of first bumper car; u = 4 m/s.
Before collision velocity of second bumper car; U = -5 m/s.
After collision velocity of first bumper car; v = -2 m/s.
After collision velocity of second bumper ; V= ?
From principle of conservation of momentum,
Total momentum before collision = Total momentum after collision
⇒ 120 × 4 + 90 × (-5) = 120 × (-2) + 90 × V
⇒ 90 × v = 270
⇒ v = 3 m/s.
The velocity of the second bumper car must be 3 m/s after the collision.
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An electroscope is a device that detects charge on
What methods of charging does John use?
objects that touch it or are brought near it. John rubs a
piece of cotton fabric on a plastic rod and then louches
John charges the rod through induction, then charges
the rod to the electroscope.
the electroscope through friction.
• John charges the rod through conduction, then
charges the electroscope through induction.
• John charges the rod through friction, then charges
the electroscope through induction.
John charges the rod through friction, then charges
the electroscope through conduction.
John charges the rod through friction, then charges the electroscope through induction.
What is induction charging?A charging technique called induction charging involves charging a thing without actually contacting it to another charged object.
The charged particle is held close to an uncharged conductive substance that is grounded on a neutrally charged material during the charging by induction process. When a charge is transferred between two objects, an uncharged conductive substance produces an oppositely polarized charge.
The rod is firstly charged by friction with the cotton fabric then John charges the rod through induction, then charges the rod to the electroscope.
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as the temperature of a gas increases . (select all the options that complete this sentence correctly.) multiple select question. the average kinetic energy of the gas particles increases the speed of individual gas particles increases but the average speed remains the same the distribution of the speeds of the gas particles narrows the average speed of a gas particle increases
As the temperature of a gas increases.
The average kinetic energy of the gas particles increase. The average speed of a gas particle increases.
Temperature is a physical quantity that expresses quantitatively the perceptions of hotness and coldness. Temperature is measured with a thermometer.
Thermometers are calibrated in various temperature scales that traditionally have trusted diverse reference points and thermometric substances for definition. The most common scales are the Celsius scale with the unit image °C (formerly known as centigrade), the Fahrenheit scale (°F), and the Kelvin scale (k), the latter getting used predominantly for scientific purposes. The kelvin is one of the seven base units within the worldwide device of gadgets (SI).
Absolute 0, i.e. zero kelvin or −273.15 °C, is the bottom factor in the thermodynamic temperature scale. Experimentally, it could be approached simplest very intently, however not truly reached, as identified in the 1/3 law of thermodynamics. it might be impossible to extract strength as warmth from a frame at that temperature.
Temperature is vital in all fields of natural technology, along with physics, chemistry, Earth technology, astronomy, medicinal drug, biology, ecology, cloth technological know-how, metallurgy, mechanical engineering and geography as well as most aspects of daily life.
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A monochromatic laser is exciting hydrogen atoms from the n=2 state to the n=5 state.
A monochromatic laser is responsible for exciting hydrogen atoms from their n=2 state to their n=5 state in which :
wavelength λ of the laser =435 nm
longest wavelength = λmax = 4052 nm
shortest wavelength = λmin= 95 nm
To do excitation, the energy of the laser should be greater than or equal to the energy of transition of the hydrogen atom.
In this case, the states of energy are explained by the Bohr model.
En = - 13,606 /n² [eV]
therefore the energy of the transition is
ΔE = E 5 - E2
ΔE = 13.606 (1 n2^2 - 1 n5^5 )
ΔE = 13.606(1 /2^2 - 1 /5^5).
ΔE = 2,85726 eV
Using the Planck's equation
E = h f
Light’s relation to wavelength and frequencies
c = λ f
f = c /λ
λ = h c / E
reducing energy to the SI system
E = 2,85726 eV (1.6x10⁻¹⁹ J /1 eV) = 4.5716 x 10⁻¹⁹ J
hence, λ = 6,626 x 10⁻³⁴ 3 x 10⁸ /4 ,5716 x 10⁻¹⁹
λ = 4.348x 10⁺⁷ m (10⁹ nm / 1 m)
λ = 435 nm
photon emission [e] , to the base state n = 1, from n = 5.
