10. Luther is designing a roller coaster for an amusement park. At one point, the roller coaster will enter a horizontal loop at the speed of 31.8 m/s. If Luther does not want to centripetal acceleration to exceed 29.0 m/s^2, what is the minimum radius of the horizontal loop?

16. When a certain roller coaster is at the top of a 61 m hill, it has no velocity. As the coaster descends the hill, it gains speed. What is the roller coasters speed when the it has a height of 34 m above the ground?

Please answer both of you can!!

Answer:

The car is considered to be speeding

Explanation:

The following data were obtained from the question:

Constant acceleration (a) = 7.4 m/s²

Time (t) = 2.4 s

Speed limit = 15.64 m/s

To know if the car speeding at any point, we shall determine the velocity of the car.

This can be obtained as follow:

Constant acceleration (a) = 7.4 m/s²

Time (t) = 2.4 s

Constant velocity (v) =?

a = v/t

7.4 = v / 2.4

Cross multiply

v = 7.4 × 2.4

v = 17.76 m/s

Thus, the velocity of the car is 17.76 m/s.

Comparing the velocity of the car (i.e 17.76 m/s) with the speed limit (i.e 15.64 m/s), we can see that the velocity of the car is higher than the speed limit. Therefore, the car is considered to be speeding.

Answer:

a) 37.70 m/s

b)710.6 m/s²

Explanation:

Given that ;

Mass of object = 2 kg

Radius of the motion = 2m

Frequency of motion = 3 rev/s

The formula to apply is;

v= 2πrf   where v is linear speed

v = 2×π×2×3 =12π = 37.70 m/s

Centripetal acceleration is given as;

a= 4×π²×r×f²  

a= 4×π²×2×3²

a=710.6 m/s²

Answer:

5m

Explanation:

[tex]4^{2}+3^{2}=5^{2}\\5^{2}=25[/tex]

Use the Pythagorean theorem to calculate the long edge of the triangle, which would be his displacement.

Explanation:

Given that,

Number of turns in the coil, N = 100

Area of the coil, A = 100 cm² = 0.01 m²

It is placed at an angle of 70°.

Magnetic field, B = 0.1 Wb/m²

We need to find the magnetic flux through the coil and the emf is induced in the coil after 10⁻³ s.

Magnetic flux is given by :

[tex]\phi =BA\cos\theta\\\\\text{For N turns},\\\phi =NBA\cos\theta \\\\\phi=100\times 0.1\times 0.01\times \cos(70)\\\\=0.034\ Wb[/tex]

So, the magnetic flux through the coil is 0.1 Wb.

Emf induced in the coil is :

[tex]\epsilon=\dfrac{-d\phi}{dt}\\\\=\dfrac{0.034}{10^{-3}}\\\\=34\ V[/tex]

So, 34V of emf is induced in the coil.

Answer:

2.3 newtons of force

Explanation:

Divide the weight by the speed of the bike

Answer:

7.5N

Explanation:

Given parameters:

Mass of the ball  = 0.5kg

Acceleration  = 15m/s²

Unknown:

Force exerted by the kicker = ?

Solution:

To know the force exerted by the kicker, we use the mathematical expression below:

 Force  = mass x acceleration

This is based on Newton's second law of motion;

Now insert the parameters and solve;

  Force  = 0.5 x 15  = 7.5N

Answer:

Look Below

Explanation:

Let's say you are kicking certain things. The first object is a soccer ball. Assume the ball is at rest using the Earth frame of reference. If you kick as hard as you can the ball it will go flying. Now change the soccer ball into a bowling ball. If you kick it as hard as you can again. It will not go as far. The same force that you applied to both the soccer ball and bowling ball allow it to accelerate, but the bowling ball which has more mass does not accelerate as much compared to the soccer ball due to the amount of mass it has.

In order to find the formula for net force, multiply both sides by mass.

Newton's second law of motion states that the rate of change of momentum is directly proportional to the force applied.

Given is the acceleration as the ratio of net force and mass.

We can write acceleration as -

a = F[net]/m

If we have to find the formula for net force, we will multiply both sides by mass (m). Therefore -

a x m = (F[net]/m) x m

am = F[net]

or

F[net] = ma

Therefore, in order to find the formula for net force, multiply both sides by mass.

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Answer:Total Inductive reactance XL =538.63 Ω

Explanation:

Parallel combination for Effective inductance is calculated as

L total =  [tex]\frac{1}{1/L1 + 1/L2 + ... 1/Ln}[/tex]

=[tex]\frac{1}{1/5 + 1/2}[/tex]

[tex]\frac{1}{0.2 + 0.5 \\}[/tex]

=[tex]\frac{1}{0.7}[/tex]

=1.42857H

Inductive reactance XL = 2 πFL

where f= frequency= 60Hz

L=  Effective inductance=1.42857H

Inductive reactance , XL = 2 X 3.142 X 60 X 1.42857

=538.63Ω

Answer:

b and c

Explanation:

NASA might hire U.S. businesses and universities to do:  Research new ideas, build complex equipment. Hence, option (b) and (c) are correct.

Astronomy and space technology are used in space exploration to learn more about the universe. While astronomers use telescopes to explore the universe, both unmanned robotic space missions and human spaceflight also participate in the physical exploration of space. One of the main sources of space science, like its traditional form astronomy, is space exploration.

Although astronomy, or the study of celestial objects, has existed since the beginning of trustworthy written history, it wasn't until the mid-20th century that the possibility of physical space exploration became a reality.

Space exploration can lead to money going to U.S. businesses and universities. Hence,  NASA might hire U.S. businesses and universities to do:  Research new ideas, build complex equipment.

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Answer:

61.9°

Explanation:

The formula for calculating the workdone is expressed as

Workdone = Fdsin theta

F is the force applied on the crate

d is the distance covered

theta is the angle that the rope makes with the horizontal

Given

F = 40N

d = 7m

Workdone = 247J

Substituting into the formula:

247 = 40(7)sin theta

247 = 280sin theta

sin theta = 247/280

sin theta = 0.88214

theta = arcsin(0.88214)

theta = 61.9°

Hence the angle that the rope makes with the horizontal is 61.9°

[tex]\displaystyle v = 5.7735 \ m/s[/tex]

Math

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Physics

SI Units

Energy

Kinetic Energy Formula: [tex]\displaystyle KE = \frac{1}{2} mv^2[/tex]

Step 1: Define

Mass m = 30 kg

Kinetic Energy KE = 500 J

Step 2: Solve for v

Answer:

536.56 m/s

Explanation:

We'll begin by calculating the momentum of the Porsche. This can be obtained as follow:

Mass (m) of Porsche = 1361 kg

Velocity (v) of Porsche = 26.82 m/s

Momentum of Porsche =?

Momentum = mass × velocity

Momentum = 1361 × 26.82

Momentum of Porsche = 36502.02 Kgm/s

Finally, we shall determine the velocity you need to be running with in order to have the same momentum as the Porsche. This can be obtained as follow:

Your Mass = 68.03 kg

Your Momentum = Momentum of Porsche = 36502.02 Kgm/s

Your velocity =?

Momentum = mass × velocity

36502.02 = 68.03 × velocity

Divide both side by 68.03

Velocity = 36502.02 / 68.03

Velocity = 536.56 m/s

Thus you must be running with a speed of 536.56 m/s in order to have the same momentum as Porsche.

Answer:

s = 2.79 m

Explanation:

Given that,

A ball have a speed of 7.4 m/s just before it hits the ground.

Initial velocity of the ball was 0 (at rest)

We need to find the height from where the ball was dropped. It means we need to find the distance covered by it. Let it is h.

Using the third equation of motion to find it as follows :

[tex]v^2-u^2=2as\\\\s=\dfrac{v^2}{2g}\\\\s=\dfrac{(7.4)^2}{2\times 9.8}\\\\s=2.79\ m[/tex]

So, the ball is dropped from a height of 2.79 m.

The height from which you would have to drop a ball so that it would have a speed of 7.4 m/s just before it hits the ground is 2.79m

According to the third equation of motion;

[tex]v^2=u^2+2as[/tex]

where;

v is the final velocity = 7.4m/s

Initial velocity = 0m/s

s is the distance

a = g= 9.8m/s²

Substitute the values into the formula to have:
[tex]7.4^2=0^2+2(9.8)s\\54.76 + 19.6s\\s=\frac{54.76}{19.6}\\ s=2.79m[/tex]

Hence the height from which you would have to drop a ball so that it would have a speed of 7.4 m/s just before it hits the ground is 2.79m

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Answer:

Kinetic energy is energy of motion

Explanation:

Of potential energy which is energy that is stored

Answer:

3N

Explanation:

The frictional force always acts directly opposite to the force of motion, that is it opposes motion. According to the Newton second law of motion:

Sum of horizontal forces = 0

Hence:

5N - 4(0.5) - F = 0

5 - 2 = F

F = 3N

This question is incomplete, the complete question is;

Super fine 40-gauge copper wire has a diameter of only 0.080 mm and weighs only 44.5 g/km. Suppose a spool of 40-gauge wire weighs 205 g less after some wire is pulled off to wind a magnet. How could you calculate how much wire was used ?

Answer: length of wire to be used is 4.6067 km

Explanation:

Circular diameter = d mm

Linear mass density of wire = μ g/km

let m be the mass of wire un-winded from spool to wind a magnet.

If M is mass of wire initially

then

Δm = M - m  { which represents decrease of mass }

Also if L rep the length of wire pulled off,

then

Δm = μ × L grams

⇒ L = Δm/μ km

now given that weight Δm = 205 g and length per unit weight μ = 44.5 g/km

we substitute

L = 205 g  / 44.5 g/km

L =  4.6067 km

Therefore length of wire to be used is 4.6067 km

Answer:

clear out the junk, and plant some stuff

Explanation:

clear out all of the nasties, unless it is biodegradable, or you could get some mushrooms to break everything down, then you can go and plant some stuff or do whatever. You could turn it into a playground, park, whatever.

Answer:

Ball moves up and down repeatedly on surface because waves consist of successive crests and troughs moving across surface, each crest pushes ball up and each trough allows it to move down.

Explanation:

Answer:

8000Ns

Explanation:

Given parameters:

Mass of the truck  = 1000kg

Initial velocity  = 9m/s

Final velocity  = 17m/s

Unknown:

Impulse  = ?

Solution:

The impulse experienced by the truck is the the change in momentum of the body.

  Impulse  = Ft

        Momentum  = m(v  - u)

        Ft  = m( v - u )

 F is the force

 t is the time

 m is the mass

  v is the final velocity

 u is the initial velocity

     Impulse  = 1000(17 - 9) = 8000Ns

Answer:

On the way to the Moon the Apollo astronauts reached a point where the. Moon's gravitational pull became stronger, than the Earth's. (a) Determine the distance of ...

Explanation:

Answer:

10000N

Explanation:

Given parameters:

Mass of the car  = 1000kg

Acceleration = 3m/s²

g  = 10m/s²

Unknown:

Weight of the car  = ?

Solution:

To solve this problem we must understand that weight is the vertical gravitational force that acts on a body.

 Weight  = mass x acceleration due to gravity

So;

    Weight  = 1000 x 10  = 10000N

Answer:

Simply, it's just the velocity at a given moment in time.

Explanation:

Instantaneous velocity is basically just short for the velocity of something at any given time. To give an example, let's say I wind up a toy car and set him to go forward for 10 seconds, and 5 seconds in, I freeze time. The speed of the car at that moment is the instantaneous velocity.

Answer:

0.63 m/s²

Explanation:

Given that

Distance of meteor from earth's surface, r = 2.98R,

where R = radius of the Earth.

The force of the meteor due to the Earth is usually given by

F = GMM(a)/(R + r)² where

F = force exerted

G = gravitational constant

M = Mass of the earth

M(a) = mass of meteor

Remember that F = Ma, so applying that here, we have

acceleration of meteor = GM/(R + r)²

where r = 2.98R so that

acceleration of meteor = GM/(R + 2.98R)²

acceleration of meteor = GM/(3.98R)²

acceleration of meteor = GM / 15.84R²

It should be noted that GM/R² = 10, so

acceleration of meteor = 10/15.84

acceleration of meteor = 0.63 m/s²

Therefore as calculated, the acceleration of the meteor is 0.63 m/s²

Answer:B, universe, galaxy, solar system, earth

Explanation:

A p e x

Answer:

universe, Galaxy, solar system, earth

Explanation:

A P E X

Answer:

a)     F _total = 15.08 10⁻³ N ,   b)   m = 1,539 10⁻³ kg

Explanation:

a) To solve this problem we can use Coulomb's law to find the force created by each charge

          F =[tex]k \frac{\ q_{1} q_{2} }{r_{12}^{2} }[/tex]

and the total force is

          F = F₁₅ + F₂₅ + F₃₅ + F₄₅

The bold are vectros, In the exercise they indicate the charges

          q₁ = q₂= q₃ = q₄ =  1 10⁻⁶ C

          q₅ = 2 10⁻⁶ C

Let's set a reference system where the sphere is on the z axis and the other charges on the xy plane, let's write the coordinates of card charge

sphere (subscript 5)

   x₅ = 0

   y₅ = 0

   z₅ = 2 m

charge 1

   x = 0.5 m

   y = 0.5 m

   z = 0

charge 2

   x = -0.5 m

   y = 0.5 m

   z = 0

charge 3

   x = -0.5 m

   y = -0.5 m

   z = 0

charge 4

   x = 0.5 m

   y = -0.5 m

   z = 0

With these values ​​we can calculate the distance between each charge and the sphere

charge 1 and sphere

       r₁₅² = (x₅ -x₁)² + (y₅ - y₁)² + (z₅ -z₁)²

substitute

       r₁₅² = (0- 0.5)² + (0 - 0.5)² + (2 -0)²

       r₁₅² = 0.5² + 0.5² + 2²

       r₁₅² = 4.5

we can see that for the other charges the result is the same since being squared always gives positive

      r₁₅ = r₂₅ = r₃₅ = r₄₅

the force created by the card charge on the sphere is the projection on the Z axis of the total force

Let's find the angle with respect to the Z axis

            tan φ = r / z

where r is the magnitude of the vector in the xy plane

          r = [tex]\sqrt{0.5^{2} + 0.5^{2} }[/tex]

          r = 0.7071 m

         φ = tan⁻¹ r / z

         φ = tan⁻¹ (0.7071 / 2)

         φ = 19.5

consequently the total force is

        F_total = 4 F cos 19.5

        F _total =   [tex]4 \frac{k \ q_{1} q_{5} }{r_{15}^{2}}[/tex]   cos 19.5

let's calculate

        F_toal = 4 9 10⁹ 1 10⁻⁶ 2 10⁻⁶ /4.5    cos 19.5

        F _total = 15.08 10⁻³ N

b) For this part indicate that the sphere is in equilibrium with the weight

           F_total - W = 0

           W = mg

           F_total = mg

           m = F_total / g

           m = 15.08 10³ / 9.8

           m = 1,539 10⁻³ kg

Answer:

F = G  \frac{2 m^{2} }{r^{2} }

action and reaction forces with the same magnitude, but in the opposite direction, one applied to each body.

Explanation:

The force between the asteroids is given by the law of universal gravitation

           F = G m₁ m₂ / r²

in this case they give us the mass of each asteroid

           m₁ = m

           m₂ = 2m

we substitute

           F = G m 2m / r²

           F = G 2 m² / r²

            [tex]F = G \frac{2 m^{2} }{r^{2} }[/tex]

Let's analyze this expression, this is the force that one asteroid exerts on the other, therefore there are two forces, one applied to each asteroid, as the order of the products does not affect the result, the magnitude of the force is the same on each asteroid.

These are action and reaction forces with the same magnitude, but in the opposite direction, one applied to each body.

Consequently the two asteroid experiences the same magnitude of force