Answers
Complete Question
The complete question is shown on the first uploaded image
Answer:
The expression for the velocity of the sixth ball is
[tex]v_2 = \frac{u_1 sin\theta }{sin \phi cos\theta + cos \phi sin\theta}[/tex]
Explanation:
From the question we are told that
The mass of the 8 ball is [tex]m_1 = 0.5 \ kg[/tex]
The initial velocity of the 8 ball is [tex]u_1 = 3.7 \ m/s[/tex]
The initial velocity of the 6 ball is [tex]u_2 = 0 \ m/s[/tex]
The mass of the 6 ball is [tex]m_2 = 0.5 \ kg[/tex]
Generally from the law of momentum conservation is
[tex]m_1 *u_1 + m_2 * u_2 = m_1 * v_1 +m_2 *v_2[/tex]
Now along the y axis
[tex]u_1 =u_y_1 = 0 \ m/ s[/tex]
[tex]u_2 =u_y_2= 0 \ m/ s[/tex]
[tex]v_1 =v_y_1= v_1 sin \theta \ m/ s[/tex]
[tex]v_2 =v_y_2= v_2 sin \phi \ m/ s[/tex]
So
[tex]m_1 *0 + m_2 * 0 = m_1 * (v_1 sin \theta) +m_2 *(v_2 sin \phi )[/tex]
=> [tex]v_1 = \frac{v_2 sin \phi }{ sin \theta}[/tex]
Now along the x axis
[tex]u_1 =u_x_1 = u_1 \ m/ s[/tex]
[tex]u_2 =u_2_2= 0 \ m/ s[/tex]
[tex]v_1 =v_x_1= v_1 cos \theta \ m/ s[/tex]
[tex]v_2 =v_x_2= v_2 cos \phi \ m/ s[/tex]
So
[tex]m_1 *u_1 + m_2 * 0 = m_1 *(v_1 cos \theta) +m_2 *(v_2 cos \phi)[/tex]
=>[tex]m_1 *u_1 = m_1 *(v_1 cos \theta) +m_2 *(v_2 cos \phi)[/tex]
substituting for [tex]v_1[/tex] in the above equation
=>[tex]m_1 *u_1 = m_1 *([ \frac{v_2 sin \phi }{ sin \theta}] cos \theta) +m_2 *(v_2 cos \phi)[/tex]
=>[tex]m_1 *u_1 = m_1 *([ \frac{v_2 sin \phi }{ sin \theta}] cos \theta) +m_2 *(v_2 cos \phi)[/tex]
given that [tex]m_1 = m_2 = m[/tex]
=>[tex]m *u_1 = m *([ \frac{v_2 sin \phi }{ sin \theta}] cos \theta) +m *(v_2 cos \phi)[/tex]
=>[tex]m *u_1 = m [([ \frac{v_2 sin \phi }{ sin \theta}] cos \theta) + (v_2 cos \phi)][/tex]
=>[tex]u_1 = ([ \frac{v_2 sin \phi }{ sin \theta}] cos \theta) + (v_2 cos \phi)[/tex]
=>[tex]u_1 = v_2 sin\phi cot \theta + v_2 cos\phi [/tex]
[tex]v_2 = \frac{u_1 }{sin\phi cot\theta + cos\phi }[/tex]
converting [tex]cot \phi[/tex] back to [tex]\frac{cos \theta}{sin\theta }[/tex]
So
[tex]v_2 = \frac{u_1 }{sin\phi [\frac{cos \theta}{sin\theta }] + cos\phi }[/tex]
multiply through by [tex]\frac{sin \theta}{sin \theta }[/tex]
[tex] \frac{sin \theta}{sin \theta } *v_2 = \frac{sin \theta}{sin \theta } * \frac{u_1 }{sin\phi [\frac{cos \theta}{sin\theta }] + cos\phi }[/tex]
=> [tex]v_2 = \frac{u_1 sin\theta }{sin \phi cos\theta + cos \phi sin\theta}[/tex]
Related Questions
my mom is dum and anoying asl, what should i do?
Answers
Answer:
stop being an annoying child and appreciate everything your mother does for you because she cares for you
Explanation:
its the right thing to do
Be thankful for everything your mom does bc one day she wont be here any more! Love her while you can
What is the net work, in joules, required to stop a crate of mass 64.5 kg that is moving at a speed of 1.26 m/s
Answers
Answer:
51.2Joules
Explanation:
Work done = Force × distance
Force = mg = 64.5×9.81
Force = 632.745N
Next is to get the distance using the equation of motion
v² = u²+2gS
1.26² = 0+2(9.81)S
1.5876 = 19.62S
S = 1.5876/19.62
S = 0.0809m
Get the work done:
Work done = F×S
Work done = 632.745×0.0809
Work done = 51.2Joules
Hence the net work done in Joules is 51.2Joules
The net work done required to stop a crate will be "51.2 Joules".
Force and MassAccording to the question,
Mass, m = 64.5 kg
Speed, v = 1.26 m/s
Acceleration due to gravity, g = 9.8
We know,
The force, F = mg
By substituting the values,
= 64.5 × 9.8
= 632.745 N
By using Equation of motion,
→ v² = u² + 2gS
(1.26)² = 0 + 2(9.81) S
1.5876 = 19.62 S
S = [tex]\frac{1.5876}{19.62}[/tex]
= 0.0809 m
hence,
The work done (W) will be:
= F × S
= 632.745 × 0.0809
= 51.2 Joules
Thus the above response above is correct.
Find out more information about mass here:
https://brainly.com/question/25545050
a. In one short sentence, explain why we call the force of gravity an attractive force.
b. Does a force of gravity exist between any two objects
Answers
Answer:
Explanation:
(a) The force of gravity is called an attractive force because it is the force (although weak) in which a planetary body or matter uses to attract an object towards itself.
(b) Yes, it does and the formula for force of gravity between any two object is
F = G[tex]\frac{m1m2}{r}[/tex]
where m1 and m2 are masses of the first and second object respectively
r is the distance between the center of the two masses
G is the gravitational constant
A small box with mass 0.600 kg is placed against a compressed spring at the bottom of an incline that slopes upward at 37.0∘ above the horizontal. The other end of the spring is attached to a wall. The coefficient of kinetic friction between the box and the surface of the incline is μk=0.400. The spring is released and the box travels up the incline, leaving the spring behind.
What minimum elastic potential energy must be stored initially in the spring if the box is to travel 2.00 m from its initial position to the top of the incline?
Answers
Answer:
[tex]10.845\ \text{J}[/tex]
Explanation:
m = Mass of box = 0.6 kg
[tex]\theta[/tex] = Angle of incline = [tex]37^{\circ}[/tex]
[tex]\mu_k[/tex] = Coefficient of kinetic friction = 0.4
l = Distance the box travels = 2 m
g = Acceleration due to gravity = [tex]9.81\ \text{m/s}^2[/tex]
The potential energy in the spring is given by
[tex]U=mgl\sin\theta+mg\mu_k\cos\theta l\\\Rightarrow U=mgl(\sin\theta+\mu_k\cos\theta)\\\Rightarrow U=0.6\times 9.81\times 2\times(\sin37^{\circ}+0.4\times\cos37^{\circ})\\\Rightarrow U=10.845\ \text{J}[/tex]
The minimum elastic potential energy required is [tex]10.845\ \text{J}[/tex].
Sally is on a large sailboat that comes to a stop a small distance from the dock. Since it is such a small distance, Sally decides to jump to the dock. She makes the jump, but the large sailboat moves away from her as she jumps. Since Sally is interested to see what happens on other boats, she makes the same jump from a rowboat that is much smaller than the large sailboat. Which boat will move away from Sally more slowly
Answers
Answer:
The rowboat will move away from sally more quickly because the rowboat because the sailboat is larger in mass
Explanation:
Gnerally the row boat will move away from her quicker than the sailboat this is because the mass of the sail boat is larger than the row boat , hence the frictional force that opposes motion will be greater in the sailboat than in the row boat.
If the experimenter knows who is in the experimental and control groups and treats them accordingly, she runs the risk of ________.
Answers
Answer:
Experimenter bias
Explanation:
If the experimenter knows who is in the experimental and control groups and treats them accordingly, she runs the risk of Experimenter bias.
Definitions of Experimenter bias
1) Research bias, also called experimenter bias, is a process where the scientists performing the research influence the results, in order to portray a certain outcome.
2) Observer bias (also called experimenter bias or research bias) is the tendency to see what we expect to see, or what we want to see. When a researcher studies a certain group, they usually come to an experiment with prior knowledge and subjective feelings about the group being studied.
A squirrel drops an acorn from a tree. Starting from rest, it reaches the ground 22.0 meters
below. What is the acorn's velocity as it hits the ground?
Answers
Briefly explain why arterial injuries are more dangerous than damage to veins
or capillaries. Explanation should address structure and function of the
blood vessels.
IF YOU SEE THIS PLZ ANSWER RN
Answers
Answer:
Injury to a vein increases the risk of forming a blood clot.
Explanation:
hoped this helped
A small child weighs 60 N. If mommy left him sitting on top of the stairs, which are 12 m high, how much energy does the child have!
Please help ASAP
Answers
Answer:
6000 joules
Explanation:
I jus learned dis
Answer:6000j
Explanation:
Hope that helps
Find the distance along an arc on the surface of the earth that subtends a central angle of 1 minutes (1 minute = 1/60 degree). The radius of the earth is 3960 miles. Round to the thousandths. (3 decimal places)
Answers
Answer:
1.152 miles
Explanation:
Given: central angle = 1 minute = [tex](\frac{1}{60}) ^{o}[/tex]
radius of the earth = 3960 miles
The length of an arc = [tex]\frac{\alpha }{360^{o} }[/tex] 2[tex]\pi[/tex]r
where: [tex]\alpha[/tex] is the central angle, and r is the radius.
Thus,
Distance along the arc = [tex]\frac{\alpha }{360^{o} }[/tex] 2[tex]\pi[/tex]r
Distance along the arc = [tex]\frac{(\frac{1}{60}) ^{o} }{360^{o} }[/tex] x 2 x [tex]\frac{22}{7}[/tex] x 3960
= [tex]\frac{(\frac{1}{60}) ^{o} }{360^{o} }[/tex] x 24891.4286
= 1.1524
The required distance along an arc is 1.152 miles.
An ion has unequal numbers of which two particles?
Answers
Vertical acceleration of the stone thrown upwards at the top of the trajectory (where its velocity vanishes) is equal to
A. g
B. g/2
C. 0
D. nine of the above
Answers
Answer:
A. g
Explanation:
The public is not yet able to purchase cars powered by hydrogen fuel cells because engineers have to determin
how the cars perform based on which scenario?
on racetracks
Answers
Answer:
The options are
A.on racetracks
B.in real-world conditions
C.in flooded environments
D.on closed courses
The answer is B. In real world conditions
The public is not yet able to purchase cars powered by hydrogen fuel cells because engineers have to determin
how the cars perform based on real world conditions.
This will ensure they encounter the real and first hand experiences about the challenges and also the advantages associated with using this type of fuel.
Which simple machines are used in the tool or device
Answers
Answer:
Explanation:
What are simple machines?
Simple machines reduce effort or extend the ability to perform tasks beyond their abilities.
Why do we use simple machines?
Simple machines are used widely as they help humans and save time.
Simple Machine Examples:
MachineScrewWheel and axle - wheeled carry-on luggageLever - see sawPulley - flag polesInclined planeWedge - knifeGibbons, small Asian apes, move by brachiation, swinging below a handhold to move forward to the next handhold. A 9.0 kg gibbon has an arm length (hand to shoulder) of 0.60 m. We can model its motion as that of a point mass swinging at the end of a 0.60-m-long, massless rod. At the lowest point of its swing, the gibbon is moving at 3.5 m/s. What upward force must a branch provide to support the swinging gibbon
Answers
Answer:
The correct solution will be "271.95 N".
Explanation:
The given values are:
velocity
v = 3.5 m/s
mass
m = 9.0 kg
r = 0.6 m
According to the question:
⇒ [tex]F_{branch}=F_{gravity}+F_{centrifugal}[/tex]
⇒ [tex]=mg+\frac{mv^2}{r}[/tex]
On substituting the values, we get
⇒ [tex]=9\times 9.8+\frac{9\times (3.5)^2}{0.6}[/tex]
⇒ [tex]=88.2+\frac{110.35}{0.6}[/tex]
⇒ [tex]=271.95 \ N[/tex]
An airline employee tosses two suitcases in rapid succession with a horizontal velocity of 7.2 ft/s onto a 50-lb baggage carrier which is initially at rest. Problem 14.003.a Conservation of momentum: two colliding suitcases Knowing that the final velocity of the baggage carrier is 4.8 ft/s and that the first suitcase the employee tosses onto the carrier has a weight of 30 lb, determine the weight of the other suitcase. (You must provide an answer before moving on to the next part.) The weight of the other suitcase is lb.
Answers
Answer:
m₁ = 70 lb
Explanation:
Here we will use the law of conservation of momentum:
m₁u₁ + m₂u₂ + m₃u₃ = m₁v₁ + m₂v₂ + m₃v₃
where,
m₁ = mass of first suitcase = ?
m₂ = mass of second suitcase = 30 lb
m₃ = mass of baggage carrier = 50 lb
u₁ = initial speed of first suitcase = 7.2 ft/s
u₂ = initial speed of second suitcase = 7.2 ft/s
u₃ = initial speed of baggage carrier = 0 ft/s
v₁ = Final speed of first suitcase = 4.8 ft/s
v₂ = Final speed of second suitcase = 4.8 ft/s
v₃ = Final speed of baggage carrier = 4.8 ft/s
because after collision all three will have same speed
Therefore,
(m₁)(7.2 ft/s) + (30 lb)(7.2 ft/s) + (50 lb)(0 ft/s) = (m₁)(4.8 ft/s) + (30 lb)(4.8 ft/s) + (50 lb)(4.8 ft/s)
(m₁)(7.2 ft/s) + (216 lb ft/s) + (0 lb ft/s) = (m₁)(4.8 ft/s) + (144 lb ft/s) + (240 lb ft/s)
(m₁)(7.2 ft/s) - (m₁)(4.8 ft/s) = 168 lb ft/s
m₁ = (168 lb ft/s)/(2.4 ft/s)
m₁ = 70 lb
1. A jogger jogs 25 m East, stops to rest, then continues for 10 more meters
East? What is the jogger's displacement?
Answers
Answer:
35m
Explanation:
25m + 10m = 35m east.
*(adding since it's in the same direction)
A hydraulic press has a safety feature which consists of a hydraulic cylinder with a piston at one end and a safety valve at the other. The cylinder has a radius of 0.0200 m and the safety valve is simply a 0.00750-m radius circular opening at one end, sealed with a disk. The disk is held in place by a spring with a spring constant of 950 N/m that has been compressed 0.0085 m from its natural length. Determine the magnitude of the minimum force that must be exerted on the piston in order to open the safety valve.
Answers
Answer:
Explanation:
radius of cylinder r₁ = .02 m
radius of safety valve r₂ = .0075 m
force exerted by spring on safety valve = 950 x .0085 = 8.075 N .
Force required on piston of cylinder = F
Applying Pascal's law
8.075 / 3.14 x .0075² = F / 3.14 x .02²
F = 8.075 x .02² / .0075²
= 8.075 x 7.111
= 57.42 N .
Which property of a substance can be determined using a pH indicator.
Answers
Answer:
Acidity
Explanation:
A pH indicator measures how acidic or basic a substance is.
Hope this helped :)
You and some friends visit the Florida State Fair and decide to play a game. To play the game you must slide a metal hockey-type puck up a wooden ramp so that it drops through a hole at the top of the ramp. Your prize, if you win, is a large, stuffed gorilla. You realize the secret to winning is giving the puck just enough velocity at the bottom of the ramp to make it to the hole. You estimate the distance from the bottom of the ramp to the hole at about 3 m, and the ramp appears to be inclined with an angle of 10o from the horizontal. You just got out of physics class and recall the coefficient of static friction between steel and wood is 0.1 and the coefficient of kinetic friction between steel and wood is 0.08. The mass of the puck is about 1 kg. You decide to impress your friends by sliding the puck at the precise speed on the first try so as to land it in the hole. You slide the puck at 2.0 m/sec. Do you win the stuffed poodle? Let g = 10 m/s2. Note: A slightly too hard throw will win since your aim is so good the puck would drop in the hole.
Answers
Answer:
No you didn't win the stuffed poodle
Explanation:
From the question we are told that
The distance of the ramp to the hole is d = 3 m \
The angle of inclination is [tex]\theta = 10^o[/tex]
The coefficient of static friction is [tex]\mu_s = 0.1[/tex]
The coefficient of kinetic friction is [tex]\mu_k = 0.08[/tex]
The mass of the puck is m = 1 kg
The velocity of the first slide is [tex]v_1 = 2.0 m/s[/tex]
Generally the kinetic energy at the bottom of the ramp is equal the energy loss due to friction and this can be mathematically represented as
[tex]\frac{1}{2} m * v^ 2 = \mu_k * [m * g] * cos (theta ) * d[/tex]
=> [tex]\frac{1}{2} * v^ 2 = 0.08 * 9.8 * cos (10 ) * 3[/tex]
=> [tex] v= 2.17 \ m/s [/tex]
Comparing the relative velocity obtained and the velocity of your first throw we can see that you didn't win the stuffed animal
Streams compensate for changes in their systems by adjusting other factors in order to return to _______
Answers
Answer:
Equilibrium.
Explanation:
Streams compensate for changes in their systems by adjusting other factors in order to return to equilibrium because so as to maintain their watershed. When the surface runoff move downslope, it also cause a concentration in small areas and create small channels of streams. These channels normally allow the flow of water during rainfall.
Suppose you are given two clay balls of equal size and shape. The two clay balls also weigh the same. One ball is flattened into a pancake-shaped piece. Which of these statements is correct and why?
Answers
A 1000-turn solenoid is 50 cm long and has a radius of 2.0 cm. It carries a current of 18.0 A. What is the magnetic field inside the solenoid near its center
Answers
Answer:
The value is [tex]B = 0.0452 \ T [/tex]
Explanation:
From the question we are told that
The number of turns is N = 1000
The length is L = 50 cm = 0.50 m
The radius is r = 2.0 cm = 0.02 m
The current is I = 18.0 A
Generally the magnetic field is mathematically represented as
[tex]B = \mu_o * \frac{N }{L} * I[/tex]
Here [tex]\mu_o[/tex] is the permeability of free space with value
[tex]\mu_o = 4\pi * 10^{-7} N/A^2[/tex]
So
[tex]B = 4\pi * 10^{-7} * \frac{1000}{0.50} * 18.0[/tex]
=> [tex]B = 0.0452 \ T [/tex]
What determines the path that an object in projectile motion follows? (Ignore air resistance)
gravity only
inertia only
gravity and inertia
neither gravity or inertia
Answers
Answer:
C
gravity and inertia
Explanation:
Answer:
c :)
Explanation:
Please help which one is correct
Answers
Answer:
option (i) is correct
Explanation:
as there is no air resistance, no force is acting on the object horizontally, but gravitational acceleration will obviously act, regardless of the air resistance... option (i) is correct
The latent heat of fusion of mercury is 11.8 J/g. The amount of energy, rounded to the nearest tenth, needed to change 8.00 grams of mercury to a liquid is
Answers
Answer:
94.4
Explanation:
it is
Answer:
94.4 i took the test and got it right :)
hope that helps
for an emitted wavelength of 500 nanometers and a redshift of 0.4 what will be the observed wavelength g
Answers
Answer:
The observed wavelength is [tex] \lambda = 700nm[/tex] (color - Red)
Explanation:
From the question we are told that
The wavelength of the emitter is [tex]\lambda_ e = 500 nm = 500 *10^{-9} \ m[/tex]
The redshift is R = 0.4
Generally red shift is mathematically represented as
[tex]R = \frac{ \lambda - \lambda_e }{\lambda_e}[/tex]
=> [tex]0.4 = \frac{ \lambda - 500 *10^{-9} }{500 *10^{-9} }[/tex]
=> [tex] \lambda - 500*10^{-9} = 200*10^{-9} [/tex]
=> [tex] \lambda = 700 *10^{-9}[/tex]
=> [tex] \lambda = 700nm[/tex]
how can philosophy help you become a productive citizen
Answers
Answer:
Philosophy is a study that involves the nature of knowledge and truth. It serves as a guide that helps an individual seek which things are valuable and essential in life. ... It gives you a sense of direction, knowing the weight of things, therefore making you more productive.
What happens to the energy in a closed system?
Answers
Answer:
can exchange energy with its surroundings through heat and work transfer. In other words, work and heat are the forms that energy can be transferred across the system boundary.
Forces are expressed in ________. (newtons or mass)
Answers
Mass isn’t even a unit of measurement