Initial state, n = 5
final state, n = 4
ΔE = 13.606 (1/4² - 1/5²)
ΔE = 0.306 eV
λ =h c / E
λ = 4052 nm
n = 5
final / level ΔE (eV) λ (nm)
4 0.306 4052
3 0.9675 1281
2 2,857 435
1 13.06 95
n = 4
3 0.661 1876
2 2,551 486
1 11,905 104
n = 3
2 1.89 656
1 12.09 102.5
n = 2
1 10.20 121.6.
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What does it mean to tare a balance and why do you think it is important to complete this before you begin measuring mass?.
When weighing chemicals on a balance, the term "tare" is used. Pressing the tare button enables you to record only the weight of the substance being measured, not the weight of the container it is being measured in.
Why is tare the balance prior to use important?Weighing by difference is automatically accomplished by tarring a balance. When a balance is tared with an object on the balance pan, the weight of the object is automatically subtracted from each reading up until the balance is re-tared or zeroed.
Testing a balance is crucial because you want an accurate result when you weigh an object. The calculations could all be off if a balance is not set to zero.
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a child pulls a friend in a little red wagon with constant speed. if the child pulls with a force of 16 n for 10.0 m, and the handle of
The work done by the child to pull the wagon is found to be 67.61N.
The child pulls the wagon with a force 16N and the handle of the wagon is inclined at the angle of 25°. The wagon is puled till a distance of 10m.
So, the force will have to component, one vertical and one is horizontal,
The horizontal component will move the wagon,
So, the work done by the child is given by,
W = F.S.sin(25°)
F is the force and S is the distance, Putting values,
W = 16 x 10 x 0.42
W = 67.61 N.
The work done by the child in pulling the wagon is 67.61 N.
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Complete Question - A child pulls a friend in a little red wagon with constant speed. If the child pulls with a force of 16 N for 10.0 m, and the handle of the wagon is inclined at an angle of 25° above the horizontal, how much work does the child do on the wagon?
An object is launched at a velocity of 20 m/s in a direction making an angle of 22° upward with the horizontal.What is the maximum height achieved by the projectile?
Given data:
Initial velocity,
[tex]u=20\text{ m/s}[/tex]Angle of projection,
[tex]\theta=22\degree[/tex]The maximum height achieved by the projectile is given as,
[tex]H=\frac{u^2\sin ^2\theta}{2g}[/tex]Here, g is the acceleration due to gravity.
Substituting all known values,
[tex]\begin{gathered} H=\frac{(20\text{ m/s})^2\times\sin ^2(22\degree)}{2\times(9.8\text{ m/s}^2)} \\ \approx2.86\text{ m} \end{gathered}[/tex]Therefore, the maximum height achieved by the projectile is 2.86 m.
What diagrams can help support my answer and explain why is does it support?
Sunburn is caused by UV radiation by damaging DNA, as the following diagram shows:
Visible light and UV radiation differ in wavelength:
Since only Sunscreen A blocks UVA and UVB radiation, then it effectively prevents sunburn.
A bus goes 500km east from town A to town B in the morning and comes back halfway in the evening travelling west. What is the distance and displacement of the bus?
Given:
Distance the bus goes from town A to town B = 500 km east
Given that the bus comes back halfway in the evening travelling west, let's find the distance and the displacement of the bus.
• To find the distance of the bus, we have:
[tex]\begin{gathered} d=500+(\frac{500}{2}) \\ \\ d=500+250 \\ \\ d=750\operatorname{km} \end{gathered}[/tex]Therefore, the distance the bus covered is 750 km
• To find the displacement, we have:
[tex]\begin{gathered} Displacement\text{ = 500 - (}\frac{500}{2}) \\ \\ \text{Displacement = 500 - 250} \\ \\ \text{Displacement = 250 km} \end{gathered}[/tex]Therefore, the displacement of the bus is 250 km east
ANSWER:
Distance = 750 km
Displacement = 250 km east
what is the magnetic field amplitude b0b0 of an electromagnetic wave that has an electric field amplitude e0e0e 0 of 0.465 v/mv/m ?
An electromagnetic wave with an electric field amplitude E0 of 0.165V/m has a magnetic field amplitude b0 of 5.5 × [tex]10^{-10}[/tex]T.
What is electromagnetic?In terms of physics, electromagnetic radiation is made up of electromagnetic field waves that move over space while carrying radiant energy. It is made up of radio waves, microwaves, infrared, light, and X and gamma rays. The electromagnetic spectrum includes all of these wavelengths.Radio waves, microwaves, infrared, visible light, ultraviolet, x-rays, and gamma rays are all examples of electromagnetic waves. The smallest energy, frequency, and wavelength are found in radio waves. The highest energy, frequency, and shortest wavelength are found in gamma rays.How to calculate the magnetic field amplitude Bo?Speed of light / Electric field amplitude (Eo) = magnetic field amplitude (Bo)
where C = 3 × [tex]10^{8}[/tex] m/s
Bo = 0.165 / 3 × [tex]10^{8}[/tex]
Bo = 5.5 × [tex]10^{-10}[/tex]T (magnetic field amplitude)
The complete question is:
what is the magnetic field amplitude b0b0 of an electromagnetic wave that has an electric field amplitude e0e0e 0 of 0.165 v/mv/m ? express your answer with the appropriate units.
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The photo shows a roller coaster. Assume the system is closed. Which roller-coaster car has the least potential energy due to gravity?
A. Car A
B. Car B
C. Car C
D. Car D
Answer: it's rather A or B
Explanation: those are the moments it stops but most likely it is answer A.
what is the direction of the magnetic force on a positive charge moving into the page in a b field that is facing to the right?
According to the right hand rule, the thumb of the right hand should point in the direction of the magnetic force acting on a positive moving charge.
Which magnetic field direction is positive?It is demonstrated that the magnetic line's direction is from north to south and the electric line's direction is from positive to negative.
What direction does the coil's left-hand side force come from?A downward force is produced when current flows through the left hand of the coil, and an upward force is produced when current flows through the right hand of the coil.
What direction does this magnetic force go in?The direction of the magnetic field's force is opposite the direction that it acts.
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a child is sledding down a hill. the child has 200 j of potential energy and 500 j of kinetic energy at one point on the hill. how much more kinetic energy does the child gain for the remainder of the motion to the bottom of the hill?
The additional kinetic energy that the child gains after reaching the bottom of the hill is 200 Joule. The result is obtained by using the principle of Conservation of Mechanical Energy.
What is Conservation of Mechanical Energy?The principle of conservation of energy states that "The total energy is neither increased nor decreased in any process. Energy can be transformed from one form to another, and transferred from one object to another, but the total amount remains constant."
In the same way, the Conservation of Mechanical Energy states that the total mechanical energy of a system is conserved. It can be expressed as
[tex]E_{1} = E_{2}[/tex]
[tex]K_{1} + U_{1} = K_{2} + U_{2}[/tex]
[tex]\frac{1}{2} mv_{1} ^{2} + mgh_{1} = \frac{1}{2} mv_{2} ^{2} + mgh_{2}[/tex]
Where
E₁ = mechanical energy at point 1E₂ = mechanical energy at point 2K₁ = kinetic energy at point 1K₂ = kinetic energy at point 2U₁ = potential energy at point 1U₂ = potential energy at point 2m = mass of an objectv₁ = velocity of object at point 1v₂ = velocity of object at point 2h₁ = height of object at point 1h₂ = height of object at point 2At one point, a child has:
U₁ = 200 JK₁ = 500 JHow much more kinetic energy does the child gain at the bottom of the hill?
At the bottom of the hill, the height of the child is zero, h₂ = 0. So, the potential energy is
[tex]U_{2} = mgh_{2}[/tex]
[tex]U_{2} = mg(0)[/tex]
[tex]U_{2} = 0[/tex]
The kinetic energy at the bottom of the hill is
[tex]K_{1} + U_{1} = K_{2} + U_{2}[/tex]
[tex]500 + 200 = K_{2} + 0[/tex]
[tex]K_{2} = 700 J[/tex]
The kinetic energy added for the remainder of the motion is
[tex]K = K_{2} - K_{1}[/tex]
[tex]K = 700 - 500[/tex]
[tex]K = 200 J[/tex]
Hence, the additional kinetic energy that the child gains after reaching the bottom of the hill is 200 Joule.
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A light ray travels through water and reflects off a glass surface back into the water. How do the phases of the incident light and the reflected light compare?.
The light travels through water and gets reflected off on the glass surface into the water. There had been a 180° phase change between the incident and the reflected wave. This is called Total internal reflection (TIR).
In total internal reflection, in physics, a ray of light in a medium such as water or glass is completely reflected back into the medium from the surrounding surfaces. This phenomenon occurs when the angle of incidence is greater than a certain critical angle called the critical angle.
TIR only occurs when both of the following two conditions are met
Light is in a denser medium and is approaching a less dense medium. The angle of incidence should be greater than the so-called critical angle.Thus, the phases which include the TIR are the incident and the reflected phase and the incident light hits the surface while the reflected light reflects back.
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An object rolls off a 8 m tall table with a velocity of 3 and lands 6 away from the base of the table. What is the vertical acceleration of the object? (Answer must be negative!!!)
Answer:
-9.81 m/s/s or -4 m/s/s
Explanation:
Technically, the only vertical component of force and therefore acceleration on the object after it leaves the table will be acceleration due to gravity. So we can say the value of acceleration is g, -9.81m/s/s.
Though after checking your parameters, maybe you are on another planet with a different gravitation constant.
in this case, assuming your other values are in the standard m/s and m, we can determine how long the ball should be in the air to land 6 meters away and thus use that to find downward acceleration.
6m = 3m/s • t
2s = t
8 = 1/2 g • (2)^2
2m/s/s = 1/2 g
4 m/s/s = g
this would approximate to doing this experiment on mercury
Which one of these objects has kinetic energy?
an Iphone laying on a table
a frisbee sitting on a roof
a ball rolling down the driveway
Answer: A ball rolling down the driveway.
Explanation:
Kinetic is when an object is in motion. Potential is when an object rests.
A lemming take off from the roof of a building 56m tall and lands 45m from the base. What was the lemming’s initial speed ?
Given data
*The given height of the building h = 56 m
*The distance from the base is d = 45 m
*The value of the acceleration due to gravity is g = 9.8 m/s^2
The formula for the time taken by the lemming is given as
[tex]t=\sqrt[]{\frac{2h}{g}}[/tex]Substitute the known values in the above expression as
[tex]\begin{gathered} t=\sqrt[]{\frac{2\times56}{9.8}} \\ =3.38\text{ s} \end{gathered}[/tex]The formula for the lemming's initial speed is given as
[tex]v=\frac{d}{t}[/tex]Substitute the known values in the above expression as
[tex]\begin{gathered} v=\frac{45}{3.38} \\ =13.3\text{ m/s} \end{gathered}[/tex]Hence, the lemming's initial speed is v = 13.3 m/s
this is a 3 part question6) (a) Your heart beats with a frequency of 1.45 Hz. How many beats occur in a minute? (b) If the frequency of your heartbeat increases, will the number of beats in a minute increase, decrease, or stay the same? (c) How many beats occur in a minute if the frequency increases to 1.55 Hz?
Given,
The initial frequency of the heartbeat, f₁=1.45 Hz
The increased heartbeat, f₂=1.55 Hz
The frequency of the heartbeat can be described as the number of occurence of the heartbeat per second. That is every second, the heart beats 1.45 times.
(a)
Thus for a minute, the number of the heartbeats is,
[tex]\begin{gathered} N_1=f_1\times60 \\ =1.45\times60=87 \end{gathered}[/tex]Thus 87 beats occur for a minute.
(b)The increase in the frequency of the heartbeat implies the increase in the number of the heartbeat for every second. And hence the beats in a minute increase when the frequency of the heartbeat increases.
(c)
The number of the beats per minute after the increase of the frequency is,
[tex]\begin{gathered} N_2=f_2\times60 \\ =1.55\times60 \\ =93 \end{gathered}[/tex]Thus after the increase in the frequency, 93 beats occur in a minute.
A 50 kg child is on a carnival ride with a radius of 5 meters. If the ride spins at a velocity of 5
m/s, what is the centripetal force on the child?
Explanation:
Find a force is F=mv^2/r, so F=50*5^2/5 = 250N
I need to find out number 51.Can you help me ?
v= constant
mass of the cart = 1.5 kg
m2 (added)= 7.5 kg
In FIGURE 2, a block of mass m=2.5 kg slides heads on into a spring of spring constant k=320 N/m. When the block stops, it has compressed the spring by 7.5 cm. The coefficient of kinetic friction between block and floor is 0.25. While the block is in contact with the spring and being brought to rest, calculatea. the work done by the spring force.b. the increase in thermal energy of the block-floor system.c. What is the block's speed just as it reaches the spring?
(a)
The work done by the spring force can be calculated with the formula below:
[tex]W=\frac{1}{2}kx^2[/tex]Using k = 320 N/m and x = 0.075 m, we have:
[tex]\begin{gathered} W=\frac{1}{2}\cdot320\cdot0.075^2\\ \\ W=0.9\text{ J} \end{gathered}[/tex](b)
The increase in thermal energy is given by the work done by the friction force.
To calculate this work, first let's find the friction force:
[tex]\begin{gathered} F_{friction}=F_{normal}\cdot\mu\\ \\ F_{friction}=m\cdot g\cdot\mu\\ \\ F_{friction}=2.5\cdot9.8\cdot0.25\\ \\ F_{friction}=6.125\text{ N} \end{gathered}[/tex]Now, calculating the work, we have:
[tex]\begin{gathered} W=F\cdot d\\ \\ W=6.125\cdot0.075\\ \\ W=0.46\text{ J} \end{gathered}[/tex](c)
The block speed can be found by converting the potential energy from the spring (same value of the calculated work in item a) into kinetic energy for the block:
[tex]\begin{gathered} PE=KE\\ \\ 0.9=\frac{mv^2}{2}\\ \\ mv^2=1.8\\ \\ 2.5v^2=1.8\\ \\ v^2=\frac{1.8}{2.5}\\ \\ v^2=0.72\\ \\ v=0.8485\text{ m/s} \end{gathered}[/tex]A runner covers the last straight stretch of a race in 8s.During that time he speeds up from 7 m/s to 9m/s. What is the acceleration
Given
Time taken is t=8 s.
The initial speed is u=7 m/s
The final speed is v=9 m/s.
To find
The acceleration
Explanation
We know the acceleration is the ratio of the difference in the speed to the time taken.
Thus,
[tex]\begin{gathered} a=\frac{v-u}{t} \\ \Rightarrow a=\frac{9-7}{8} \\ \Rightarrow a=\frac{2}{8}=\frac{1}{4}=0.25\text{ m/s}^2 \end{gathered}[/tex]Conclusion
The acceleration is
[tex]0.25\text{ m/s}^2[/tex]When can the normal force of an object have the same value as the force of weight? Explain.
Answer:
at rest
Explanation:
at rest
If the object is at rest, net force on the object is equal to zero; therefore, the downward force (weight) must be equal to the upward force (normal force).
A 4.3-kg bat is traveling 21 m/s just before it strikes a 2.5-kg baseball that’s moving 37 m/s. After the collision, the bat travels in the same direction at 19 m/s. What is the baseball’s speed just after impact?
The speed of the baseball is 30.38m/s .
We are given that,
The mass of bat = m₁ = 4.3 kg
The mass of baseball = m₂ = 2.5 kg
The initial velocity of bat = v₁ = 37 m/s
The final velocity of bat = v₁' = 19 m/s
So that the speed in baseball can be calculated from the law of conservation of momentum which can be given as,
mₙvₙ = m₁v₁ +m₂v₂
(m₁ + m₂)vₙ = m₁v₁ + m₂v₂
Where, vₙ is the speed of the baseball after impact, mₙ is the total mass of the system ,
(4.3kg + 2.5kg)vₙ = (4.3kg × 37m/s) + (2.5kg × 19m/s)
(6.8kg) vₙ = 159.1kg-m/s + 47.5kg-m/s
vₙ = (206.6kg-m/s)/6.8kg
vₙ = 30.38 m/s
Therefore, the speed of the baseball would be 30.38m/s after impact.
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a projectile lands at the same height from which it was launched. which initial velocity will result in the greatest horizintal displacment of the projectile
The initial velocity that will result in the greatest horizontal displacement of the projectile is V cosθ
The required initial velocity that will result if a projectile lands at the same height from which it was launched is V₀ = V cosθ. Since we are provided with a projectile that lands at the same height from which it was launched, so the component of the velocity in the vertical direction is usin θ, and the component along the horizontal direction is ucosθ.Neglecting the air resistance, the velocity will be constant for the object throughout the flight, so the initial velocity will be equal to the final velocity.Therefore the initial velocity will be, V₀ = V cosθ
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