A pan-galactic gargle (an alien) whose mass is 85 kg exploring a large asteroid. What is the force of
gravity holding it down?

The acceleration is 2.2 m/s^2 and the net force is  62N towards the right

The net force is the effective force that acts on a body in a give direction.

1. The net force in the y axis is; ∑Fy = 0

2. The net force along the y axis is; ∑Fx =  277 N - 215 N

3. The normal reaction is given by;  28 kg * 9.8 m/s^2 = 274.4 N

4. The net force in the x axis is  277 N - 215 N = 62N towards the right

5. The acceleration of this force is obtained from;

F = ma

62 = 28 a

a = 62/28

a = 2.2 m/s^2

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The time  period of the pendulum is  0.65 second.

The time period is a period of time during which a behavior takes place or a condition persists. Depending on the type of activity or condition under consideration, it may be expressed either in seconds or in millions of years.

The mass of the object is = 0.10 kg

Length of the string is = 0.10 m.

Acceleration due to gravity is = 9.8 m/s²

Hence,  the time  period of the pendulum is = 2π√(0.10/9.8) sec

= 0.65 second.

Hence, the time period of the pendulum is  0.65 second.

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The student's path traces out a rectangle and she ends up at the same spot, so her displacement is 0 m.

On the other hand, she travels a total distance equal to the perimeter of that rectangle,

4.0 m + 8.0 m + 4.0 m + 8.0 m = 24 m

I don't think the provided solution is correct because it's not dimensionally consistent. The quantity [tex]8h-1[/tex] in particular doesn't make sense since it's mixing a distance with a dimensionless constant.

Here's how I think the proper answer should look:

The net force on the box acting perpendicular to the ramp is

[tex]\sum F_\perp = F_{\rm normal} - mg \cos(\theta) = 0[/tex]

where [tex]F_{\rm normal}[/tex] is the magnitude of the normal force due to contact with the ramp and [tex]mg\cos(\theta)[/tex] is the magnitude of the box's weight acting in this direction. The net force is zero since the box doesn't move up or down relative to the plane of motion.

The net force acting parallel the ramp is

[tex]\sum F_\| = mg\sin(\theta) - F_{\rm friction} = ma[/tex]

where [tex]mg\sin(\theta)[/tex] is the magnitude of the parallel component of the box's weight, [tex]F_{\rm friction}[/tex] is the magnitude of kinetic friction, and [tex]a[/tex] is the acceleration of the box.

From the first equation, we find

[tex]F_{\rm normal} = mg \cos(\theta)[/tex]

and since [tex]F_{\rm friction} = \mu F_{\rm normal}[/tex], we get from the second equation

[tex]mg\sin(\theta) - \mu mg\cos(\theta) = ma[/tex]

and with [tex]\mu = 0.25[/tex] and [tex]\theta=60^\circ[/tex], we get

[tex]a = g\sin(60^\circ) - 0.25g \cos(60^\circ) = \left(\dfrac{\sqrt3}2 - \dfrac18\right) g[/tex]

Let [tex]x[/tex] be the length of the ramp, i.e. the distance that the box covers as it slides down it. Then the box attains a final velocity [tex]v[/tex] such that

[tex]v^2 = 2ax[/tex]

From the diagram, we see that

[tex]\sin(\theta) = \dfrac hx \implies x = \dfrac h{\sin(60^\circ)} = \dfrac{2h}{\sqrt3}[/tex]

and so

[tex]v^2 = \dfrac{4ah}{\sqrt3} = \left(2 - \dfrac1{2\sqrt3}\right) hg = \dfrac14 \left(8 - \dfrac2{\sqrt3}\right) hg[/tex]

[tex]\implies v = \dfrac12 \sqrt{\left(8 - \dfrac2{\sqrt3}\right) hg}[/tex]

Answer:

A

Explanation:

ggtytryofttytrtuuyytyuygy

Their velocity (in m/s) just after impact if they cling together is -0.9 m/s.

Apply the principle of conservation of linear momentum;

Pi = Pf

where;

(92.5)(5.5)  +  (116)(-6)  =  v(92.5 + 116)

508.75 - 696 = v(208.5)

-187.25 = 208.5v

v = -187.25/208.5

v = -0.9 m/s

Thus, their velocity (in m/s) just after impact if they cling together is -0.9 m/s.

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The change in kinetic energy of the proton is 4.8 x 10⁻²⁰.

The change in kinetic energy of the proton is calculated as follows;

ΔK.E = W = eV

where;

V = Ed

V = 3 V/m x 0.1 m = 0.3 V

ΔK.E  = 1.6 x 10⁻¹⁹ x 0.3 = 4.8 x 10⁻²⁰ J

Thus, the change in kinetic energy of the proton is 4.8 x 10⁻²⁰ J.

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The magnitude and direction of the resultant force will be 7.65 units and 40.2°.

Force is explained as the multiplication of mass and acceleration. Its unit is N. It is the external agent which helps to change the shape and size of an object.

Force is used to push and pull the object and sometimes changes the direction of motion. The net force acting on an object is equal to the sum of all forces acting upon it.

F = F1 + F2 + F3

Given data;

Megnitude of force 1, F₁ =  5.90 units

Megnitude of force 2, F₂ = 5.00 units

α is the angle between the two forces=36.0°

Θ is the angle of the resultant force

The megnitude of the resultant force is;

[tex]\rm F =\sqrt{ F_{1}+F_{2}+2F_{1}F_{2}cos \alpha }\\\\ F = \sqrt{5.90 + 5.00 +2 \times 5.90 \times 5 \times cos 36^0 } \\\\ F = 7.65 \ units[/tex]

The direction of the resultant force is;

[tex]\rm \theta = tan^{-1}(\frac{F_{2}}{F_{1}} )[/tex]

[tex]\rm \theta = tan^{-1}(\frac{5.00}{5.90})\\\\ \theta = 40.2 ^0[/tex]

Hence the magnitude and direction of the resultant force will be 7.65 units and 40.2°.

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Answer:

B) Quickly understanding something without needing mental reasoning

Answer:

[tex]\huge\boxed{\sf Option \ B}[/tex]

Explanation:

So, Intuition actually means quickly understanding something without needing mental reasoning.

[tex]\rule[225]{225}{2}[/tex]

Answer:

A

Explanation:

As it begins to fall

F = ma        a = 9.81

F = .21 * 9.81 = 2.06 N

The definition of force in physics is the push or pull on a massed object that changes its velocity. An external force is an agent that has the power to alter the resting or moving condition of a body. The correct option is A.

Force is a physical factor that alters or has the potential to alter an object's state of rest or motion as well as its shape. Newton is the SI unit of force.

One of the most fundamental types of physical entities is the force. Due to the fact that force is a vector quantity, it possesses both a magnitude and a direction. Frictional force and contact force are the two categories under which all forces can be classified.

F = m × a

F = 0.21 × 9.81

F = 2.06 N

Thus the correct option is A.

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The acceleration and time is mathematically given as

a=gsinθ

[tex]t=\frac{2d}{gsinθ}[/tex]

Generally, the equation for the Force of the car is mathematically given as

[tex]N = mg cos\theta[/tex]

Therefore

[tex]ma=mgsin\theta[/tex]

a=gsinθ

The acceleration of the car is mathematically given as

a=gsinθ

Generally, the equation for the final velocity of the car is mathematically given as

[tex]v^2−u^2=2as[/tex]

Therefore

[tex]v 2 −(0) 2 =2(gsin\theta)d[/tex]

[tex]v= \sqrt {2gsin\theta.d}[/tex]

​

Generally, the equation for the motion of the car is mathematically given as

v−u=at

[tex]2gsin\thetad =(gsin\theta)t[/tex]

[tex]t=\frac{2d}{gsinθ}[/tex]

In conclusion, the time it takes the front bumper to reach the bottom of the hill is

[tex]t=\frac{2d}{gsinθ}[/tex]

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The magnitude of the current in the third wire is 8 A.

E₁ + E₂ + E₃ = 0

Equidistance from the two wires = 0.5 m

Apply Biot Savart rule to determine the magnitude of the magnetic field.

μI/2πr₁ + μI/2πr₂ + μI/2πr₃ = 0

(4π x 10⁻⁷ x 4)/(2π x 0.5) + (4π x 10⁻⁷ x 4)/(2π x 0.5) + (4π x 10⁻⁷ x I₃)/(2π x 0.5) = 0

4 x 10⁻⁷ I₃ = -3.2 x 10⁻⁶

I₃  = (-3.2 x 10⁻⁶)/(4 x 10⁻⁷)

I₃ = - 8 A

Thus, the magnitude of the current in the third wire is 8 A.

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(a) The maximum height reached by the projectile is 10.2 m and

(b) The horizontal distance traveled by the projectile is 40.8 m.

H = u²sin²θ/2g

H = (20²(sin(45))² / (2 x 9.8)

H = 10.2 m

T = (2u sinθ)/g

T = (2 x 20 x sin(45) )/(9.8)

T = 2.886 s

x = (v cos(45) x t

x = (20 x cos(45)) x 2.886

x = 40.8 m

Thus, the maximum height reached by the projectile is 10.2 m and the horizontal distance traveled by the projectile is 40.8 m.

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The ball's height [tex]y[/tex] at time [tex]t[/tex] is given by

[tex]y = 29.2\,\mathrm m - \left(8.30\dfrac{\rm m}{\rm s}\right) t - \dfrac12 gt^2[/tex]

where [tex]g=9.80\frac{\rm m}{\mathrm s^2}[/tex].

Solve for [tex]t[/tex] when [tex]y=0[/tex]. Omitting the units, we have

[tex]29.2 - 8.30t - \dfrac g2 t^2 = 0[/tex]

I'll solve by completing the square.

[tex]29.2 - \dfrac g2 \left(t^2 + \dfrac{16.6}g t\right) = 0[/tex]

[tex]29.2 - \dfrac g2 \left(t^2 + \dfrac{16.6}g t + \dfrac{8.3^2}{g^2}\right) = -\dfracg2 \times \dfrac{8.3^2}{g^2}[/tex]

[tex]29.2 - \dfrac g2 \left(t + \dfrac{8.3}g\right)^2 = -\dfrac{8.3^2}{2g}[/tex]

[tex]\dfrac g2 \left(t + \dfrac{8.3}g\right)^2 = 29.2 + \dfrac{8.3^2}{2g}[/tex]

[tex]\left(t + \dfrac{8.3}g\right)^2 = \dfrac{58.4}g + \dfrac{8.3^2}{g^2}[/tex]

[tex]t + \dfrac{8.3}g = \pm \sqrt{\dfrac{58.4}g + \dfrac{8.3^2}{g^2}}[/tex]

[tex]t = -\dfrac{8.3}g \pm \sqrt{\dfrac{58.4}g + \dfrac{8.3^2}{g^2}}[/tex]

[tex]\implies t \approx -3.43 \text{ or } t \approx 1.74[/tex]

Ignore the negative solution; the ball hits the ground about 1.74 s after being thrown.

Answer:

B. why you must push harder to move a car farther.

Explanation:

acceleration (gaining speed) happens when a force acts on a mass (object). FORCE=MASSxACCELERATION

The answer to the question is that the vertical distance the ball clear the cross bar is 1.465 metres.

We have horizontal distance as 28 m, and velocity as 18 m/s and the angle of projection 46.8 degree.

so, we can say that

In horizontal direction,

28 = (18 cos 46°) t

t = 2.2723 seconds

Now, in vertical direction,

Let be the height of the ball

h = (18 sin 46°)t - (1/2)gt²

h = (18 sin 46°)t - 4.9t²

h = ( (13.1214) × (2.2723) ) - ( (4.9) × (2.2723)² )

h = 4.5154 metre

Vertical distance the ball clear the cross bar = h - 3.05

Vertical distance the ball clear the cross bar = 4.5154 - 3.05

Vertical distance the ball clear the cross bar = 1.465

Thus, we can conclude that after solving and applying the concepts of projectile motion we find out the vertical distance the ball will clear the cross bar is 1.465 metres.

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Two mirrors are arranged such that they are parallel to each and perpendicular to the third mirror.

Also, the light is placed at the center of the three mirrors to produce multiple images by reflection.

Reflection is the bouncing back of light waves of a reflective surface when light shines on that surface.

The knowledge of reflection of light can be used by the Barber to set up a good salon.

The mirrors are arranged in the salon such that two of the mirrors are parallel to each and perpendicular to the third mirror. Also, the light is placed at the center of the three mirrors.

The parallel arrangement of the mirror will ensure that the clients will be able to have a full frontal and back view of themselves.

The parallel and perpendicular arrangement of the mirrors will also ensure that the light placed at the center will produce reflected to produce infinite images thus lighting up the salon.

In conclusion, the reflective properties of the mirrors as well as the angle between mirrors is used to create a well-lit salon by the barber.

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The uniformly distributed load per meter the beam may carry will be 1.275 × 10 ⁶ N/mm.

When an object is subjected to a heavy load at a specific spot, it often experiences bending stress, which causes the object to bend and tire.

The given data in the problem is;  

Bending stress, σ = 120 N/mm2  

Moment of inertia, I = 8.5 × 106 mm⁴

Depth of beam, y = d/2 = 200/2 = 100 mm  

Length of beam, L = 8 m = 8000 mm  

Width of beam, W = 300 mm

The maximum bending moment of the beam with UDL;

[tex]\rm W = \frac{wL^2}{8}[/tex]

From the bending equation;

[tex]\rm M = \frac{\sigma I}{y_{max}} \\\\ M = \frac{120 \ N / mm^2 \times 8.5 \times 10^6 }{100 \ mm } \\\\ M = 10.2 \times 10^6 \ N - mm[/tex]

The maximum bending moment of the beam with UDL;

[tex]\rm M = \frac{wL^2}{8} \\\\ 10.2 \times 10^6 = \frac{w \times 8^2}{8} \\\\ w = 1.275 \times 10^6 \ N/mm[/tex]

Hence the uniformly distributed load per meter the beam may carry will be 1.275 × 10 ⁶ N/mm.

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The number of windings that would be needed to produce an output of 110V AC will be 2750.

Electromagnetic induction is what causes the induced voltage. Electromagnetic induction is the process of generating emf (induced voltage) by subjecting a conductor to a magnetic field.

Typically, a transformer's primary winding is attached to the input voltage source and changes electrical power into a magnetic field.

The secondary winding's role is to turn this alternating magnetic field into electricity, generating the necessary output voltage.

The relation between the primary and the secondary winding is;

[tex]\rm \frac{V_s}{V_p}= \frac{N_s}{N_p} \\\\ \frac{110}{12000}= \frac{N_S}{300000} \\\\ N_s = 2750 \[/tex]

Transformers can only operate on AC current, since a flux shift is required for the induction process.

Additionally, since there won't be any flux change phenomena in the DC supply, the induction process can't take place. Transformers are utilized in AC supplies because of this.

Hence, the number of windings that would be needed to produce an output of 110V AC will be, 2750 and a transformer only works with AC.

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Answer:

A. To determine jobs for people

The difference in weight  of a 117 kg person as measured at sea level and at the top of the Vinson Massif, the highest peak in Antarctica is -1.847 N

To find the difference in weight, we find the change in acceleration due to gravity.

The acceleration due to gravity is the acceleration exerted by the force of gravity on an object. It is given by

g = GM/r² where

Now, to find the change in g, we differentiate g with respect to r,

So, dg/dr = d(GM/r²)

= -2GM/r³

So, the change in acceleration due to gravity, Δg is

Δg = dg/dr × Δr

= -2GM/r³ × Δr

Now, Δr = height above sea level of Vinson Massif = 5.14 × 10³ m

Substituting the values of the variables into the equation, we have

Δg = -2GM/r³ × Δr

Δg = [(-2 × 3.99 × 10¹⁴ Nm²/kg)/(6.38 × 10⁶ m)³] × 5.14 × 10³ m

Δg =[ (-7.98 × 10¹⁴ Nm²/kg)/259.69 × 10¹⁸ m³] × 5.14 × 10³ m

Δg = -0.03073 × 10⁻⁴ N/mkg × 5.14 × 10³ m

Δg = -0.1579 × 10⁻¹ N/kg

Δg = -0.01579 N/kg

Since weight W = mg where

The difference in weight is dW = mdg

Since

dW = mdg

= 117 kg × -0.01579 N/kg

= -1.847 N

So, the difference in weight  of a 117 kg person as measured at sea level and at the top of the Vinson Massif, the highest peak in Antarctica is -1.847 N

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Hi there!

Let's break this problem up into two parts.

Part A: Solenoid

The magnetic field everywhere inside a solenoid is constant, and can be found using the equation:

[tex]B = \mu_0 nI[/tex]

B = Magnetic field strength (? T)
μ₀ = Permeability of Free Space (4π × 10⁻⁷ Tm/A)
n = number of turns/meter (900)

I = current (0.03 A)

We are given all of these values, so let's solve.

[tex]B = (4\pi \times 10^{-7})(900)(0.03) = 34\mu T[/tex]

However, we also have a long wire that produces a magnetic field perpendicular to that produced by the solenoid.

Part B: Long wire

The equation for the magnetic field produced by a long wire is found by:

[tex]B = \frac{\mu_0 I}{2\pi r}[/tex]

Where 'r' is the distance from the wire.

Plug in what we know:

[tex]B = \frac{(4\pi \times 10^{-7})(3)}{2\pi (0.02)} = \mu 30 T[/tex]

Now, we must do the vector sum of these two fields to find the total magnetic field. Since they are perpendicular (solenoid field points to the side, wire fire points in or out), we can use the Pythagorean Theorem.

[tex]B_T = \sqrt{B_s^2 + B_w^2}\\\\B_T = \sqrt{(34\mu T)^2 + (30\mu T)^2} \approx \boxed{45\mu T}[/tex]

And here's our answer!

Time taken by the ball to reach the ground is 1.8s.

When an object is released from rest in free air considering no friction, the motion is depend only on the acceleration due to gravity, g.

A ball is thrown directly downward with an initial speed of 7.30 m/s, from a height of 29.0 m

Using the second equation of motion,

s = ut + 1/2 at²

Plug the values, we get

29 = 7.3t + 1/2 x9.81t²

4.905t² + 7.3t -29 =0

t =1.79871 or −3.28699

As time can't be negative, time taken to strike the ground is  approximately 1.8 s.

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The option above which most directly shows how society affects physics is that physicists work on projects that will get them nominated for Nobel prize.

A physicist is a person who who studies physics.

Physics is one of the branches of science which involves the study of matter, light, mechanics...

In conclusion: the option below which most directly shows how society affects physics is that physicists work on projects that will get them nominated for Nobel prize.

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A. The angle at which the arrow must be released to hit the bull's-eye is 20.7 °

B. The arrow will go over the branch.

R = u²Sine(2θ) / g

74 = 33² × Sine (2θ) / 9.8

Cross multiply

74 × 9.8 = 33² × Sine (2θ)

725.2 = 1098 × Sine (2θ)

Divide both sides by 1098

Sine (2θ) = 725.2 / 1098

Sine (2θ) = 0.6605

Take the inverse of sine

2θ = Sine⁻¹ 0.6605

2θ = 41.3

Divide both sides by 2

θ = 41.3 / 2

θ = 20.7 °

To determine if the arrow will go over or under the branch situated mid way, we shall determine the maximum height attained by the arrow. This can be obtained as follow:

H = u²Sine²θ / 2g

H = [33² × (Sine 20.7)²] / (2 ×9.8)

H = 6.94 m

Thus, the maximum height attained by the arrow is 6.94 m which is greater than the height of the branch (i.e 3.50 m).

Therefore, we can conclude that the arrow will go over the branch

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(a) The angular speed of the rod, when it lands on the horizontal surface is 1.61 rad/s.

(b) The the angular acceleration of the rod, just before it touches the horizontal surface is 1.06 rad/s² .

The angular acceleration of the rod is calculated as follows;

Apply the principle of conservation of angular momentum;

τ = Iα

where;

τ = Fr = mg(L/2) cosθ

I = mL²/3

mg(L/2) cosθ =  mL²/3(α)

g(1/2) cosθ =  L/3(α)

(³/₂)g cosθ  = L(α)

(³/₂ L)g cosθ  = α

1.5Lg cosθ  = α

1.5(2.1) cos (70.4) = α

1.06 rad/s² = α

ωf² = ω₁² + 2αθ

ωf² = 0 + 2(1.06)(70.4π/180)

ωf² = 2.605

ωf = √2.605

ωf = 1.61 rad/s

Thus, the angular speed of the rod, when it lands on the horizontal surface is 1.61 rad/s.

The the angular acceleration of the rod, just before it touches the horizontal surface is 1.06 rad/s² .

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A magnetic field is a field explaining the magnetic influence on an object in space.

A electric field is a field defined by the magnitude of the electric force at any given point in space.

A magnetic field is a field explaining the magnetic influence on an object in space.

A electric field is a field defined by the magnitude of the electric force at any given point in space.

The difference between magnetic fields and electric filed are:

Electric Filed

Magnetic Filed:

Similarities between Electric and Magnetic Field

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Answer:

1. Information Gathering

2. Analysis and Planning.

3. Implementation of a solution.

4. Assessment of the effectiveness of the solution.

5. Documentation of the incident.