While standing on the roof of a building, a child tosses a tennis ball with an initial speed of 13 m/s at an angle of 35° below the horizontal. The ball lands on the ground 2.6 s later. How tall, in meters, is the building?

Answer:

The time is 5.71 sec.

Explanation:

Given that,

Acceleration [tex]a= -4.20 m/s^2[/tex]

Initial velocity = 24.0 m/s

We need to calculate the time

Using equation of motion

v = u+at[/tex]

Where, v = final velocity

u = inital velocity

t = time

a = acceleration

Put the value into the formula

[tex]0 =24.0 +(-4.20)\times t[/tex]

[tex]t = \dfrac{-24.0}{-4.20}[/tex]

[tex]t=5.71\ sec[/tex]

Hence, The time is 5.71 sec.

Answer:

The rock will rise 3.3 m above the top of the window.

Explanation:

The equations used to find the height and velocity of the rock at any given time are as follows:

y = y0 + v0 · t + 1/2 · g · t²

v = v0 + g · t

Where:

y = height of the rock at time t

y0 = initial height

v0 = initial velocity

t = time

g = acceleration due to gravity

v = velocity of the rock at time t

If we place the frame of reference at the bottom of the window, we can say that at time t = 0.19 s the height of the rock is 1.7 m. That will allow us to find the initial velocity needed to find the time at which the rock is at its maximum height.

y = y0 + v0 · t + 1/2 · g · t²

1.7 m = 0 m + v0 · 0.19 s - 1/2 · 9.8 m/s² · (0.19 s)²

1.7 m + 1/2 · 9.8 m/s² · (0.19 s)²  = v0 · 0.19 s

(1.7 m + 1/2 · 9.8 m/s² · (0.19 s)²) / 0.19 s = v0

v0 = 9.9 m/s

With the initial velocity, we can find at which time the rock reaches its max- height. We know that at maximum height, the velocity of the rock is 0. Then, using the equation of velocity:

v = v0 + g · t

0 = 9.9 m/s - 9.8 m/s² · t

-9.9 m/s / -9.8 m/s² = t

t = 1.0 s

Now calculating the position at time t = 1.0 s, we will find the maximum heigth:

y = y0 + v0 · t + 1/2 · g · t²

y = 0 m + 9.9 m/s · 1.0 s - 1/2 · 9.8 m/s² · (1.0 s)²

y = 5.0 m  (this is the max-height meassured from the bottom of the window)

Then, the rock will rise (5.0 m - 1.7 m) 3.3 m above the top of the window.

Answer:

4.18 μC

Explanation:

given,

charge place at the center of conducting spherical shell = -3.07 μC                    

total charge place in the shell itself = +7.25 μC                        

to calculate charge on the outer surface = ?                          

total charge on the outer surface = +7.25 μC - 3.07 μC

                                                    = 4.18 μC

hence, the charge on the outer surface of the shell is 4.18 μC

Answer:

285 seconds

Explanation:

Jenny speed is 3.8 m/s

Alyssa speed in 4.0 m/s

Alyssa starts after 15 seconds

Find the distance covered by Jenny, when Alyssa starts

Distance=Speed*time

Distance covered by Jenny in 15 seconds= 3.8×15=57m

Relative speed of the two members heading same direction will be;

4.0m/s-3.8m/s=0.2m/s

To find the time Alyssa catch up with Jenny you divide the distance to be covered by Alyssa by the relative speed of the two

Distance=57m, relative speed=0.2m/s  t=57/0.2 =285 seconds

=4.75 minutes

Answer:

Explanation:

[tex]v_{Jenny} =3.8m/s[/tex]

[tex]t_{Jenny}=t[/tex]

[tex]d_{Jenny}=d[/tex]

[tex]v_{Alyssa}=4.0m/s[/tex]

[tex]t_{Alyssa}=t-15[/tex], because she has a difference of 15 seconds.

[tex]d_{Alyssa}=d[/tex]

Both move at a constant speed, that means there's no acceleration, their speed is always the same.

Now, the equation of each movement is

[tex]d=3.8t[/tex] and [tex]d=4(t-15)[/tex], then we solve this two.

We replace the first equation into the second one

[tex]3.8t=4(t-15)\\3.8t=4t-20\\20=4t-3.8t\\0.2t=20\\t=\frac{20}{0.2}\\ t=100[/tex]

That means after 100 seconds Alyssa catch up with Jenny.

a. There is nothing suggesting that the balloon is accelerating horizontally, so we can assume that its horizontal speed is constant. The time before the balloon crash into the hill is simply the distance between the balloon and the hill divided by its velocity. Remember that velocity is simply the amount of distance that a object travels in a certain amount of time:

[tex]t = \frac{130m}{2.8 m/s} = 46.43 s[/tex]

b. Know that you know the maximum amount of time that the balloon can take to gain 28m of altitude, the minimum acceleration can be found using the  equations constant acceleration motion:

[tex]x = \frac{1}{2}at^2 + v_ot +x_0[/tex]

where a is the acceleration, v_o is the initial vertical velocity, 0 as the balloon is not moving vertically before starting to ascend. xo is the initial position, which we will give a value of 0m.

[tex]x = \frac{1}{2}at^2\\ 28m = \frac{1}{2}(46.43s)^2a\\ a = \frac{2*28m}{(46.43s)^2} = 0.026 m/s^2[/tex]

c. As we said before, there isn't any kind of force that accelerates the balloon horizontally, therefore, we can consider that its horizontal velocity is constant and equal to 2.8m/s

d. Acceleration is the amount of change in velocity after a given amount of time. So, with the acceleration and the time we can fin the velocity:

[tex]v_y = a_y*t = 0.026m/s^2*46.43s=1.206 m/s[/tex]

The pilot has approximately 46.43 seconds to gain 28 m in altitude to clear the hill. The minimum constant upward acceleration needed is approximately 0.026 m/s². The horizontal component of the balloon's velocity at clearance will be 2.8 m/s, while the vertical component will be approximately 1.21 m/s.

The time the pilot has to make the altitude change without crashing into the hill can be found using the horizontal velocity and the distance to the hill. Since the balloon drifts horizontally at 2.8 m/s and needs to cover 130 m, the time (t) it will take can be calculated as:

t = distance / horizontal velocity = 130 m / 2.8 m/s = 46.43 seconds.

To find the minimum constant upward acceleration (a) needed to clear the hill, we use the kinematic equation:

s = ut + (1/2)at2

Where s is the vertical displacement (28 m), u is the initial vertical velocity (0 m/s), and t is the time calculated above. Rearranging for a gives:

a = 2s / t2 ≈ 2(28 m) / (46.43 s)2 ≈ 0.026 m/s2.

As the horizontal velocity is not affected by the vertical motion in the absence of air resistance, the horizontal component of the balloon's velocity when it clears the top of the hill will remain 2.8 m/s.

To find the vertical component of the velocity at the instant it clears the top of the hill, we can use the equation:

vf = u + at

Where vf is the final vertical velocity, u is the initial vertical velocity, a is the acceleration, and t is the time taken. Substituting the known values gives:

vf = 0 m/s + (0.026 m/s2)(46.43 s) ≈ 1.21 m/s.

Answer:

84.44N

Explanation:

Hi!

The force F between two charges q₁ and q₂ at a distance r from each other is given by Coulomb's law:

[tex]F = k_c \frac{q_1 q_2}{r^2}[/tex]

The force on the negative charge q₁ is the sum of the forces from the other two charges. This forces have equal magnitude as both distances are 48cm. The magnitud is:

[tex]F_{1,2} =F_{1,3} = -k_c\frac{(26\mu C)^2}{(48cm)^2}=-9*10^9Nm^2C^{-2}*0.54*\frac{10^{-12}C^2}{10^{-4}m^2}=-48.75N\\[/tex]

(negative means attractive)

The sum of the forces, because of symmetry reasons actos along line L (see the figure), and its magnitud is:

[tex]F = 2*48.75*\cos(30\º)N = 84.44N[/tex]

Answer:

25 times greater

Explanation:

Let the mass of the car is m

Initial speed, u = 20 km/h = 5.56 m/s

Final speed, v = 100 km/h = 27.78 m/s

The formula for the kinetic energy is given by

[tex]K = \frac{1}{2}mv^{2}[/tex]

So, initial kinetic energy

[tex]K_{i} = \frac{1}{2}m(5.56)^{2}[/tex]

Ki = 15.466 m

final kinetic energy

[tex]K_{f} = \frac{1}{2}m(27.78)^{2}[/tex]

Kf = 385.86 m

Increase in kinetic energy is given by

= [tex]\left ( \frac{K_{f}}{K_{i}} \right )[/tex]

= 385.86 / 15.466 = 25

So, the kinetic energy is 25 times greater.

The kinetic energy of the car increases by a factor of 25.

The increase in kinetic energy of the car can be determined by comparing the initial kinetic energy to the final kinetic energy. Kinetic energy is directly proportional to the square of velocity.

In this case, the velocity is increased from 20 km/hr to 100 km/hr. Let's calculate the ratio of the final kinetic energy to the initial kinetic energy.

The initial kinetic energy is given by 1/2 * (mass of the car) * (initial velocity)^2, and the final kinetic energy is given by 1/2 * (mass of the car) * (final velocity)^2.

Let's substitute the values and calculate the ratio:

Ratio = (1/2 * (mass) * (final velocity)^2) / (1/2 * (mass) * (initial velocity)^2) = (final velocity)^2 / (initial velocity)^2.

Substituting the numbers, Ratio = (100 km/hr)^2 / (20 km/hr)^2 = 10000 / 400 = 25.

Therefore, the factor by which the kinetic energy of the car increases is 25 times greater.

Answer:

[tex]Q=4.0*10^{-9}C[/tex]

Explanation:

Electric field of a charge:

[tex]E=k*\frac{Q}{R^{2}}[/tex]

[tex]Q=\frac{E*R^{2}}{K}=1.7*4.6^{2}/(9*10^{9})=4.0*10^{-9}C[/tex]

Answer:

43.3 m

Explanation:

d1 = 25.1 m in 15.4° west of north

d2 = 38.8 m in 23.1° south of west

Write the displacements in vector form

[tex]\overrightarrow{d_{1}}=25.1\left ( -Sin15.4\widehat{i}+Cos15.4\widehat{j} \right )=-6.67\widehat{i}+24.2\widehat{j}[/tex]

[tex]\overrightarrow{d_{2}}=38.8\left ( -Cos23.1\widehat{i}-Sin23.1\widehat{j} \right )=-35.69\widehat{i}-15.22\widehat{j}[/tex]

The resultant displacement is given by

[tex]\overrightarrow{d}=\overrightarrow{d_{1}}+\overrightarrow{d_{2}}[/tex]

[tex]\overrightarrow{d}}=\left ( -6.67-35.69 \right )\widehat{i}+\left ( 24.2-15.22 \right )\widehat{j}[/tex]

[tex]\overrightarrow{d}}=\left ( -42.36 \right )\widehat{i}+\left ( 8.98 \right )\widehat{j}[/tex]

The magnitude of the resultant displacement is given by

[tex]d=\sqrt{8.98^{2}+\left ( -42.36 \right )^{2}}=43.3 m[/tex]

Thus, you are 43.3 m far from your starting point.

Final answer:

The bead rests at a height of 9.03 x 10^7 meters above the fixed charge.

Explanation:

To find the height above the fixed charge where the bead rests in equilibrium, we need to consider the electric forces acting on the bead. The electric force is given by the equation:

F = k * (q1 * q2) / r^2

Where F is the force between the two charges, q1 and q2 are the charges, r is the distance between them, and k is the electrostatic constant. In this case, the two charges are the fixed charge at the base of the rod and the charge on the bead. Setting the gravitational force equal to the electric force, we can solve for the height.

First, we need to convert the given charge of 20 nC to coulombs by dividing it by 10^9:

q2 = 20 nC / 10^9 = 20 * 10^-9 C

Next, we calculate the gravitational force and the electric force:

F_gravity = m * g

F_electric = k * q1 * q2 / r^2

Since the bead is in equilibrium, the two forces must be equal:

m * g = k * q1 * q2 / r^2

Now, we can solve for the height:

h = sqrt(k * q1 * q2 / (m * g))

Plugging in the given values:

h = sqrt((9 * 10^9 N * m^2 / C^2) * (20 * 10^-9 C) / (0.050 x 10^-3 kg * 9.8 m/s^2))

Simplifying:

h = sqrt(4 * 10^11 / (0.049 x 10^-3))

h = sqrt(8.16 x 10^14)

h = 9.03 x 10^7 m

Therefore, the bead rests at a height of 9.03 x 10^7 meters above the fixed charge.

Answer:

[tex]B=2.01 \times 10^{-5}\ T[/tex]

Explanation:

Distance between plates = 0.8 cm

Distance from one plate = 1 mm

Current density (J)= 16 A/m

Currents are flowing in opposite direction.

[tex]\mu _o=4\pi \times 10^{-7}[/tex]

When current is flowing in opposite direction then magnetic field given as

[tex]B=\dfrac{\mu _oJ}{2}+\dfrac{\mu _oJ}{2}[/tex]

[tex]B=\mu _oJ[/tex]

Now by putting the values we get

[tex]B=4\pi \times 10^{-7}\times 16[/tex]

[tex]B=2.01 \times 10^{-5}\ T[/tex]

The magnitude of the magnetic field between the plates at the given point is 2.011 x 10⁻⁵ T.

The magnitude of magnetic field between the plates due to the current flowing in opposite directions is determined by using the following formula;

B = μ₀J/2 + μ₀J/2

B = μ₀J

where;

Substitute the given parameters and solve for the magnetic field as follows;

B = (4π x 10⁻⁷) x (16)

B = 2.011 x 10⁻⁵ T

Thus, the magnitude of the magnetic field between the plates at the given point is 2.011 x 10⁻⁵ T.

Learn more about magnetic field here: https://brainly.com/question/7802337

Answer:

The magnetic field at the center of a circular loop is [tex]3.14\times10^{-5}\ T[/tex].

Explanation:

Given that,

Radius = 4.0 cm

Current = 2.0 A

We need to calculate the magnetic field at the center of a circular loop

Using formula of magnetic field

[tex]B = \dfrac{I\mu_{0}}{2r}[/tex]

Where, I = current

r = radius

Put the value into the formula

[tex]B =\dfrac{2.0\times4\pi\times10^{-7}}{2\times4.0\times10^{-2}}[/tex]

[tex]B =0.00003141\ T[/tex]

[tex]B=3.14\times10^{-5}\ T[/tex]

Hence, The magnetic field at the center of a circular loop is [tex]3.14\times10^{-5}\ T[/tex].

Answer:

[tex]\mu=180\times 10^{-3}A-m^2[/tex]      

Explanation:

Given that,

Area of the loop, [tex]A=10^{-3}\ m^2[/tex]

Current flowing in the wire, I = 180 A

We need to find the magnetic moment of the current loop. It is given by :

[tex]\mu=I\times A[/tex]

[tex]\mu=180\times 10^{-3}[/tex]      

[tex]\mu=180\times 10^{-3}A-m^2[/tex]      

So, the magnetic moment of the current loop is [tex]180\times 10^{-3}A-m^2[/tex]. Hence, this is the required solution.

Answer:

V=37.5miles/h

Explanation:

For convenience, let's convert the average speed to miles per minute:

V=7miles/h * 1h/60min = 0.1167 miles/min.

The distance traveled during the first 15 min was:

D = V*t = 1.75 miles   So, the remaining distance is 6.25miles.

Since you only have 10min left:

Vr = Dr / tr = 6.25 / 10 = 0.625 miles / min. If we take that to miles per hour we get final answer:

Vr = 0.625 miles/min * 60min/1h = 37.5 miles/h

Answer:

1) Speed in m/s equals 22.22 m/s.

2) Speed in miles per hour equals 49.712 mph.

Explanation:

Since we know that in 1 kilometer there are 1000 meters and in 1 hour there are 3600 seconds hence we can write

[tex]80km/h=\frac{80\times 1000m}{3600s}=22.22m/s[/tex]

Now we know that 1 mile equals 1.609 kilometer  hence we conclude that 1 kilometer equals [tex]\frac{1}{1.609}=0.6214[/tex]mile

Hence

[tex]80km/h=\frac{80\times 0.6214miles}{1h}=49.712mph[/tex]

The speed limit of 80 km/h is approximately 22.2 meters per second and 49.7 miles per hour.

The speed limit on some interstate highways is roughly 80 km/h. To convert this speed to meters per second, you divide by 3.6 (since 1 km/h is equal to about 0.27778 m/s). So, 80 km/h divided by 3.6 gives us approximately 22.2 m/s.

To convert the speed to miles per hour, you would use the conversion factor that 1 kilometer is approximately 0.621371 miles. Therefore, 80 km/h multiplied by 0.621371 gives us approximately 49.7 mi/h.

Answer:

21.75 m

Explanation:

t = Time taken for the car to slow down = 0.75 s

u = Initial velocity = 50 m/s

v = Final velocity = 8 m/s

s = Displacement

a = Acceleration

Equation of motion

[tex]v=u+at\\\Rightarrow a=\frac{v-u}{t}\\\Rightarrow a=\frac{8-50}{0.75}\\\Rightarrow a=-56\ m/s^2[/tex]

Acceleration is -56 m/s²

[tex]v^2-u^2=2as\\\Rightarrow s=\frac{v^2-u^2}{2a}\\\Rightarrow s=\frac{8^2-50^2}{2\times -56}\\\Rightarrow s=21.75\ m[/tex]

The distance covered in the 0.75 seconds is 21.75 m

Answer:

The uncertainty in the volume of the sphere is [tex]1.059\times 10^{4} m^{3}[/tex]

Solution:

As per the question:

Measured radius of the sphere, R = 135.4 m

Uncertainty in the radius, [tex]\Delta R = 4.6 cm = 4.6\times 10^{- 2} = 0.046 m[/tex]

We know the volume of the sphere is:

[tex]V_{s} = \frac{4}{3}\pi R^{3}[/tex]

We know that the fractional error for the given sphere is given by:

[tex]\frac{\Delta V_{s}}{V_{s}} = \frac{4}{3}\pi.\frac{|Delta R}{R}[/tex]

where

[tex]\Delta V_{s}[/tex] = uncertainty in volume of sphere

Now,

[tex]\Delta V_{s} = \frac{4}{3}\pi 3R^{2}\Delta R[/tex]

Now, substituting  the suitable values:

[tex]\Delta V_{s} = 4\pi (135.4)^{2}\times 0.046 = 1.059\times 10^{4} m^{3}[/tex]

Answer:

The charge q₃ must be placed at X = +2.5 cm

Explanation:

Conceptual analysis

The electric field at a point P due to a point charge is calculated as follows:

E = k*q/d²

E: Electric field in N/C

q: charge in Newtons (N)

k: electric constant in N*m²/C²

d: distance from charge q to point P in meters (m)

The electric field at a point P due to several point charges is the vector sum of the electric field due to individual charges.

Equivalences

1µC= 10⁻6 C

1cm= 10⁻² m

Data

k = 8.99*10⁹ N×m²/C²

q₁ =+3 µC =3*10⁻⁶ C

q₂ = -10 µC =-10*10⁻⁶ C

q₃= +6µC =+6*10⁻⁶ C

d₁ = 3cm =3×10⁻² m

d₂ = 4cm = 4×10⁻² m

Graphic attached

The attached graph shows the field due to the charges:

E₁:Field at point P due to charge q₁. As the charge is positive ,the field leaves the charge. The direction of E1 is (+ x).

E₂: Field at point P due to charge q₂. As the charge is positive ,the field leaves the charge. The direction of E1 is (+ x).

Problem development

E₃: Field at point P due to charge q₃. As the charge q₃ is positive, the field leaves the charge.

The direction of E₃ must be (- x) so that the electric field can be equal to zero at point P since E₁ and E₂ are positive, then, q₃must be located to the right of point P.

We make the algebraic sum of fields at point P due to the charges q1, q2, and q3:

E₁+E₂-E₃=0

[tex]\frac{k*q_{1} }{d_{1}^{2}  } +\frac{k*q_{2} }{d_{2}^{2}  } -\frac{k*q_{3} }{d_{3}^{2}  } =0[/tex]

We eliminate k

[tex]\frac{q_{1} }{d_{1} ^{2} } +\frac{q_{2} }{d_{2} ^{2} }+\frac{q_{3} }{d_{3} ^{2} }=0[/tex]

We replace data

[tex]\frac{3*10^{-6} }{(3*10^{-2})^{2} } +\frac{10*10^{-6} }{(4*10^{-2})^{2} } +\frac{6*10^{-6} }{d_{3} ^{2} } =0[/tex]

we eliminate 10⁻⁶

[tex]\frac{3}{9*10^{-4} } +\frac{10}{16*10^{-4} } =\frac{6}{d_{3}^{2}  }[/tex]

[tex](\frac{1}{10^{-4} }) *(\frac{1}{3} +\frac{5}{8}) =\frac{6}{d_{3}^{2}  }[/tex]

[tex]\frac{23*10^{4} }{24} =\frac{6}{d_{3} ^{2} }[/tex]

[tex]d_{3} =\sqrt{\frac{6*24}{23*10^{4} } }[/tex]

[tex]d_{3} =2.5*10^{-2} m\\d_{3} =2.5 cm[/tex]

The charge q₃ must be placed at X = +2.5 cm

Answer:

[tex]a_{c}=v^{2}/R[/tex]

The radius of curvature changes so that centripetal acceleration is similar along the entire roller coaster.

Explanation:

We know that the centripetal acceleration is directly proportional to the tangential velocity and inversely proportional to the radius of curvature:

[tex]a_{c}=v^{2}/R[/tex]

By energy conservation (and common sense), we know that the speed at the top of the roller coaster is smaller. Therefore if the roller coaster has similar accelerations (therefore also similar normal forces) at the top and at the bottom, it is necessary that the difference in speed be compensated with the radius of curvature, i.e. smaller radius at the top than at the bottom.

Answer:

0.5 rad / s

Explanation:

Moment of inertia of the disk I₁ = 1/2 MR²

M is mass of the disc and R is radius

Putting the values in the formula

Moment of inertia of the disc  I₁  = 1/2 x 100 x 2 x 2

= 200 kgm²

Moment of inertia of man about the axis of rotation of disc

mass x( distance from axis )²

I₂  = 40 x 1.25²

= 62.5 kgm²

Let ω₁ and ω₂ be the angular speed of disc and man about the axis

ω₂ = tangential speed / radius of circular path

= 2 /1.25 rad / s

= 1.6 rad /s

ω₁ = ?

Applying conservation of angular moment ( no external torque is acting on the disc )

I₁ω₁ = I₂ω₂

200 X ω₁ = 62.5 X 1.6

ω₁ =  0.5 rad / s

Final answer:

The magnitude of the magnetic force on an electron moving with a speed of 5.0 × [tex]10^4[/tex] m/s perpendicular to a magnetic field of 0.20 Tesla is calculated using the formula F = qvB, resulting in a force of 1.6 × [tex]10^{-15}[/tex] Newtons.

Explanation:

The magnetic force on an electron moving perpendicular to a magnetic field can be calculated using the formula F = qvB, where F is the magnetic force, q is the charge of the electron (-1.6 × [tex]10^{-19}[/tex] C), v is the velocity of the electron, and B is the magnetic field strength. Given that the electron moves with a speed of  5.0 × [tex]10^4[/tex] m/s perpendicular to a uniform magnetic field of 0.20 T, we use the formula to find the magnitude of the force:

F = (1.6 ×[tex]10^{-19}[/tex]C)( 5.0 × [tex]10^4[/tex] m/s)(0.20 T) =1.6 ×[tex]10^{-19}[/tex]C× 104 m/s × 2 × [tex]10^{-1}[/tex] T

F = 1.6 ×[tex]10^{-15}[/tex] N

The magnitude of the magnetic force on the electron is  1.6 ×[tex]10^{-15}[/tex] Newtons.

Answer: A little more that 5 Kg for a healthy person

Explanation: First, we know the following:

The regular adult has from 9 to 12 pints of blood. This is around 5 liters for a healthy male adult.

The human body is composed mostly on water, around 80%.

Blood is mostly composed on plasma, which makes blood thicker than water.

Knowing that, almost all the body is compose of water, it is safe to think that blood density should be near to that of water but higher.

The density on water is a know value. Which makes the following true:

1 Liter of Water weights 1 Kg

It could be said then, that the total mass of blood for a healthy person should be a little more that 5 kgs.

Answer:

Force between two equal charges will be 608.4 N

Explanation:

We have given charges [tex]q_1=0.65C\ and\ q_2=0.65C[/tex]

Distance between the charges = 2.5 km = 2500 m

According to coulombs law force between two charges is given by

[tex]F=\frac{1}{4\pi \varepsilon _0}\frac{q_1q_2}{r^2}=\frac{Kq_1q_2}{r^2}[/tex], here K is constant which value is [tex]9\times 10^9Nm^2/C^2[/tex]

So force [tex]F=\frac{9\times 10^9\times 0.65\times 0.65}{2500^2}=608.4N[/tex]

Answer:

The moment is 81.102 k N-m in clockwise.

Explanation:

Given that,

Force = 260 N

Side = 580 mm

Distance h = 370 mm

According to figure,

Position of each point

[tex]O=(0,0)[/tex]

[tex]A=(0,-b)[/tex]

[tex]B=(h,0)[/tex]

We need to calculate the position vector of AB

[tex]\bar{AB}=(h-0)i+(0-(-b))j[/tex]

[tex]\bar{AB}=hi+bj[/tex]

We need to calculate the unit vector along AB

[tex]u_{AB}=\dfrac{\bar{AB}}{|\bar{AB}|}[/tex]

[tex]u_{AB}=\dfrac{h\hat{i}+b\hat{j}}{\sqrt{h^2+b^2}}[/tex]

We need to calculate the force acting along the edge

[tex]\hat{F}=F(u_{AB})[/tex]

[tex]\hat{F}=F(\dfrac{h\hat{i}+b\hat{j}}{\sqrt{h^2+b^2}})[/tex]

We need to calculate the net moment

[tex]\hat{M}=\hat{F}\times OA[/tex]

Put the value into the formula

[tex]\hat{M}=F(\dfrac{h\hat{i}+b\hat{j}}{\sqrt{h^2+b^2}})\times(-b\hat{j})[/tex]

[tex]\hat{M}=\dfrac{F}{\sqrt{h^2+b^2}}((h\hat{i}+b\hat{j})\times(-b\hat{j}))[/tex]

[tex]\hat{M}=\dfrac{F}{\sqrt{h^2+b^2}}(-bh\hat{k})[/tex]

[tex]\hat{M}=-\dfrac{bhF}{\sqrt{h^2+b^2}}[/tex]

Put the value into the formula

[tex]\hat{M}=-\dfrac{580\times10^{-3}\times370\times10^{-3}\times260}{\sqrt{(370\times10^{-3})^2+(580\times10^{-3})^2}}[/tex]

[tex]\hat{M}=-81.102\ \hat{k}\ N-m[/tex]

Negative sign shows the moment is in clockwise.

Hence, The moment is 81.102 k N-m in clockwise.

The moment will be  81.102 k N-m in a clockwise direction. The moment is used to rotate or twist the object.

The moment is defined as the product of the force and the perpendicular distance from the pivot point. Its unit is KN-m.

The given data in the problem is;

F is the Force = 260 N

b is the Side = 580 mm

h is the distance = 370 mm

Position of the points is found by;

O(0,0)

A(0,-b)

B(h,0)

The position vector for the AB will be;

[tex]\vec AB = (h-0)+ (0-(-b))j \\\\ \vec AB =h \vec i + b \vec j[/tex]

The unit vector along with AB

[tex]\rm u_AB = \frac{\vec AB }{|\vec AB|} \\\\ \rm u_AB = \frac{h \vec i + b \vec j}{\sqrt{h^2+b^2} }[/tex]

The net moment is found by;

[tex]\hat M = \hat F \times OA \\\\ \hat M =F \frac{h \vec i + b \vec j}{\sqrt{h^2+b^2} }\times (b \vec j) \\\\ \hat M =\frac{F}{\sqrt{h^2+b^2}} \times (bh \hat k) \\\\ \hat M =- \ \frac{bhf}{\sqrt{h^2+b^2}}[/tex]

[tex]\hat M =- \ \frac{bhf}{\sqrt{h^2+b^2}} \\\\ \hat M =- \ \frac{580 \times 10^-3 \times 370 \times 10^-3 \times 260 }{\sqrt{(370\times 10^-3)^2+(580\times 10^-3)^2}} \\\\ \hat M =- 81.102 \ KNm[/tex]

-ve sign shows that moment is clockwise.

Hence the moment will be  81.102 k N-m in a clockwise direction.

To learn more about the moment refer to the link;

https://brainly.com/question/6278006

Answer:

[tex]\frac{W}{F} = 8.8\times10^7[/tex]

Explanation:

According to newton's law of gravitation

[tex]F=G\frac{m_1\times m_2}{r^2}[/tex]

here m_1=m_2=15000 kg

r= 3 meters and G= 6.67[tex]6.67\times10^{-11}[/tex]

putting values we get

[tex]F= 6.67\times10^{-11}\frac{15000^2}{3^2}[/tex]

solving the above equation we get

Force of gravitation F= [tex]1.6675\times 10^{-3}[/tex] newton

weight of the one of the truck W = mg= 15000×9.81 N

=147000 N

therefore [tex]\frac{W}{F} = \frac{147000}{1.66\times10^{-3}}[/tex]

=8.8×10^{7)

Answer:

221754385964.9123

Explanation:

Convert miles to nanometer

1 mile = 1.6 km

1 km = 1×10³×10³×10³×10³ nm

1 mile = 1.6×10¹² nm

So,

158 miles = 158×1.6×10¹² = 252.8×10¹² nm

Length of each molecule = 1140 nm

Number of molecules = Total length / Length of each molecule

[tex]\text{Number of molecules}=\frac{252.8\times 10^{12}}{1140}\\\Rightarrow \text{Number of molecules}=221754385964.9123[/tex]

There are 221754385964.9123 number of molecules in a stretch of 158 miles

Answer:

(A) Torque required is 21.205 N-m

(b) Wok done will be equal to 1199.1286 j

Explanation:

We have given moment of inertia [tex]I=12kgm^2[/tex]

Wheel deaccelerate from 135 rpm to 0 rpm

135 rpm = [tex]135\times \frac{2\pi }{60}=14.1371rad/sec[/tex]

Time t = 8 sec

So angular speed [tex]\omega _i=135rpm[/tex] and [tex]\omega _f=0rpm[/tex]

Angular acceleration is given by [tex]\alpha =\frac{\omega _f-\omega _i}{t}=\frac{0-14.1371}{8}=--1.7671rad/sec^2[/tex]

Torque is given by torque [tex]\tau =I\alpha[/tex]

[tex]=12\times 1.7671=21.205N-m[/tex]

Work done to accelerate the vehicle is

[tex]\Delta w=K_I-K_F[/tex]

[tex]\Delta W=\frac{1}{2}\times 12\times 14.137^2-\frac{1}{2}\times 12\times0^2=1199.1286J[/tex]

Answer:

a) [tex]v_{1}=14.29m/s\\v_{2}=9.25m/s\\v_{3}=6.36m/s[/tex]

b) [tex]v=+9.97m/s[/tex]

Explanation:

From the exercise we know that

[tex]x_{1} =15m, t_{1}=3s[/tex]

[tex]x_{2} =-3m, t_{1}=1.74s[/tex]

[tex]x_{3} =29m, t_{3}=5.20s[/tex]

From dynamics we know that the formula for average velocity is:

[tex]v=\frac{x_{2}-x_{1}  }{t_{2}-x_{1}  }[/tex]

a) For the three intervals:

[tex]v_{1}=\frac{x_{2}-x_{1}  }{t_{2}-t_{1}  }=\frac{(-3-15)m}{(1.74-3)s}=14.29m/s[/tex]

[tex]v_{2}=\frac{x_{3}-x_{2}  }{t_{3}-t_{2}  }=\frac{(29-(-3))m}{(5.20-1.74)s}=9.25m/s[/tex]

[tex]v_{3}=\frac{x_{3}-x_{1}  }{t_{3}-t_{1}  }=\frac{(29-15)m}{(5.20-3)s}=6.36m/s[/tex]

b) The average velocity for the entire motion can be calculate by the following formula:

[tex]v=\frac{v_{1}+v_{2}+v_{3}   }{n} =\frac{(14.29+9.25+6.36)m/s}{3}=+9.97m/s[/tex]

Answer:

The compression is [tex] \sqrt{2} \  d [/tex].

Explanation:

A Hooke's law spring compressed has a potential energy

[tex]E_{potential} = \frac{1}{2} k (\Delta x)^2[/tex]

where k is the spring constant and [tex]\Delta x[/tex] the distance to the equilibrium position.

A mass m moving at speed v has a kinetic energy

[tex]E_{kinetic} = \frac{1}{2} m v^2[/tex].

So, in the first part of the problem, the spring is compressed a distance d, and then launch the mass at velocity [tex]v_1[/tex]. Knowing that the energy is constant.

[tex]\frac{1}{2} m v_1^2 = \frac{1}{2} k d^2[/tex]

If we want to double the kinetic energy, then, the knew kinetic energy for a obtained by compressing the spring a distance D, implies:

[tex] 2 * (\frac{1}{2} m v_1^2) = \frac{1}{2} k D^2[/tex]

But, in the left side we can use the previous equation to obtain:

[tex] 2 * (\frac{1}{2} k d^2) = \frac{1}{2} k D^2[/tex]

[tex]  D^2 =  \frac{2 \ (\frac{1}{2} k d^2)}{\frac{1}{2} k} [/tex]

[tex]  D^2 =  2 \  d^2 [/tex]

[tex]  D =  \sqrt{2 \  d^2} [/tex]

[tex]  D =  \sqrt{2} \  d [/tex]

And this is the compression we are looking for

Answer:

[tex]d'=\sqrt{2} d[/tex]

Explanation:

By hooke's law we have that the potential energy can be defined as:

[tex]U=\frac{kd^{2} }{2}[/tex]

Where k is the spring constant and d is the compression distance, the kinetic energy can be written as

[tex]K=\frac{mv^{2} }{2}[/tex]

By conservation of energy we have:

[tex]\frac{mv^{2} }{2}=\frac{kd^{2} }{2}[/tex] (1)

If we double the kinetic energy

[tex]2(\frac{mv^{2} }{2})=\frac{kd'^{2} }{2}[/tex] (2)

where d' is the new compression, now if we input (1) in (2) we have

[tex]2(\frac{kd^{2} }{2})=\frac{kd'^{2} }{2}[/tex]

[tex]2(\frac{d^{2} }{2})=\frac{d'^{2} }{2}[/tex]

[tex]d'=\sqrt{2} d[/tex]

Answer:

Part a)

[tex]W = 1.38 eV[/tex]

Part b)

[tex]\lambda = 901.22 nm[/tex]

Part c)

[tex]KE = 1.2 eV[/tex]

Explanation:

As we know by Einstein's equation of energy that

incident energy of photons = work function of metal + kinetic energy of electrons

here we know that incident energy of photons is given as

[tex]E = \frac{hc}{\lambda}[/tex]

[tex]E = \frac{(6.6 \times 10^{-34})(3 \times 10^8)}{480 \times 10^{-9}}[/tex]

now we have

[tex]E = 4.125 \times 10^{-19} J[/tex]

[tex]E = 2.58 eV[/tex]

kinetic energy of ejected electrons = qV

so we have

[tex]KE = e(1.2 V) = 1.2 eV[/tex]

Part a)

now we have

[tex]E = KE + W[/tex]

[tex]2.58 = 1.2 + W[/tex]

[tex]W = 1.38 eV[/tex]

Part b)

in order to find cut off wavelength we know that

[tex]W = \frac{hc}{\lambda}[/tex]

[tex]1.38 eV = \frac{1242 eV-nm}{\lambda}[/tex]

[tex]\lambda = 901.22 nm[/tex]

Part c)

Maximum energy of ejected electrons is the kinetic energy that we are getting

the kinetic energy of electrons will be obtained from stopping potential

so it is given as

[tex]KE = 1.2 eV[/tex]