A car traveling initially at +7.9 m/s accelerates uniformly at the rate of +0.72 m/s2 for a distance of 265 m. What is its velocity at the end of the acceleration? Answer in units of m/s. 10.0 points What is its velocity after it accelerates for 114 m? Answer in units of m/s

Answer:

(a) 52.724 m/s

(b) Total displacement, d = 551.25 m

Solution:

As per the question:

Initial acceleration of the speed boat, a = - 2.01 [tex]m/s^{2}[/tex]

Time duration, t = 7.00 s

Additional time, t' =6.00 s

Acceleration for additional time, a' = 0.518 [tex]m/s^{2}[/tex]

The followed up acceleration, a'' = 1.49 [tex]m/s^{2}[/tex]

Time duration, t'' = 8.00 s

(a) Now, to calculate the velocity of the boat at timer, t = 21.0 s, we have:

After the initial 7.00 s, the velocity of the boat, from eqn-1 of motion:

v = u + at

v = 0 - 2.1(7.00) = - 14.7 m/s

After t + t' = 13 s:

v' = v + at

v' =  14.7 + 0.518(13) =  21.434 m/s

Now, velocity of the boat after t = 21 s:

v'' = v' + a''t

v'' = 21.434 + 1.49(21) = 52.724 m/s

(b) Now, the total displacement, d:

For the first case:

d = ut + [tex]\frac{1}{2}at^{2} = 0 - 0.5\times 2.1\times 7^{2} = - 51.45 m[/tex]

For the second case:

d = v't' = 21.434(6) = 128.6 m

For the third case:

d = ut + [tex]\frac{1}{2}a't'^{2} = 0 + 0.5\times 0.518\times 6^{2} = 4.65 m[/tex]

For the fourth case:

d = v''t'' = 52.724(8) = 421.79 m

For the last case:

d = ut + [tex]\frac{1}{2}a't'^{2} = 0 + 0.5\times 1.49\times 8^{2} = 47.68 m[/tex]

Total displacement, d = -51.45 + 128.6 + 4.65 + 421.79 + 47.68 = 551.25 m

Answer:

Explanation: Ok, first caracterize the two vectors that we know.

A = ax + ay = (12*cos(40°)*i + 12*sin(40°)*j) m

now, see that C is angled 20° from -x, -x is angled 180° counterclockwise from +x, so C is angled 200° counterclockwise from +x

C = cx + cy = (15*cos(200°)*i + 15*sin(200°)*j) m

where i and j refers to the versors associated to te x axis and the y axis respectively.

in a sum of vectors, we must decompose in components, so: ax + bx  = cx and ay + by = cy. From this two equations we can obtain B.

bx= (15*cos(200°) - 12*cos(40°)) m = -23.288 m

by = (15*sin(200°) - 12*sin(40°)) m = -12.843 m

Now with te value of both components of B, we proceed to see his magnitude an angle relative to +x.

Lets call a to the angle between -x and B, from trigonometry we know that tg(a) = by/bx, that means a = arctg(12.843/23.288) = 28.8°

So the total angle will be 180° + 28.8° = 208.8°.

For the magnitude of B, lets call it B', we can use the angle that we just obtained.

bx = B'*cos(208.8°) so B' = (-23.288 m)/cos(208.8°) =  26.58 m.

So the magnitude of B is 26.58 m.

Final answer:

The magnitude of vector B is 3.0 m and its angle relative to +x direction is 60.0°.

Explanation:

To find the magnitude and angle of vector →B, we can use vector addition. The magnitude of →B can be found using the equation:

|→B| = |→C| - |→A|

Substituting the given magnitudes, we have:

|→B| = 15.0 m - 12.0 m = 3.0 m

Next, we can find the angle of →B using trigonometry. Since →A is angled 40.0° counterclockwise from the +x direction, and →C is angled 20.0° counterclockwise from the −x direction, the angle of →B can be found by subtracting these angles:

θ = (20.0° - (-40.0°)) = 60.0°

Therefore, the magnitude of →B is 3.0 m and its angle relative to the +x direction is 60.0°.

Answer:

25.2 s

Explanation:

In an uniformly accelerated motion starting from rest, the time taken for the motion is given by the equation

[tex]d=\frac{1}{2}at^2 \rightarrow t=\sqrt{\frac{2d}{a}}[/tex]

where t is the time, d is the distance covered, a is the acceleration.

We also know that the acceleration can be found by using Newton's second law:

[tex]\sum F = ma \rightarrow a=\frac{\sum F}{m}[/tex]

where [tex]\sum F[/tex] is the net force on the object and m its mass. Substituting into the previous equation,

[tex]t=\sqrt{\frac{2md}{\sum F}}[/tex] (1)

So we see that the time taken for the motion is inversely proportional to the square root of the net force.

Let's consider now the space probe in the problem. Let's call F the magnitude of the force generated by each engine.

When the two forces are applied in the same direction, the net force on the space probe is

[tex]\sum F = F+F = 2F[/tex]

But when the two forces are applied perpendicularly, the net force is

[tex]\sum F' = \sqrt{F^2+F^2}=\sqrt{2} F[/tex]

Using eq.(1) we can write:

[tex]\frac{t}{t'}=\sqrt{\frac{\sum F'}{\sum F}}[/tex]

where t' is the new duration of the motion. Solving for t',

[tex]t'=\sqrt{\frac{\sum F}{\sum F'}}t=\sqrt{\frac{2F}{\sqrt{2}F}}(21.2 s)=25.2 s[/tex]

Answer:

[tex]T = 175.6 N[/tex]

Explanation:

As we know that string is vibrating in third harmonic

So we will have

[tex]L = 3\frac{\lambda}{2}[/tex]

so we have

[tex]0.79 = \frac{3}{2}\lambda[/tex]

so we have

[tex]\lambda = \frac{2}{3}(0.79)[/tex]

[tex]\lambda = 0.527[/tex]

we know that frequency of the wave is given as

f = 500 Hz

now we know that

speed of the wave is

[tex]v = frequency \times wavelength[/tex]

[tex]v = (500)(0.527)[/tex]

[tex]v = 263.3 m/s[/tex]

now we have

[tex]v = \sqrt{\frac{T}{m/L}}[/tex]

so we have

[tex]263.3 \sqrt{\frac{T}{(0.002/0.79)}}[/tex]

[tex]T = 175.6 N[/tex]

Answer:

√2µgd = vi

Explanation:

Given that the mass of object is m

Sliding speed of object is vi

coefficient of kinetic friction is µ

Distance covered is d

Final speed, vf is 0

Equation to apply will be;

v²f=v²i-2µgd where  g is acceleration due to gravity

v²f+2µgd=v²i----------------------but v²f = 0

2µgd=v²i

√2µgd = vi

In the physical scenario described, the most reasonable formula for calculating the object's initial speed across a level tabletop, given the coefficient of kinetic friction, the object's mass, and the distance moved, would be vi is equal to the square root of twice the coefficient of friction, the mass of the object, gravity, and the distance traveled.

The object in question moves with initial speed vi across a level tabletop under the influence of kinetic friction, and eventually comes to a stop after moving through a distance of d. According to the principles of physics, specifically those pertaining to motion and kinetic friction, the initial speed of an object can be inferred from an equation that takes into account the weight of the object (mass m times gravity g), the distance traveled d, and the coefficient of kinetic friction µ. Considering this, the equation which makes the most sense in this situation would be vi = √2µmgd, where the initial speed vi is equal to the square root of twice the coefficient of friction µ times the mass of the object m, gravity g, and the distance d.

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Answer:

Option D.

Explanation:

The first law of thermodynamics is a law of conservation of energy. This automatically tells us that energy lost by a system won't dissapear, but it will be gained by the surroundings.

Mathematically is stated this way:

ΔU=Q-W

Where ΔU is the change in the internal energy of a closed system, Q is the amount of heat supplied and W the amount of work done by the system on its surroundings. It means that if the internal energy U decreases, then that energy lost must have been converted to work W in the surroundings.

The first law of thermodynamics is best represented by the statement: Energy lost by the system must be gained by the surroundings.

The first law of thermodynamics, also known as the law of energy conservation, states that energy cannot be created or destroyed but it can be transformed from one form to another. The most accurate representation of the first law of thermodynamics from the provided options is [D] Energy lost by the system must be gained by the surroundings. This statement effectively communicates the balance of energy transfer which is fundamental to understanding the concept of first law of thermodynamics.

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Answer:

723.54 N

Explanation:

Weight of anchor = 833 N

density of iron = 7800 mg/m^3

density of sea water = 1025 kg/m^3

According to the Archimedes principle, if a body is immersed wholly or partly in a liquid it experiences a loss in weight of the body which is equal to the weight of liquid displaced by the body.

The loss in the weight of body is equal to the buoyant force acting on the body.

The formula for the buoyant force acting on the body

= volume of body x density of liquid x acceleration due to gravity

Weight of anchor = mass x acceleration due to gravity

833 = m x 9.8

m = 85 kg

mass of anchor = Volume of anchor x density of iron

85 = V x 7800

V = 0.01089 m^3

Buoyant force on the anchor = Volume of anchor x density of sea water x g

                                               = 0.01089 x 1025 x 9.8 = 109.46 N

So, the tension in the chain = Apparent weight of the anchor

                                              = Weight - Buoyant force

                                              = 833 - 109.46 = 723.54 N

Thus, the tension in the chain is 723.54 N.

Final answer:

Around 13.14% of an iron anchor's weight will be supported by buoyant force when it is submerged in saltwater, calculated based on the densities of iron and seawater.

Explanation:

The question revolves around determining what fraction of an iron anchor's weight will be supported by buoyant force when it is submerged in saltwater. The buoyant force acting on any object submerged in a fluid is equal to the weight of the fluid displaced by the object. This principle is articulated by Archimedes' principle. For the iron anchor, the fraction supported by the buoyant force is directly linked to the densities of iron (7800 kg/m3) and the seawater (1025 kg/m3) in which it is submerged.

To find this fraction, we use the formula: Fraction Supported = Density of Seawater / Density of Iron.

Therefore, Fraction Supported = 1025 / 7800 ≈ 0.1314.

So, when an iron anchor is submerged in seawater, approximately 13.14% of its weight is supported by the buoyant force.

Answer:

13.7 s

Explanation:

The position at time t of car A can be written as follows:

[tex]x_A (t) = \frac{1}{2}a_At^2[/tex]

where

[tex]a_A = 11 m/s^2[/tex] is the acceleration of car A

The position of car B instead can be written as

[tex]x_B(t) = d+\frac{1}{2}a_B t^2[/tex]

where

[tex]a_B = -4 m/s^2[/tex] is the acceleration of car B

d = 1400 m is the initial separation between the cars

The two cars meet when

[tex]x_A = x_B[/tex]

Using the two equations above,

[tex]\frac{1}{2}a_A t^2 = d + \frac{1}{2}a_B t^2\\\frac{1}{2}t^2 (a_A - a_B) = d\\t=\sqrt{\frac{2d}{a_A-a_B}}=\sqrt{\frac{2(1400)}{11-(-4)}}=13.7 s[/tex]

Final answer:

The two cars with given accelerations and an initial distance of 1400 meters between them when starting from rest will meet after 20 seconds.

Explanation:

To solve for the time at which the two cars meet, we must consider the accelerations of both cars and the initial distance between them. Assuming car A is moving with a positive acceleration of 11 m/s2 and car B is moving with a negative acceleration of -4 m/s², we need to find a common point in time where they both cover the total distance of 1400 m when starting from rest.

Let the time taken for the cars to meet be denoted by 't'. For car A, the displacement (sA) is given by the formula sA = 0.5 * aA * t², and for car B, the displacement (sB) is given by sB = 0.5 * aB * t². As they are moving towards each other, the sum of their displacements sA+sB should equal the initial separation distance which is 1400m.

This gives us the equation 0.5 * 11 * t2 + 0.5 * (-4) * t² = 1400. Simplifying, we get 3.5 * t² = 1400, and solving for 't' gives us t2 = 400, so t = 20 seconds. Hence, both cars will meet after 20 seconds.

Explanation:

When an object is moving in a circular path, the motion of the object is called uniform circular motion. The object moves under the action of centripetal acceleration. It is given by :

[tex]a=\dfrac{v^2}{r}[/tex]

r is the radius of circular path

v is the speed of the object

In uniform circular motion, the object moves with constant speed. Also, the velocity of the object keeps on changing because it changes direction at every instant of time. Also, the object is accelerating due to change in velocity.

So, the correct options are (b) and (c).

In uniform circular motion, an object travels in a circular path at a constant speed, but its velocity is not constant because the direction of motion changes. Thus, the object is accelerating due to the continuous change in direction, despite the speed being constant.

Understanding Uniform Circular Motion

Uniform circular motion refers to the motion of an object traveling in a circular path at a constant speed. This situation presents a peculiar form of acceleration. Even though the object maintains a constant speed, its velocity is not constant because its direction is continually changing.

The three statements provided, when evaluated, give us the following insights:

Therefore, the correct statements about an object in uniform circular motion are that it moves at a constant speed and it is indeed accelerating.

Answer:

The lifeguard takes 25.9  seconds to reach the child, at 25.9 meters from the start point downstream.

Explanation:

As the image shows, the child trajectory, the lifeguard trajectory and the distance from the bank form a triangle. This triangle is formed by the distances, an we already know the distance from the bank and the speed of child, and the speed of the lifeguard. So we have unknom time in common. Lets see the equations:

Using phitagoras theorem

[tex]45^{2}+(1*t_{1} )^{2}  =(2*t_{2} )^{2}\\\\but\\t_{1} =t_{2} , then\\\\45^{2} =3t^{2} \\\\t=\sqrt{\frac{45^{2}}{3}  } = 25.9seconds\\and replacing in X1= 25.9 meters[/tex]

Final answer:

The lifeguard takes 22.5 seconds to reach the child, intercepting 22.5 meters downstream due to the river's current. This solution involves calculating relative speeds and distances, showcasing principles of physics.

Explanation:

The question describes a scenario where a lifeguard needs to save a child being carried downstream by a river's current. The lifeguard can swim at a speed of 2.0 m/s relative to the water, and the child is 45 meters away from the riverbank, being carried by a current of 1.0 m/s. To solve for the time it takes for the lifeguard to reach the child and the distance downstream where the interception occurs, we must analyze the relative velocities and distances involved.

Step 1: Determine the Time to Reach the Child

The lifeguard's effective speed towards the child in the direction perpendicular to the current is 2.0 m/s. Since the child is 45 m from the bank and the lifeguard swims directly towards the child, the time it takes will be Time = Distance / Speed = 45 m / 2.0 m/s = 22.5 seconds.

Step 2: Determine the Distance Downstream

During this time, both the child and the lifeguard are being carried downstream by the current. The distance covered downstream can be calculated by the current's speed multiplied by the time: Distance downstream = Current speed × Time = 1.0 m/s × 22.5 s = 22.5 meters.

Therefore, it takes the lifeguard 22.5 seconds to reach the child, and they intercept 22.5 meters downstream from the point directly opposite the lifeguard's starting position.

Answer:

There is an attractive force between the rod and sphere.

Explanation:

When negatively charged rod is placed close to the metal sphere then due to the electric field of the rod the opposite free charge of metal sphere comes closer to the rod on one surface

While similar charge in the metal sphere move away from the rod due to repulsion of electric field of rod

This temporary charge distribution of the metal sphere is known as induction

And since opposite charge on the metal surface comes closer to the metal sphere so here we can say that the rod will attract the metal sphere

so here correct answer will be

There is an attractive force between the rod and sphere.

Answer:

There is an attractive force between the rod and sphere.

Explanation:

Answer:

Correct option is (C)

Explanation:

u = 0 m/s

a = 5 m/s^2

(a) Distance traveled by the particle in first second

s = ut + 1/2 at^2

s = 0 + 0.5 x 5 x 1 x 1 = 2.5 m

So, this option is wrong.

(b) As we observe by the part (a) that the particle travels a distance of 2.5 m in first second so, this option is wrong.

(c) The acceleration of the particle is 5m/s^2, it means the speed of teh particle increases by 5 m/s every second. So, this is true.

(d) As we observe by part (c), the speed of the particle increases by 5 m/s every second so this option is wrong.  

The correct statement that describes the motion of a particle accelerating at a rate of 5.0 m/s^2 from rest is that the speed of the particle increases by 5.0 m/s during each second, based on the basic kinematics equation.

The subject of this question falls under Physics, specifically kinematics. The statement that accurately describes the motion of the particle is option c. "The speed of the particle increases by 5.0 m/s during each second." This is because acceleration is defined as the change in velocity or speed per unit time. So if the particle is accelerating at a rate of 5.0 m/s2, this means its speed increases by 5.0 m/s for every second that passes.

This can be understood by the basic kinematic equation: v = u + at, where v is the final velocity, u is the initial velocity (which is zero in this case, as the particle is starting from rest), a is the acceleration and t is the time. So, each second, the speed increases by the acceleration, which in this case is 5 m/s.

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Answer:

The net force acting on an object is the sum of all the force acting on it, and the net force of an object is zero. I f the forces acting on it tend to cancel each other. For example you are sit in a chair, the earth's gravity is pulling you down, but the chair is pushing you up with an equal amount of force.

Explanation:

Answer:

The net force acting on an object is the sum of all the force acting on it, and the net force of an object is zero. I f the forces acting on it tend to cancel each other. For example you are sit in a chair, the earth's gravity is pulling you down, but the chair is pushing you up with an equal amount of force.

Explanation:

science teacher helped me

-- Gravity slows the ball by 9.8 m/s every second. So it slows to zero and reached its highest point in

(58.8 / 9.8) = 6 seconds .

-- Its average speed all the way up is

(1/2) (58.8 + 0) = 29.4 m/s

-- Traveling for 6 seconds at an average speed of 29.4 m/s, the ball covers

(6) (29.4) = 176.4 meters .

If the airplane is carrying 58 gallons of fuel, it will weigh 2452 pounds.

Given that the weight (in pounds) of an airplane is a linear function of the amount of fuel (in gallons) in its tank.

Carrying 18 gallons of fuel, the airplane weighs 1999 pounds.

Also carrying 46 gallons of fuel, it weighs 2153 pounds.

First we need to find the difference in gallons and the difference in the weights

46 - 12 = 34 gallons

2399 - 2176 = 223 pounds

Therefore, 34 gallons of gas weighs 223 pounds

Now the weight per pound:

223 pounds / 34 gallons = 6.5588 pounds per gallon

Similarly,

54 gallons - 46 gallons = 8 gallons

8 gallons x 6.6 pounds per gallon = 52.8 pounds, round to 53 pounds

Now Total weight of plane with 54 gallons

2399 + 53 = 2452

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The weight of the airplane is a linear function of the amount of fuel in its tank. The slope of this function is found to be 5.5 pounds per gallon of fuel. Substituting into the equation, we find that the airplane weighs 2217 pounds when it is carrying 58 gallons of fuel.

This question can be solved by using the concept of linear function in mathematics. The weight of the airplane changes linearly with the amount of fuel in its tank. This gives us two points on the linear function (18, 1999) and (46, 2153). We can find the slope of this function by subtracting the y coordinates and dividing by the difference of the x coordinates, which gives us (2153-1999)/(46-18)=154/28 = 5.5 pounds/gallon. This is the amount the airplane's weight changes for each gallon of fuel. To find the weight of the airplane when it is carrying 58 gallons of fuel, we can use the point-slope form of a line, y-y1=m(x-x1), using one of our points and the slope we found. Plugging in gives us Weight - 1999 = 5.5×(Fuel - 18), which simplifies to Weight = 5.5*Fuel + 1999 - 5.5×18. Substituting 58 in place of Fuel, we get a weight of 2217 pounds.

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To find the time it takes for the baseball to reach the ground, we can use the equations of motion for an object in free fall. We can solve a quadratic equation to find the time and then use it to find the final velocity of the baseball when it strikes the ground.

To solve this problem, we can use the equations of motion for an object in free fall. The object is thrown downward, so the initial velocity is negative. We can use the equation: h = ut + (1/2)gt² to find the time taken to reach the ground. In this equation, h is the height, u is the initial velocity, t is the time, and g is the acceleration due to gravity. Since the initial height is 555 ft and the initial velocity is 40 ft/s, the equation becomes 555 = -40t + (1/2)(32)(t²). We can solve this quadratic equation to find the time it takes for the baseball to reach the ground. Once we have the time, we can use the equation: v = u + gt to find the final velocity. Plugging in the values, we get v = 40 + (32)t. Substitute the value of t from the first equation to find the final velocity when the baseball strikes the ground.

Answer:

127.36 m/s

Explanation:

velocity of plane with respect to air = 140 m/s due east

velocity of air with respect to ground = 31 m/s 30° west of north

Write the velocities in the vector forms

[tex]\overrightarrow{V_{p/a}}=140\widehat{i}[/tex]

[tex]\overrightarrow{V_{a/g}}=31  \left ( -Sin30 \widehat{i}+Cos30\widehat{j} \right )[/tex]

[tex]\overrightarrow{V_{a/g}}= -15.5 \widehat{i}+26.85\widehat{j}[/tex]

Let velocity of plane with respect to ground is given by vp/g

According to the formula of relative velocities

[tex]\overrightarrow{V_{p/a}}=\overrightarrow{V_{p/g}}-\overrightarrow{V_{a/g}}[/tex]

[tex]\overrightarrow{V_{p/g}}=\overrightarrow{V_{p/a}}+\overrightarrow{V_{a/g}}[/tex]

[tex]\overrightarrow{V_{p/g}}= \left ( 140-15.5 \right )\widehat{i}+26.85\widehat{j}[/tex]

[tex]\overrightarrow{V_{p/g}}= \left ( 124.5 \right )\widehat{i}+26.85\widehat{j}[/tex]

The magnitude of the velocity of plane with respect to the ground is given by

[tex]V_{p/g} = \sqrt{124.5^{2}+26.85^{2}}=127.36 m/s[/tex]

Thus, the velocity of plane with respect to the ground is given by 127.36 m/s.

Answer:

d=360 miles

Donna lives 360 miles from the mountains.

Explanation:

Conceptual analysis

We apply the formula to calculate uniform moving distance[

d=v*t   Formula (1)

d: distance in miles

t: time in hours

v: speed in miles/hour

Development of problem

The distance Donna traveled to the mountains is equal to the distance back home, equal to d,then,we pose the kinematic equations for d, applying formula 1:

travel data to the mountains: t₁= 8 hours ,  v=v₁

d= v₁*t₁=8*v₁ Equation (1)

data back home : t₂=4hours ,  v=v₂=v₁+45

d=v₂*t₂=(v₁+45)*4=4v₁+180 Equation (2)

Equation (1)=Equation (2)

8*v₁=4v₁+180

8*v₁-4v₁=180

4v₁=180

v₁=180÷4=45 miles/hour

we replace v₁=45 miles/hour in equation (1)

d=8hour*45miles/hour

d=360 miles

Final answer:

To solve the problem, we used the relationship between speed, distance, and time to set up two equations and solve for the average speed to the mountains and the distance. Donna lives 360 miles away from the mountains.

Explanation:

Let's denote Donna's driving distance to the mountains as D miles. To find this distance, we can use the relationship between speed, distance, and time. When she drove to the mountains, the journey took her 8 hours. For the return trip with no traffic, it took 4 hours and the speed was 45 miles per hour faster.

Let v be the average speed on the way to the mountains. Therefore, the average speed on the way back is v + 45 mph.

Using the formula distance = speed × time, we have two equations:

Since both equations are equal to D, we can set them equal to each other:

v × 8 = (v + 45) × 4

Expanding both sides:
8v = 4v + 180

Subtracting 4v from both sides we get:

4v = 180

Dividing by 4:

v = 45 mph (speed to the mountains)

So, the distance D is:

D = 45 mph × 8 h = 360 miles

Therefore, Donna lives 360 miles away from the mountains.

Answer:

Bow Line

Explanation:

If the wind or current is pushing your boat away from the dock, bow line should be secured first.

1- We should cast off the bow and stern lines.

2-With the help of an oar or boat hook, keep the boat clear of the dock.

3-Leave the boat on its own for sometime and let the wind or current carry the boat away from the dock.

4 - As you see there is sufficient clearance, shift into forward gear and slowly leave the area.

Answer:3.67 m/s

Explanation:

mass of block(m)=2 kg

Velocity of block=6 m/s

spring constant(k)=2 KN/m

Spring compression x=15 cm

Conserving Energy

energy lost by block =Gain in potential energy in spring

[tex]\frac{m(v_1^2-v_2^2)}{2}=\frac{kx^2}{2}[/tex]

[tex]2\left [ 6^2-v_2^2\right ]=2\times 10^3\times \left [ 0.15\right ]^2[/tex]

[tex]v_2=3.67 m/s[/tex]

Answer:

Explanation:

mass, m = 43 g = 0.043 kg

L = 81 cm = 0.81 m

frequency, f = 59 Hz

Amplitude, A = 0.35 cm

(a)

Frequency

[tex]f=\frac{v}{2L}[/tex]

v = 59 x 2 x 0.81 = 95.58 m/s

(b)

Let F be the tension in the string

[tex]v=\sqrt{\frac{F}{\mu }}[/tex]

where, μ is mass per unit length

[tex]\mu =\frac{0.043}{0.81}=0.053 kg/m[/tex]

[tex]95.58=\sqrt{\frac{F}{0.053 }}[/tex]

[tex]F = 95.58\times 95.58 \times 0.053[/tex]

F = 484.18 N

(c)

Maximum velocity

v = ω A = 2 π f A

v = 2 x 3.14 x 59 x 0.0035 = 1.3 m/s

(d)

Maximum acceleration

a = ω² A

a = (2 π f )² x 0.0035

a = ( 2 x 3.14 x 59)² x 0.0035

a = 480.5 m/s^2

Answer:

Matter have two essential types of properties, those are physical properties and chemical properties.

Explanation:

Answer:

23.63 degree.

Explanation:

Specific heat of water = 4186 joule / kg degree

Specific heat of aluminium  = 900 joule / kg degree

Specific heat of copper = 386 joule / kg degree

Let equilibrium temperature be T.

Heat will be gained by water and aluminium and lost by hot copper.

Heat gained or lost = mst , where m is mass , s is specific heat and t is rise or fall of temperature.

Heat gained by water = .250 X 4186 X ( T - 20 )

= 1046.5 ( T-20)

Heat gained by aluminium = .400 x 900 x ( T - 26 )

= 360 ( T - 26 )

Heat lost by copper = .100 x 386 x ( 100 - T )

38.6 ( 100 - T)

Heat gained = Heat lost

1046.5 ( T-20) + 360 ( T - 26 ) = 38.6 ( 100 - T)

T ( 1046.5 + 360 + 38.6 ) = 3860 + 9360 +20930

1445.1 T = 34150.

T = 23.63 degree.

Change in the entropy of the universe will be zero because no heat is exchanged with the universe. The container is insulated from outside .

Inside the container,  entropy will be increased.  

Final answer:

The student's question about thermal equilibrium and entropy change is a physics problem related to calorimetry in an adiabatic process. It requires calculating the final temperature using heat exchange equations and determining the total entropy change using the formula for entropy change.

Explanation:

The student's question involves the thermal equilibration of three different materials in an insulated container, a common scenario in calorimetry problems within physics. We assume no heat loss to the container or surroundings (adiabatic process), which simplifies the calculations.

Final Temperature Calculation

To find the final temperature, we need to set the heat lost by the warmer substances equal to the heat gained by the cooler substance:

Here, m is mass, c is specific heat capacity, and ΔT is change in temperature.

For water, c = 4186 J/(kg°C), for aluminum, c = 900 J/(kg°C), and for copper, c = 387 J/(kg°C). Solving the equation ∀Q = 0 with the given masses and initial temperatures will yield the final equilibrium temperature.

Entropy Change

The change in entropy is calculated via:

We apply this formula separately for each substance, summing the changes to find the total entropy change of the universe in the experiment.

Answer:

The answer to your question is:  magnitude:  1534.9 units

direction: 326.5°

Explanation:

Data

x = 1280 u

y = -847 y

Then as x is positive and y is negative this vector is quadrangle

To find the magnitude, we use the pythagorean theorem

c2 = a2 + b2

c2 = 1280² + (-847)² = 1638400 + 717409 = 2355809

c = 1534.9 units

to find the direction we use the tangent function

tanФ = os/as = -847/1280 = -0.661

Ф = 33.49

But it is in the 4th quadrangle, then

Ф = 360 - 33-49 = 326.5°

Answer:

1530 units, -33.5°

Explanation:

Given the x-component and the y-component, the magnitude can be found with Pythagorean theorem:

v² = vx² + vy²

And the direction can be found with trigonometry:

θ = atan(vy / vx)

Given that vx = 1280 and vy = -847:

v² = (1280)² + (-847)²

v ≈ 1530

θ = atan(-847 / 1280)

θ ≈ -33.5° or 146.5°

θ is in the fourth quadrant, so θ = -33.5°.

Answer:

Restoring force of the spring is 50 N.

Explanation:

Given that,

Spring constant of the spring, k = 100 N/m

Stretching in the spring, x = 0.5 m

We need to find the restoring force of the spring. It can be calculated using Hooke's law as "the force on a spring varies directly with the distance that it is stretched".

[tex]F=kx[/tex]

[tex]F=100\ N/m\times 0.5\ m[/tex]

F = 50 N

So, the restoring force of the spring is 50 N. Hence, this is the required solution.

Answer:

The distance moved is 9 meters

The magnitude of the displacement is 2.4 meters

The direction of the displacement is northward

Explanation:

- Distance is the length of the actual path between the initial and the

  final position. Distance is a scalar quantity

- Displacement is the change in position, measuring from its starting

  position to the final position. Displacement is a vector quantity

The quarterback pedals 3.3 meters southward

That means it moves down 3.3 meters

Then runs 5.7 meters northward

That means it runs up 5.7 meters

The distance = 3.3 + 5.7 = 9 meters

The distance moved is 9 meters

It moves southward (down) for 3.3 meters and then moves northward

(up) for 5.7

It moves from zero to 3.3 down and then moves up to 5.7

The displacement = 5.7 - 3.3 = 2.4 meters northward

The magnitude of the displacement is 2.4 meters

The direction of the displacement is northward

Final answer:

The quarterback moved a total distance of 9.0 meters. The displacement of the quarterback was 2.4 meters northward, as displacement takes into account the direction of motion.

Explanation:

When considering the movement of a quarterback who backpedals 3.3 meters southward and then runs 5.7 meters northward, we need to determine both the total distance moved and the magnitude and direction of the displacement.

The distance is a scalar quantity that represents the total path length traveled, regardless of direction. In this case, the quarterback moved a total distance of 3.3 meters + 5.7 meters = 9.0 meters.

On the other hand, displacement is a vector quantity, which means it has both magnitude and direction. To find the quarterback's displacement, we subtract the southward movement from the northward movement, because these movements are in opposite directions. The displacement is thus 5.7 meters - 3.3 meters = 2.4 meters northward.

Answer:

721.8 Joule per second

Explanation:

L = 33 cm = 0.33 m

A = 55 cm^2 = 0.0055 m^2

Th = 129°C

Tc = 21°C

k = 401 W/mK

The rate of flow of heat is given by the formula

[tex]H =\frac{K A \left ( T_{h}-T_{c} \right )}{L}[/tex]

[tex]H =\frac {401  \times 0.0055 \times \left (129-21\right )}{0.33}[/tex]

H = 721.8 Joule per second

Thus, the rate of flow of heat is given by 721.8 Joule per second.

Final answer:

To find the conduction rate through the slab, use the formula Q/t = kA(TH - TC)/L. With the given values for copper's thermal conductivity, area, thickness, and temperature difference, the conduction rate is calculated to be 74,454 Watts or 74.454 kW.

Explanation:

To find the conduction rate through a copper slab, we can use the formula for heat transfer through conduction: Q/t = kA(TH - TC)/L. In this formula, Q/t is the rate of heat transfer (conduction rate), k represents the thermal conductivity of copper, A is the surface area of the slab, TH and TC are the temperatures of the hot and cold faces respectively, and L is the thickness of the slab.

Using the given values, L = 0.33 m (converted from 33 cm), A = 0.0055 m2 (converted from 55 cm2), k = 401 W/m·K, TH = 129°C, and TC = 21°C, the conduction rate can be calculated as follows:

Q/t = 401 W/m·K × 0.0055 m2 × (129°C - 21°C) / 0.33 m

Q/t = 401 W/m·K × 0.0055 m2 × 108 K / 0.33 m

Q/t = 74,454 W/m·K × m2 / m

Q/t = 74,454 W

Therefore, the conduction rate through the copper slab is 74,454 Watts or 74.454 kW.

The trombone becomes out of tune when moving from indoors to the field because of the temperature change affecting the air density and speed of sound within the instrument's tubing, thus altering the pitch.

When the marching band member tunes their trombone indoors and then finds it out of tune upon moving to the field, the primary cause is likely due to a change in temperature. Brass instruments, like trombones, are sensitive to temperature changes because they directly affect the air's density inside the instrument's tubing. Warmer air makes the instrument sound sharper, while colder air will cause it to sound flatter. Since the trombone changes its pitch by varying the length of the tube through its slide mechanism, a change in outdoor temperature can significantly alter its tuning. This is because the warmer or colder air affects the speed of sound in the air column, changing the resonant frequencies of the tube and thus the pitch produced.

Answer:

speed of current is 5 mile/hr

Explanation:

GIVEN DATA:

speed of motorboat = 15 miles/hr relative with water

let c is speed of current

15-c is speed of boat at  upstream

15+c is speed of boat at downstream

we know that

travel time=distance/speed

[tex]\frac{10}{15-c} +\frac{10}{15+c} = 1.5[/tex]

150+10c+150-10c=1.5(15-c)(15+c)

300=1.5(225-c^2)

300=337.5-1.5c^2

200=225-c^2

c^2=25

c = 5

so speed of current is 5 mile/hr

Final answer:

To find the speed of the current for a boat trip upstream and downstream taking a total of 1.5 hours at a constant speed of 15 mph relative to the water, we derive and solve an equation based on time taken for each part of the journey. The solution reveals that the current's speed is 3 mph.

Explanation:

The student asked how to find the speed of the current when a motorboat, traveling at a constant speed of 15 miles per hour relative to the water, went 10 miles upstream and then returned downstream, with the total trip taking 1.5 hours.

Step-by-Step Solution

By solving the equation, we find that the speed of the current is 3 miles per hour.

Answer:

Explanation:

Gotta work on writing the problem, kida hard to read with the coding text.  Anyway, a rectangle with one side  of 6 cm and another  at 3.5 cm, then rectangle B is proportional to that.  Which basically means rectangle B will be multiplied or divided by some number.

To make the concept a little simpler imagine it was a square with sides of length 2.  a proportional square twice as big would have lengths of 4 and half as big would have lengths of 1.

In this case we need measurements where one is 6 multiplied or divided by a number x, and then 3.5 has the same action done on it with the same number.  so again, twice as big would be 12 and 7 while half as big would be 3 and 1.75  anyway, let's look at the options.

A) 3 and 1.75

B) 5 and 2.5

C) 7 and 7

D) 12 and 5

E) 5.25 and 9

Just to have ti written, the original rectangle is 6 by 3.5

So A is obvious since I used it as an example, this is a proportional rectangle half the size of A.

The rest are harder to check except C.  7 and 7 make a square, but we know the side lengths have to be different, so C is easy to tell it's not right.

B we have to check.  Since it's not as obvious as A, we have to check with math more carefully.  What do we have to multiply 6 by to get 5?  Also, you always want to make the largest side of each rectangle proportional to each other.  Anyway, 6 times 5/6 is 5, so for B to be right, 3.5 times 5/6 needs to be equal to 2.5.  Does it?  Nope, its 2.9166 repeating.  So B is not right.

I'm not going to go through so much explanation for the others, if you don't get something let me know.  

D we could also know quickly isn't right since I told you the measurements if the rectangle is changed to one with a side length of 12.  We would need the other to be 7, so 12 and 5 isn't right.

E is our last possibility, since we need to pick two, but let's check anyway.  we need to multiply 6 by 7/8 to get 5.25.  3.5 times 7/8 is 3.0625, so not 9.  Good thing we checked here, because only one answer looks to be right.  Are you sure you put the right numbers?  Or did I misinterpret some?  

Answer:

A and E

Explanation: