From Newton’s Third Law, the Law of Conservation of Momentum for an elastic collision is derived as m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂.
Newton's third lawThis law states that action and reaction are equal and opposite. That is the force applied to an object is equal to the reaction received by the object.
F₁₂ = -F₂₁
m₁a₁ = -m₂a₂
m₁v₁/t = -m₂v₂/t
m₁v₁ = -m₂v₂
m₁v₁ + m₂v₂ = 0
For an elastic collision involving two objectsThe sum of the initial momentum must be equal to sum of final momentum.
let initial velocity = ulet final velocity = vm₁u₁ + m₂u₂ = m₁v₁ + m₂v₂
Thus, from Newton’s Third Law, the Law of Conservation of Momentum for an elastic collision is derived as m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂.
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How fast must a proton move so that its kinetic energy is 70% of its total
energy?
I thought it would be 0.7c but that is wrong. I really don't know how to do this type of problem and my text book isn't any help.
Try this solution, all the details are in the attachment. note, the answer is marked with orange colour. If it is possible, check the provided solution in other sources.
Answer: ≈0.81c.
How can an athlete participating in a 40m sprint modify and improve their performance based on the kinematic variable of speed and acceleration?
The athlete can improve performance by building strength, coordination and balance.
Who is an Athlete?This is an individual who is proficient in sports and other forms of physical exercise.
Improvement of performance based on the kinematic variable of speed and acceleration can be achieved by building strength, coordination and balance by performing plyometric exercises etc.
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A basketball player must jump 1.2m in the air in order to dunk. What is the total time he is in the air?
Answer:
0.98 [sec].
Explanation:
1) the time when the player is moving up equals the time the player falls, it can be 't'. Then
2) the equation of moving down can be written as
[tex]\frac{g*t^2}{2} =h, \ where[/tex]
g=10 [m/s²], t - time, h - the given height.
3) according to the formula above the time spent to moving down is:
[tex]t=\sqrt{\frac{2h}{g}};[/tex]
[tex]t=\sqrt{\frac{2.4}{10}}=\sqrt{0.24} =0.49[s].[/tex]
4) finally, the total time is t*2=0.98[sec].
A train moves from rest to a speed of 22 m/s in 34.0 seconds. What is its acceleration?
Answer: a = 0.647 m/s^2
Explanation:
Acceleration = change in speed / time → a = 22 / 34 → a = .647 m/s^2
An object of mass m is oscillating with a period T. The position x of the object as a function of time is given by the equation x(t)=Acosωt . The maximum net force exerted on the object while it is oscillating has a magnitude F. Which of the following expressions is correct for the maximum speed of the object during its motion?
What the equation given?
x(t)=Acos[tex]\omega[/tex]tMaximum velocity occurs at the equilibrium position
So
x=0Now
x(0)=Acos0[/tex]x(0)=ANow
As we know the formula
[tex]\\ \rm\rightarrowtail V_max=A\omega[/tex]
These expressions can be used
The maximum speed of the oscillating object will be given by [tex]V_{max}=Aw[/tex]
What is oscillation?An oscillation is defined as the repitative periodic motion of any object about its mean or equilibrium position.
The given equation is as follows:
x(t)=Acost
Maximum velocity occurs at the equilibrium position x=0
x(0)=Acos0
x(0)=A
Hence the maximum velocity will be [tex]V_{max}=Aw[/tex]
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To travel at a constant speed, a car engine provides 24 KW of useful power. The driving force on the car is 600 N. At what speed does it travel?
[tex]\text{Given that,}\\ \\\text{Power,} ~P=24~ KW = 24000~ W\\\\\text{Force,} ~F=600~N\\\\\text{We know that,}\\\\P=Fv\\\\\implies v = \dfrac{P}{F} = \dfrac{24000}{600}=40~ ms^{-1}\\\\\\\text{It travels at 40 m/s}[/tex]
A horizontal push of 197 N is applied to a 49.1 kg crate to slide it along a level floor. The crate is accelerating at 3.337 m/s2 (speeding up). What is the magnitude of the kinetic friction force between the crate and the floor
The magnitude of the kinetic friction force between the crate and the floor is 33.15 N.
Kinetic frictional force
The magnitude of kinetic frictional force is determined by applying Newton's second law of motion as shown below;
F - Ff = ma
where;
Ff is kinetic frictional forcea is acceleration of the crateF is the applied forceSubsitute the given parameters and solve for kinectic frictional force
197 - Ff = 49.1(3.337)
197 - Ff = 163.85
Ff = 33.15 N
Thus, the magnitude of the kinetic friction force between the crate and the floor is 33.15 N.
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A professional golfer swings a golf club, striking a golf ball that has a mass of 55.0 g. The club is in contact with the ball for only 0.00410 s. After the collision, the ball leaves the club at a speed of 32.0 m/s. What is the magnitude of the average force (in N) exerted on the ball by the club?
The magnitude of the average force exerted on the ball by the club is 429.27 N.
What is force?Force can be defined as the product of mass and acceleration
To calculate the force exerted on the ball by the club, we use the formula below.
Formula:
F = m(v-u)/t............ Equation 1Where:
F = Force exerted on the ballm = mass of the ballv = Final velocityu = initial velocityt = timeFrom the question,
Given:
m = 55 g = 0.055 kgu = 0 m/sv = 32 m/st = 0.0041 sSubstitute these values into equation 1
F = 0.055(32-0)/0.0041F = 429.27 NHence, The magnitude of the average force exerted on the ball by the club is 429.27 N.
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Read the materials on Biomolecules. Summarize and creatively translate them into a poem describing
what you have learned about biomolecules write your answer
Biomolecules are fundamental for life. They required both energy supply and building structures.
What are biomolecules?Biomolecules are organic molecules that fundamental for life and must be ingested from the regular diet.
Biomolecules include proteins (e.g., meal proteins), lipids (fats) and also carbohydrates (e.g., glucose).
Biomolecules required both energy supply (e.g., glucose) and building structures (e.g., amino acids in proteins).
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1. What is the distance covered by a T-Rex that goes from 0 m/s to 9 m/s in 6.78 seconds? (10
points)
With the use of first and third equation of motion, the distance covered by a T-Rex is 30.51 m
Linear MotionWhen a body is in linear motion, the body is moving in a straight line. some of the parameters to consider are:
Distance coveredSpeedVelocityAccelerationE.T.CGiven that a T-Rex move from 0 m/s to 9 m/s in 6.78 seconds, the distance covered can be found by calculating the acceleration.
Let us use equation 1
V = U + at
9 = 0 + 6.78a
a = 9 / 6.78
a = 1.33 m/[tex]s^{2}[/tex]
Now let us use equation 3
[tex]v^{2}[/tex] = [tex]u^{2}[/tex] + 2as
[tex]9^{2}[/tex] = 2 x 1.33 x S
81 = 2.655S
S = 81/2.655
S = 30.51 m
Therefore, the distance covered by a T-Rex is 30.51 m.
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As a block falls through the air by 40 meter it does work equal to -1800 joule. Determine the mass of a block.
Answer:
m = 4.5 kg
Explanation:
w = - 1800 j
Fd = - 1800 j
mgd = - 1800 j
m = - 1800 ÷(gd)
m = - 1800 ÷( 10×-40)
m = 4.5 kg
What is the x component of a vector that is defined as
45m at -35°?
the x- component of the vector is 36.86 m.
What is a vector?Vectors are quantities that have both magnitude and direcion
To calculate the x-component of the vector, we use the formula below.
Formula:
dx = dcosθ.......... Equation 1Where;
dx = x-component of the vectord = vector between the x-y componentθ = Angle of the vector to the horizontal.From the question,
Given:
d = 45 mθ = -35°Substitute these values into equation 1
dx = 45cos(-35°)dx = 45×0.918dx = 36.86 m.Hence, the x- component of the vector is 36.86 m.
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cornvet 500000grams in short form of using suitable prefix.
Answer:
0.5 mega grams
Explanation:
Need help with the following - question 2
Answer:
Find the change in momentum of the upper stage, that is:
∆p = m(vf - vi)
m being the mass of the upper stage
vf being the final velocity which was given
vi being the initial which was also given
find ∆p
then use ∆p in the same equation
∆p being the answer you got above
m being the mass of the lower stage (given)
vi being the initial velocity (given)
vf being the final velocity of the lower stage which you were asked to find
Explanation:
During a collision the change in momentum (∆p) for both objects is equal regardless of their speeds or masses before or after the equation
The resistance of a 60.-watt lightbulb operated at
120 volts is approximately
Answer:
The resistance of a 60 watt light bulb designed to operate at 120 volts is 240 Ω.
Explanation:
static frictional Force
Answer:
The static frictional force is the force between the magnetic forces statically and contains only two objects during this physical reaction. It results in electricity and a slight shock.
The force of a hammer drives a nail into wood. This is an example of?
A. An unbalanced force.
B. Gravitational force.
C. Friction.
D. Balanced forces.
Answer:
A. An unbalanced force.
Explanation:
There needs to be a net force in order for the nail to be driven into presumably the wall. Without the net force then the hammer and nail wouldn't move.
A grasshopper jumps at a 63.0 angle with an initial velocity of 4.22 m/s. how far away does it land
The grasshopper is 1.47 m far away from the point where it jumps to the point where its lands.
To calculate the distance of the landing point of the grasshopper to the point where its jumps, we use the formula of range.
What is horizontal range?Range can be defined as the horizontal distance between the point of projection to the point where the projectile hit the plain again.
R = u²sin2∅/g........... Equation 1Where:
R = Distance between the point of jump and the point at which it landsu = initial velocity∅ = angleg = acceleration due to gravityFrom the question,
Given:
u = 4.22 m/s∅ = 63°g = 9.8 m/s²Substitute these values into equation 1
R = (4.22)²sin(2×63)/9.8R = 1.47 mHence, The grasshopper is 1.47 m far away from the point where it jumps to the point where its lands.
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A school bus and a small Toyota Prius collide in a head-on collision
Which vehicle pushed with a greater force? Explain
Which vehicle has a greater mass?
Which vehicle has a greater acceleration after the moment of impact? Explain why
Hi there!
Part 1:
According to Newton's Third Law, every action has an EQUAL and OPPOSITE reaction.
For a collision, the objects involved exert an EQUAL and OPPOSITE impulse on each other, which means the forces exerted are equal as well.
Therefore, the school bus and Toyota Prius exert an EQUAL FORCE on each other.
Part 2:
The school bus has a greater mass.
Part 3:
Using Newton's Second Law:
[tex]\Sigma F = ma[/tex]
Using this relationship, the smaller the mass, the larger the acceleration. Since the forces are EQUAL, the Toyota Prius will experience a larger acceleration because it has a smaller mass.
You are riding a bicycle up a gentle hill. It is fairly easy to increase your potential
energy, but to increase your kinetic energy would be harder.
True or false
Which of the following is NOT an example of force?
A. gravity
B. mass
C. a push
D. remain at rest
Answer:
D. remain at rest
Explanation:
can somebody please help
The amplitude of the wave on the given sinusoidal wave graph is 10 cm.
What is amplitude of wave?
The amplitude of a wave is the maximum displacement of a wave. This is the highest vertical position of the wave from the origin.
Amplitude of the wave is calculated as follows;
From the graph, the amplitude of the wave or maximum displacement of the wave is 10 cm.
Thus, the amplitude of the wave on the given sinusoidal wave graph is 10 cm.
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define capacitance of a capacitor and state its SIbunit
Answer: what I know that the unit is farad
Explanation:
The amount of energy released when 45 g of -175° C steam is cooled to 90° C is
A. 101,700 J
B. 317,781 J
C. 419,481 J
D. 417,600 J
Answer:
The answer should be choice B.
Find out the three methods of energy transfer (conduction, convection and radiation). think about
2 situations of daily life where you know or think you know that each one applies
Explanation:
conduction- putting a metal spoon in fire
convection- boiling water. In ventilation
Radiation- suns heat reaches us by radiation. heat from fire place reaches us by radiation.
If a 40 N block is resting on a rough horizontal table with a
coefficient of static friction p=0.60, then what is the force of
static friction acting on the block?
Based in the relationship between static frictional force and coefficient of static friction, the force of static friction is 24 N.
What is friction?Friction is a force that opposes the relative motion of an object moving over another at their surafce of contact.
Frictional force is constant for each type of material. This constant is known as coefficient of friction.
The coefficient of friction is given as follows:
Coefficient of friction = Frictional force/normal reactionFrom the data given:
coefficient of static friction p = 0.60Weight of block = 40 NForce of static friction = 0.60 × 40
Force of static friction = 24 N.
Therefore, the force of static friction is 24 N.
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The resultant of two vectors is of magnitude 3 units and 4 units is 1 units, what is the value of their dot product?
Answer:
A dot B = C is the vector equation for this expression
A · B = A B cos θ
3 * 4 cos θ = 1 the value 1 is their dot product
cos θ = 1 / 12 = .083 θ = 85.2 deg
A man of mass 70 kg climbs stairs of vertical height 2.5m. Calculate the work done against the force of gravity. (Take g = 9.81 ms?)
Answer:
1716.75 J
Explanation:
Step 1: First check what we are provided with. As per given question we have:
mass (m) = 70 kg, height (h) = 2.5 m and acceleration due to gravity (g) = 9.81 m/s².
Step 2: Check what we are asked to find out.
Work done = Change in Potential energy
The stuff required to solve this question is potential energy. Using the formula: P = mgh. Where P is Potential energy, m is mass, g is acceleration due to gravity and h is height.
Step 3: Substitute the known values in the above formula.
→ P = 70 × 2.5 × 9.81
→ P = 1716.75 J
Hence, the work done against the force of gravity is 1716.75 J.
A curve is banked at an angle of 29.1 degrees above the horizontal and the road surface has a coefficient of static friction of 0.4. What must the radius of curvature be for the safe minimum speed of 27.1 m/s?
Hi there!
We can begin by summing the forces acting on the car.
Along the axis of the incline, the forces of friction and gravity are working. The force of friction points towards the top of the ramp, while the force of gravity works towards the bottom.
We can use trigonometry to determine the force due to gravity along the ramp.
[tex]F_g = Mg sin\theta[/tex]
The force due to friction is equal to:
[tex]F_f = \mu N[/tex]
The normal force is the vertical component of the force due to gravity, so:
[tex]F_f = \mu Mgcos\theta[/tex]
Now, the combination of these two forces produces a component of the centripetal force. Drawing a diagram, we see that the true centripetal force is the HYPOTENUSE, while these forces sum up to its horizontal component along the ramp.
Therefore:
[tex]F_c sin\theta = Mgsin\theta - \mu Mgcos\theta[/tex]
The centripetal force is equivalent to:
[tex]F_c = \frac{Mv^2}{r}[/tex]
m = mass (kg)
v = velocity (m/s)
r = radius (m)
Rewrite:
[tex]\frac{Mv^2}{r}sin\theta = Mgsin\theta - \mu Mgcos\theta[/tex]
Cancel out 'M'.
[tex]\frac{v^2}{r}sin\theta = gsin\theta - \mu gcos\theta[/tex]
Rearrange to solve for 'r'.
[tex]r = \frac{v^2sin\theta}{gsin\theta - \mu gcos\theta}[/tex]
Plug in values and solve.
[tex]r = \frac{(27.1^2)sin(29.1)}{(9.8)sin(29.1) - 0.4(9.8)cos(29.1)} = \boxed{266.365 m}[/tex]
Ways in which a teacher plays a role in the literacy development of the learners
Answer:
encourage all attempts at reading, writing, and speaking
Explanation: