A mass of 100 g is tied to the end of an 80.0-cm string and swings in a vertical circle about a fixed center under the influence of gravity. The speed of the mass at the top of the swing is 3.50 m/s. What is the speed of the mass at the bottom of its swing?

Answer:

[tex]q\approx 6.6\cdot 10^{13}~electrons[/tex]

Explanation:

Coulomb's Law

The force between two charged particles of charges q1 and q2 separated by a distance d is given by the Coulomb's Law formula:

[tex]\displaystyle F=k\frac{q_1q_2}{d^2}[/tex]

Where:

[tex]k=9\cdot 10^9\ N.m^2/c^2[/tex]

q1, q2 = the objects' charge

d= The distance between the objects

We know both charges are identical, i.e. q1=q2=q. This reduces the formula to:

[tex]\displaystyle F=k\frac{q^2}{d^2}[/tex]

Since we know the force F=1 N and the distance d=1 m, let's find the common charge of the spheres solving for q:

[tex]\displaystyle q=\sqrt{\frac{F}{k}}\cdot d[/tex]

Substituting values:

[tex]\displaystyle q=\sqrt{\frac{1}{9\cdot 10^9}}\cdot 1[/tex]

[tex]q = 1.05\cdot 10^{-5}~c[/tex]

This charge corresponds to a number of electrons given by the elementary charge of the electron:

[tex]q_e=1.6 \cdot 10^{-19}~c[/tex]

Thus, the charge of any of the spheres is:

[tex]\displaystyle q = \frac{1.05\cdot 10^{-5}~c}{1.6 \cdot 10^{-19}~c}[/tex]

[tex]\mathbf{q\approx 6.6\cdot 10^{13}~electrons}[/tex]

Answer: A plane mirror always forms a virtual image (behind the mirror). The image and object are the same distance from a flat mirror, the image size is the same as the object size, and the image is upright.

Explanation:

Answer:

Free Body Diagram

Explanation:

Such picture is called the "free body diagram"

Answer:

Explanation:

The pressure transmitted in the hydraulic system can be found by using the formula

[tex]p = \frac{f}{a} \\ [/tex]

f is the force

a is the area

From the question we have

[tex]p = \frac{35}{5} \\ [/tex]

We have the final answer as

Hope this helps you

Answer:

An External Stimulus is a stimulus that comes from outside an organism. Examples: You feel cold so you put on a jacket. When you sweat, the external stimulus is either you're anxious or hot.

Explanation:

hope it helps! <3

Answer:

w = 0.0436 rad/s

Explanation:

Radius of the cylinder is

3.125 * 1609m/mile = 5028 m

Using the angular acceleration formula, we have

a = v²/r = w²r.

Since we're interested in the angular speed, we make w the subject of the formula, so that

w² = a/r

w = √a/r

w = √(9.8/5028)

W = √0.0019049

w = 0.0436 rad/s

Then we can conclude that the angular speed of the rotation is w = 0.0436 rad/s

(a) The ball's height y at time t is given by

y = (20 m/s) sin(40º) t - 1/2 g t ²

where g = 9.80 m/s² is the magnitude of the acceleration due to gravity. Solve y = 0 for t :

0 = (20 m/s) sin(40º) t - 1/2 g t ²

0 = t ((20 m/s) sin(40º) - 1/2 g t )

t = 0   or   (20 m/s) sin(40º) - 1/2 g t = 0

The first time refers to where the ball is initially launched, so we omit that solution.

(20 m/s) sin(40º) = 1/2 g t

t = (40 m/s) sin(40º) / g

t ≈ 2.6 s

(b) At its maximum height, the ball has zero vertical velocity. In the vertical direction, the ball is in free fall and only subject to the downward acceleration g. So

0² - ((20 m/s) sin(40º))² = 2 (-g) y

where y in this equation refers to the maximum height of the ball. Solve for y :

y = ((20 m/s) sin(40º))² / (2g)

y ≈ 8.4 m

Answer:

what's your question I can't understand

Explanation:

Total energy (kinetic + potential)

1/2×mv^ + mgh

1/2×5×8×8+ 5×9.8×10

1/2×320 + 5×98

320/2 + 480

320/2 + 980/2 (multipling to make the denominator equal)

1300/2 = 650 joules

Hope it helps, if you don't understand try doing it yourself with the formula.

:)

Distance is the total path covered by the object

Here, 200 m is the distance covered by the person and NOT the displacement

Displacement of an object is nothing more than the shortest path between the initial and the final point

If the person travelled 100m and came back, his initial and final point will remain the same which means that he will have a displacement of 0 m

Answer:

B. Boats need to float.

Answer:

v = 17.5 m/s = 63 km/h

Explanation:

       [tex]K = \frac{1}{2}*m *v^{2} (1)[/tex]

       where m = mass of the object, v= speed of the object.

       [tex]21 km/hr * \frac{1 hr}{3600s}*\frac{1000m}{1 km} = 5.83 m/seg (2)[/tex]

       [tex]K = \frac{1}{2}*18000 kg *(5.83m/s)^{2} = 306250 J (3)[/tex]

       [tex]K = 306250 J = \frac{1}{2}*2000 kg *v^{2} (4)[/tex]

       [tex]v = \sqrt{\frac{306250}{1000} (m/s)2} = 17. 5 m/s = 63 km/h (5)[/tex]

Answer:

a

[tex]H =212.6 \ J[/tex]

b

[tex]v = 7.647 \ m/s[/tex]

Explanation:

From the question we are told that

   The child's weight is  [tex]W_c = 287 \ N[/tex]

    The length of the sliding surface of the playground is  [tex]L = 7.20 \ m[/tex]

    The coefficient of friction is  [tex]\mu = 0.120[/tex]

      The angle is [tex]\theta = 31.0 ^o[/tex]

      The initial  speed is  [tex]u = 0.559 \ m/s[/tex]

Generally the normal force acting on the child is mathematically represented as

=>    [tex]N = mg * cos \theta[/tex]

Note  [tex]m * g = W_c[/tex]

Generally the frictional force between the slide and the child is    

         [tex]F_f = \mu * mg * cos \theta[/tex]

Generally the resultant force acting on the child due to her weight and the frictional  force is mathematically represented as

      [tex]F =m* g sin(\theta) - F_f[/tex]

Here  F is the resultant force and it is represented as  [tex]F = ma[/tex]

=>   [tex]ma = m* g sin(31.0) - \mu * mg * cos (31.0)[/tex]

=>   [tex]a = g sin(31.0)- \mu * g * cos (31.0)[/tex]

=>  [tex]a = 9.8 * sin(31.0) - 0.120 * 9.8 * cos (31.0)[/tex]

=>[tex]a = 4.039 \ m/s^2[/tex]

So

   [tex]F_f = 0.120 * 287 * cos (31.0)[/tex]

=> [tex]F_f = 29.52 \ N[/tex]

Generally the heat energy generated by the frictional  force which equivalent tot the workdone by the frictional force  is mathematically represented as

     [tex]H = F_f * L[/tex]

=>  [tex]H = 29.52 * 7.2[/tex]

=>  [tex]H =212.6 \ J[/tex]

Generally from kinematic equation we have that

    [tex]v^2 = u^2 + 2as[/tex]

=>  [tex]v^2 = 0.559^2 + 2 * 4.039 * 7.2[/tex]

=>  [tex]v = \sqrt{0.559^2 + 2 * 4.039 * 7.2}[/tex]

=>  [tex]v = 7.647 \ m/s[/tex]

Answer:

The ratio is  [tex]R_c:R_e = 4 : 1[/tex]

Explanation:

From the question we are told that

   The period of the satellite is  [tex]T_c = 8 \ years[/tex]

Generally the period of earth around the sun is [tex]T_e = 1 \ year[/tex]

Generally from Kepler's third law , which is mathematically represented as

      [tex]\frac{T_c ^2}{T_e^2} = \frac{R_c^3}{R_e^3}[/tex]

Here  [tex]R_c[/tex] is the radius of the orbit which the satellite rotate around the sun

         [tex]R_e[/tex] is the radius of the orbit which the earth rotate around the sun

=>  [tex]\frac{R_c^3}{R_e^3} = [\frac{8}{1} ]^2[/tex]

=>   [tex]\frac{R_c}{R_e} = \sqrt[3]{[\frac{8}{1} ]^2}[/tex]      

=>   [tex]\frac{R_c}{R_e} = \frac{4}{1 }[/tex]      

=>   [tex]R_c:R_e = 4 : 1[/tex]

Answer:

a

Explanation:

The energy transformation occurs after a skydiver reaches terminal velocity is follows as;

A. Gravitational potential energy transforms into thermal energy.

B. Gravitational potential energy transforms into kinetic energy.

The skydiver, when he is located at a certain height h above the ground, possesses gravitational potential energy, equal to:

U = mgh

where m is the mass of the skydiver, g is the gravitational acceleration and h is the height above the ground.

The skydiver gravitational potential energy decreases as the altitude decreases and his kinetic energy store increases as his speed increases.

When a skydiver jumps out of a plane, the energy transfers take place as;

The skydiver's kinetic energy store increases as their speed increases and the thermal store of the air and the skydiver increases, as there is friction between the skydiver and the air particles.

In the given situation, both options A and B are correct.

Learn more about gravitational potential energy;

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Answer:

t = 5.16 seconds.

Explanation:

The flight time can be found using the following equation:

[tex] y_{f} = y_{0} +v_{0y}*t - \frac{1}{2}gt^{2} [/tex]

Where:

t: is the time

g: is the gravity = 9.81 m/s²

y₀: is the initial height = 0

[tex]y_{f}[/tex]: is the final height = 5.50 m

[tex]v_{0y}[/tex]: is the initial vertical velocity = v*sin(35)

v: is the speed = 46 m/s

[tex] 5.50 = 46*sin(35)*t - \frac{1}{2}9.81*t^{2} [/tex]

By solving the above cuadratic equation we have:

t₁= 0.22 s and t₂= 5.16 s      

We will take the solution equal to 5.16 seconds, since in 0.22 seconds (very short time) the ball is going up and in 5.16 seconds it landed on the green.                        

Therefore, 5.16 seconds have passed since the ball was hit until it landed.

I hope it helps you!                                                                                            

Answer:

The value is  [tex]w = 0.1167 \ rev/second[/tex]

Explanation:

From the question we are told that

    The rate at which the plate rotates is  [tex]w =7.0 \ rev/min[/tex]

Generally the revolution per second is mathematically represented as

       [tex]w = \frac{7.0}{60}[/tex]

=>    [tex]w = 0.1167 \ rev/second[/tex]

Answer:

Explanation:

horizontal component of velocity of throw = 20 cos20 = 18.8 m /s

vertical downwards component = 20 sin20 = 6.84 m /s

time to displace by height 30 m = t  , initial velocity u = 6.84 m /s

h = ut + 1/2 gt²

30 = 6.84 t + .5 x 9.8 t²

4.9 t² + 6.84 t - 30 = 0

t = - 6.84 ±√( 6.84² + 4 x 4.9 x 30 ) / 2x 4.9

=  - 6.84 ±√( 46.78 + 588 ) / 9.8

=  - 6.84 ±√(634.78 ) / 9.8

= - 6.84 ±25.2 / 9.8

= 1.87 s

horizontal displacement in 1.87 s

= 18.8 x 1.87

= 35.15 m .

Answer: 5.5m/s

Explanation:

vf=vi+at

vf= 4.0m/s + (0.50m/s^2)(3.0s)

The speed of the cart at the end of this 3.0 second interval is 5.5 meter per seconds.

Given the following data:

To find the speed of the cart at the end of this 3.0 second interval, we would use the first equation of motion;

[tex]V = U + at[/tex]

Where:

Substituting the given parameters into the formula, we have;

[tex]V = 4 + 0.5(3)\\\\V = 4 + 1.5[/tex]

Final velocity, V = 5.5 m/s.

Therefore, the speed of the cart at the end of this 3.0 second interval is 5.5 meter per seconds.

Read more: https://brainly.com/question/8898885

Answer:

c.Mechanical

Explanation:

Answer:

The ratio is  [tex]\frac{B_1}{B_2} = 1.265[/tex]

Explanation:

From the question we are told that

   The density of fresh water is  [tex]\rho__{f}} = 998 \ kg/m^3[/tex]

     The density of ethanol is  [tex]\rho_{e} = 789 \ kg /m^3[/tex]

Generally speed of a wave in a substance is mathematically represented as

    [tex]v = \sqrt{\frac{B}{\rho} }[/tex]

Here B is the adiabatic bulk modulus of the substance  while [tex]\rho[/tex]  is the density of the substance

So at constant wave speed

     [tex]\sqrt{\frac{B_1}{\rho_1} } = \sqrt{\frac{B_2}{\rho_2} }[/tex]

=>   [tex]\frac{B_1}{\rho_1} = \frac{B_2}{\rho_2}[/tex]

=>   [tex]B_1 \rho_2 = B_2\rho_1[/tex]    

=>  [tex]\frac{B_1}{B_2} = \frac{\rho_1}{\rho_2}[/tex]

Here  [tex]\rho_1 =\rho__{f}} = 998 \ kg/m^3[/tex]   and  [tex]\rho_2 = \rho_{e} = 789 \ kg /m^3[/tex]

So

  =>  [tex]\frac{B_1}{B_2} = \frac{998}{789}[/tex]    

  =>  [tex]\frac{B_1}{B_2} = 1.265[/tex]    

Answer: apple basket ✨

Explanation:

Answer:

box 1 has larger mass than box 2  (which agrees with the first answer option given.

Explanation:

We need to consider the linear momentum of the boxes immediately before and after they crash.

Recall that momentum is defined as mass times velocity.

So for before the collision, the linear momentum of the system of two boxes is:

m1 * 4km/h  - m2 * 8km/h

with m1 representing mass "1" on the left, and m2 representing mass 2 on the right.

Notice the sign of the linear momentum (one positive (moving towards the right) and the other one negative (moving towards the left)

For after the collision, we have or the linear momentum of the system:

- m1 * 2km/h - m2 * 1km/h

Then, since the linear momentum is conserved in the collision, we make the  initial momentum equal the final and study the mass relationship between m1 and m2:

4 m1 - 8 m2 = - 2 m1 - m2

combining like terms for each mas on one side and another of the equal sign, we get;

4 m1 + 2 m1 = 8 m2 - m2

6 m1 = 7 m2

therefore m1 = (7/6) m2

which (since 7/6 is a number larger than one) tells us that m1 is larger than m2 by a factor of 7/6

Therefore, the first answer option is the correct answer.

Answer:

a) they both will appear to have the same loudness

Explanation:

When we talk about how loud a sound is , we describe it in decibels (dB). The value of this unit on measurement in this question is what we are going to build our answer on.

Their sound intensity level is the same at 60db even though each of these separate sounds have different frequencies of 40Hz and 100Hz respectively.

The both of them will therefore have the same loudness actually as their sound intensity level has no difference bat 60db each.

Answer:

Explanation:

The new volume can be found by using the formula for Boyle's law which is

[tex]P_1V_1 = P_2V_2[/tex]

Since we are finding the new volume

[tex]V_2 = \frac{P_1V_1}{P_2} \\[/tex]

From the question we have

[tex]V_2 = \frac{0.4 \times 500000}{0.9} = \frac{200000}{0.9} \\ = 222222.2222... \\ = 222222[/tex]

We have the final answer as

Hope this helps you

Answer:

1.52g

Explanation:

Given parameters:

Force  = 125N

Mass combined  = 82kg

Unknown:

Acceleration of the bicycle  = ?

Solution:

From Newton second law of motion suggests that:

   Force = mass x acceleration

  Acceleration = [tex]\frac{force}{mass}[/tex]  = [tex]\frac{125}{82}[/tex]   = 1.52g

Answer:

The answer that was correct for me was A. 55 N pulling left, and 16 N, 17N p

pulling Right

Explanation:

Answer:

8.33 m/s

Explanation:

v=d/s, velocity = displacement/ time

Answer:

Explanation:

Step one:

given data

acceleration a=4m/s^2

final velocity v=35m/s

time t=5 seconds

Step two:

Required

initial velocity u=?

Applying the first equation of motion

v=u+at

substituting we have

35=u+4*5

35=u+20

u=35-20

u=15 m/s

The initial velocity is 15m/s

Answer:

  C = A - B

Explanation:

The addition of vectors takes into account the magnitude of each vector and its direction, so when adding two vectors, the result depends on the direction of the vectors.

* If the vectors have the same direction the result is maximum

            C = A + A

* if the vectors have 90 between them, the magnitude of the result is given by the Pythagorean Theorem

            C = √(A² + B²)

* if the vectors have 180º between them the result is minimal

            C = A - B

We can also perform this sum graphically, where the resulting vector goes from the origin of the first vector to the tip of the last one, it can clearly be seen that when the vectors are antiparallel (180º angle) the magnitude is minimal