which has the greater acceleration: a car that increases its speed from 50 km/h to 60 km/h, or a bike that goes from 0 km/h to 10 km/h in the same time? Explain.

The time at which the rotational acceleration is maximum is 0.26i s or 2.2i s.

The maximum tangential acceleration of the wheel is 4.1 m/s².

The rotational acceleration of the wheel is the change in the angular velocity of the wheel with time.

α = dω/dt

where;

ω = tan⁻¹(c + bt²)

α = dω/dt

α = (2bt)/[(c + bt²)² + 1]

the maximum angular acceleration =ω/t =  1.81/t

1.81/t = (2bt) / [c² + 2cbt² + b²t⁴ + 1]

1.81(c² + 2cbt² + b²t⁴ + 1) = 2bt(t)

1.81c² + 3.62cbt²  + 1.81b²t⁴  + 1.81 = 2bt²

1.81(1.5574)²  +  3.62(1.5574 x 6.53)t²   +  1.81(6.53²)t⁴ + 1.81 = 2(6.53)t²

4.39 + 36.81t²  + 77.18t⁴ + 1.81 = 13.06t²

77.18t⁴ +  23.75t²  +   6.2 = 0

23.75t²(3.25t² + 1) = -6.2

23.75t² = -6.2  or  3.25t² + 1 = -6.2

t² = -6.2/23.75

t² = -0.26

t = 0.26i  s

or

3.25t² + 1 = -6.2

3.25t² = -7.2

t² = -2.2

t = 2.2i s

The maximum tangential acceleration of the wheel at the given point is calculated as follows;

a = v²/r

a = ω²r

a = (1.81 rad/s)²(1.25 m)

a = 4.1 m/s²

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Answer:

30J

Explanation:

Δq = Δu + Δw

⇒Δu = Δq - Δw

here, Δq = 60J & Δw = 30J

∴ Δu = 60 - 30 = 30 J

The starting principal sum is multiplied by both of these variables, and the annual interest rate is increased to the number of compound periods minus one.

The full original amount of the loan is then reduced by the resulting value. Compound interest is the term for interest that is earned on interest. This may be shown using simple math: if you start with $100 and it earns 5% interest every year, you will have $105 at the end of the first year. At the end of the second year, you will have $110.25. On the initial principal sum, simple interest is calculated each time. Compound interest is calculated using the sum of the principal and interest. It is equal every year on a particular principal.

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The  correct answer is net acceleration of the car at the top of the hill is 6.6 m/s²

distance traveled by the car, d = 50 m mass of the car, m = 1600 kg radius of the hill's curvature, r = 25 m beginning speed of the car, u = 25 m/s

The third kinematic equation is applied to get the car's tangential acceleration, as shown below;

v2 = u2 + 2as, where a represents the vehicle's acceleration and 2as = v2 - u2 equals a=5.25 m/s

A net equals a2 + aca net = (5.25) 2 + 42a net = 6.6 m/s. 2

Consequently, the vehicle's net acceleration at the summit of the hill is 6.6 m/s2.

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The ball's velocity must be zero to reach the highest spot it can.

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It will take about 2,500 dump trucks to haul the material. Assuming the capacity of the dump truck is 16 cubic yards.

Note: A standard dump truck is between 10 -16 cubic yards.

1 cubic yard = 27 cubic feet.

from the question:

40,000 cubic yards= 65 cubic feet

hence,

Assuming the dump truck capacity is 16 cubic yards

Then,

number of dump trucks = 40,000 cubic yards/16 cubic yards

                                      =2,500

Therefore a dump truck of 16 cubic yards capacity, will need about 2,500 dump trucks to haul the material totaling 40,000 cubic yards.

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The type of nuclear radiation that the Americium-241 source is producing is

an alpha emitter, but also emits some gamma rays.

Nuclear radiation (also known as ionising radiation) is energy that is released in the form of high-speed charged particles or electromagnetic waves. Radiation can come from a variety of sources, both natural and man-made. Every living thing is constantly bombarded with low-level radiation from rocks, sunlight, and cosmic rays.

Am-241 emits mostly alpha rays but also some gamma rays. If ingested (swallowed) or inhaled, it poses a greater risk. Americium-241 is created in nuclear power plants by neutron activation of 239Pu and 240Pu, followed by beta decay of 241Pu (T1/2 = 14.35 years). This means that 241Am is produced in burned-up fuel by the decay of 241Pu a long time after the fuel is removed from a nuclear reactor.

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If a body has the three forces acting upon it and is in equilibrium then the vector sum of the three forces is zero. Thus, (A) I only is the correct answer.

I. The vector sum of three forces is zero means that the vector sum of all the three forces is equal to resultant zero vector.

II. If two forces act in the same direction then the body experiences more force on that side and hence is not in equilibrium. For the body to be in equilibrium, then the resultant of any two forces should be opposite, equal and collinear with the third force.

III. For the body to be in equilibrium, magnitude along with direction should be mentioned. If the three forces are in the same plane, convergent (cross the same point) and non-parallel.

Hence, the body on which three forces is acting will be in equilibrium when the vector sum of three forces is zero.

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a) The magnitude of force  exerted by cord A on block 1 is equal to magnitude of the force exerted by cord B on block 2

b) The acceleration of block 1 is equal to that if block 2

c)The force is forward and equal to the force of cord B on block 2.

We know that the force that acts along a cord can be regarded as the tension force. The magnitude of the tension force is equal to the force that is applied on the cord. If an object is hanged on the cord then the tension force would equal the weight of the object.

a) We can see that block 1 is connected to block 2 by the use of cord B and the force on cord B  must necessarily be the force on cord A  since the weight of the blocks are equal.

b) Since the force on cord A is equal to the force on cord B, the acceleration of block 1 must be equal to the acceleration of block 2.

c) Cord B exerts a force on block 1 in the forward direction and this force is equal to the force that is exerted on block 2.

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The answer is 5.6 ohms.

The electrical resistance of a circuit component or device is defined as the ratio of the applied voltage to the current through it. If the resistance is constant over a considerable voltage range. This is shown below. To calculate the total resistance of multiple resistors connected in this way, add the individual resistances.

calculation:-

V = iR

R = V/I

= 33.10/6

5.6.

Wire resistance is proportional to resistance and length and inversely proportional to wire cross-sectional area. To determine the condition of a circuit or component. The higher the resistance, the lower the current flow, and vice versa. Resistance is a measure of resistance to the flow of current in an electrical circuit. Resistance is measured in ohms and represented by the Greek letter omega.

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The value of constants A and θ will be  θ = 66.5° or 1.161 radians  and A = 3.1 cm  

Simple Harmonic Motion or SHM is defined as a motion in which the restoring force is directly proportional to the displacement of the body from its mean position. The direction of this restoring force is always towards the mean position.

x(t) = A sin (ωt + θ)

time = 0.00 seconds

2.83 = A sin ( 0 +  θ)

A sin θ = 2.83                        `equation 1

ν(t) = A ω cos (ωt+θ)

3.25 = A * 2.64 * cos (0 + θ )

3.25 = 2.64 A cos θ

A cos θ = 3.25 / 2.64 = 1.23              equation 2

dividing equation 1 and 2 , we get

tan θ = 2.30

θ = 66.5° or 1.161 radians

from equation 1

A sin θ = 2.83  

A sin ( 66.5 ) = 2.83

A = 3.1 cm  

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Difference in Gravity of 7%

The near side of the Earth is 12740 km closer to the Moon than the far side. As a result, the near side experiences a gravitational force that is 7% stronger than the far side.The force that pulls items toward the centre of a planet or other entity is called gravity. All of the planets are kept in orbit around the sun by gravity.Differential gravitational forces, or gravitational forces that are not equal across a body's finite size, are the fundamental mechanism.

Radius of the earth, r = 6.37*10^6

by solving ((Fn-Ff)/Fn)*100 answer will be of 7%

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A jury acquitted him of starting two fires in Fresno but convicted him of several fires that prosecutors claimed he started on his way home to Glendale.

Most serial arsonists only set fire to a place once. Nearly half of the samples consumed alcohol before lighting. The most common motive for arson was revenge followed by rioting vandalism profit and other crime cover-ups. Firefighters' motives for arson range from excitement and thrill to the desire to cover up a crime.

Excitement-based motivation indicates that the firefighter wanted to be seen as a hero. Gasoline is one of the most commonly used fire promoters because it is efficient, easy to ignite, and can usually be purchased and transported without question. The second most common fuels are thinner and kerosene.      

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Capacitance is the ability of an object or device to store an electric charge. It is measured by the change in charge in response to a potential difference and is expressed as a ratio of these quantities.

For charge:

Q = CV

Where Q = Charge

C = Capacitance (45 μF or 45 × 10⁻⁶ F)

V = Voltage applied (100 V)

Q = 45 × 10⁻⁶ × 100

Q = 45 × 10⁻⁴ C

For angular frequency:

ν = 1/√(LC)

ν = angular frequency

L = Inductance (45 mH or 45 × 10⁻³ H)

C = Capacitance (45 μF or 45 × 10⁻⁶ F)

ν =  1/√(45 × 10⁻³ × 45 × 10⁻⁶ )

ν =  1/4.5 × 10⁻⁵

ν =  0.22 × 10⁵ H or 22 × 10³ H

For the period of electric oscillation:

t = 1/ν

t = period of electric oscillation

ν = angular frequency (22 × 10³ H)

t = 1/22 × 10³

t = 4.5 × 10⁻⁵ sec

Now, for current:

Q = It

I = Q/t

I = current

Q = Charge (45 × 10⁻⁴ C)

t = time (4.5 × 10⁻⁵ sec)

I = 45 × 10⁻⁴ / 4.5 × 10⁻⁵

I = 1 A

If the time is 2.9 ms, then charge and current will be

Q = It

Q = 1 × 2.9 × 10⁻³

Q = 2.9 × 10⁻³ C

I = Q/t

I = 2.9 × 10⁻³/2.9 × 10⁻³

I = 1 A

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The mass of the block on the table is 2.33 kg.

The Tension in the rope is 4.9 N.

The mass of the block on the table is calculated by applying Newton's second law of motion.

Newton's second law of motion states that the force applied on an object is directly proportional to the product of mass and acceleration of the object.

F = ma

where;

F(net) = ma

m₂g - m₁g = a(m₁ + m₂)

where;

m₂g - m₁g = m₁a + m₂a

m₂g  - m₂a = m₁a  + m₁g

m₂g  - m₂a = m₁(a + g)

3.6(9.8) - 3.6(2.1) = m₁(2.1 + 9.8)

27.72 = 11.9m₁

m₁ = 27.72 / 11.9

m₁ = 2.33 kg

The tension in the rope is calculated as follows;

T = m₁a

T = 2.33 kg x 2.1 m/s²

T = 4.9 N

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The displacement covered will be 9.85 km

The distance covered will be = 10 + 4 + 1 = 15 km

using Pythagoras theorem

[tex]H^{2} = P^{2} + B^{2}[/tex]

H  = [tex]\sqrt{4^{2} + 9^{2} }[/tex]

H  = [tex]\sqrt{97}[/tex]

H   = 9.85 km

The displacement covered will be 9.85 km

The distance covered will be = 10 + 4 + 1 = 15 km

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3) unit of the following are :

a) force = Newton

b) distance = meter

c) work = Joule

4) 90 J work has been done by her

5) 51 J work was done

6) He have done  [tex]10^{4}[/tex] J  of work

7) no work is done

8) no work is done

9) 700 J is the work done on the car

10) 10.68 N  force is applied

3 ) unit of the following are :

a) force = Newton

b) distance = meter

c) work = Joule

4 ) work done = force * displacement

                       = 75 * 1.2 = 90 J

5 )  work done = force * displacement  

                        = 15 * 3.4 = 51 J

6 ) work done = force * displacement  

                        = 100 * 100 = [tex]10^{4}[/tex] J

7) no work is done because no displacement occurred

8)  no work is done because no displacement took place

9) work done = force * displacement

                        = 12.5 * 56 = 700 J

10)  force = work done / displacement

                = 142 / 13.3 = 10.68 N

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the angular speed of the bar just after the bug leaps is 0.044 ras/sec.

Given parameter:

Mass of the bug, m= 10.0g

Mass of the bar, M= 50.0 g.

Length of the bar, l = 90 cm.

Speed of the bug ,v = 20.0 cm/s.

Speed of the bar, V = ?

From conservation of momentum;

momentum of the bar = momentum of the bug

⇒ MV = mv

⇒ V = mv/M

= (10.0× 20.0)/50 cm/s.

= 4 cm/s.

Then, angular speed of the bar will be = V/l

= 4/90 rad/s.

= 0.044 rad/s.

Hence, the angular speed of the bar just after the frisky insect leaps is 0.044 rad/sec.

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The direction in which the ball a moves after the collision is east of south

What is momentum ?

Momentum, the product of a particle's mass and its velocity. Momentum is a vector quantity. It has both magnitude and direction. Isaac Newton's second law of motion states that the rate of change of momentum over time is equal to the force acting on a particle. See Newton's Laws of Motion.

From Newton's second law, if a particle is subject to a constant force over a period of time, the product of that force and the time interval (momentum) equals the change in momentum. Conversely, the momentum of a particle is a measure of the time it takes for a constant force to come to rest

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The energy needed to heat the copper from 25 °C  to 45 °C if the specific heat capacity of copper is 380 J/kg °C is 9880 J

ΔT = T - To

ΔT = Change in temperature

T = Final temperature

To = Initial temperature

T = 45 °C

To = 25 °C

ΔT = 45 - 25

ΔT = 20 °C

q = m C ΔT

q = Heat Energy

m = Mass

C = Specific heat capacity

m = 1.3 kg

C = 380 J / kg °C

q = 1.3 - 380 * 20

q = 9880 J

Therefore, the energy needed to heat the copper to 45 °C is 9880 J

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The period of Jupiter is known to be 11.9 years then the average distance of Jupiter to the Sun is given to be  5.21 AU.

Kepler's laws of planetary motion :

According to this law, the semi-major axes of the planets' orbits are directly proportional to the squares of the planets' orbital periods.

period of the Jupiter = 11.9 years

radius of the earth = 1 AU

orbital period of the earth = 1 year

According to the Kepler's 3rd law of planetary motion :

T² ∝ R³

T² = k R³

k = T²/ R³

[tex]k = \frac{T^2_j}{R^3_j} = \frac{T^2_e}{R^3_e}[/tex]

T² /(R)³ = (1)² /(1)³

Rj  =  [tex]T^{\frac{2}{3}}[/tex]

T = 5.21 AU

The period of Jupiter is known to be 11.9 years then the average distance of Jupiter to the Sun is given to be  5.21 AU.

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a) angular frequency of the motion is ω = 3.5s⁻¹

b) total mechanical energy of the bob is T.M.E = 0.029J

c) bob's speed at the lowest point is V= 0.43m/s.

A mechanical device that oscillates or sways is known as a simple pendulum. The gravitational force is primarily responsible for this motion, which takes place in a vertical plane.

Given,

Length of a simple pendulum, L = 0.80m

Mass of the bob, m = 0.31 kg

h= L- LcosΘ = L (1 - cosΘ)

a) Angular frequency, ω = 2π / T

where, T = 2π √(L/g)

ω = 2π / 2π √(g/L)

ω =√(9.8 / 0.80) s⁻¹

ω = 3.5s⁻¹

b) Total mechanical energy, T.M.E = (K.E.)ₐ + (P.E.)ₐ

As (K.E.)ₐ = 0

(P.E.)ₐ =mgh

T.M.E = 0 + mgh, where h = L (1-cosΘ)

T.M.E = ngL (1-cosΘ)

= 0.31*9.8*0.80(1-0.988)

= 0.029J

Thus, T.M.E = 0.029J

c) bob's speed at the lowest position, V

TMEb = 0.029J

(KE)b + (PE)b = 0.029J

1/2mV² + 0 = 0.029J

V =√(2*0.029/m)

V = 0.43m/s

So, the speed at the lowest point is V= 0.43m/s.

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The conductor's surface is always perpendicular to.

what is electrostatic condition?

Have you ever wondered why you experience a jolt upon contacting a doorknob? Deciphering these situations will teach you about the idea of electric charge. Two symbols, "+" and "-," can be found on batteries when they are analyzed. This is because the transmission of positive and negative charges occurs at these two ends.

The study of electric charges at rest is done by the science of electrostatics (static electricity).

The ability of some materials to collect light particles after rubbing, such as amber, has been recognised since classical times. Thus, the term "electricity" has its roots in the Greek word for amber, v (lektron). The forces that electric charges apply to one another give birth to electrostatic phenomena. Coulomb's law explains these types of forces.

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When two elements bond and form a compound, then:  A.) The neutrons remain the same in the nucleus of each atom.

There are basically two types of bonds: ionic and covalent bonds. In both the cases, electrons are involved in formation of bonds. In ionic bonds there is a complete sharing of electrons.

In covalent bonds, there is sharing of electrons. Since the neutrons reside in the nucleus of the atom along with protons contributing for the atomic mass, hence during bonds formation number of neutrons remain unchanged.

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Yes, the state of a sample of water depends on location and temperature.

Pure water has no flavour, no aroma, and no colour. There are three different states of water: solid (ice), liquid, and gas (vapour). Ice is frozen water or solid water. Because the molecules of water expand as it freezes, ice is less dense than water. As ice will weigh less than the same volume of water, it will float in the liquid. At 32° Fahrenheit, or 0° Celsius, water freezes. Water that is liquid is moist and fluid. This is the type of water that we are most accustomed to. We use liquid water in a variety of ways, such as drinking and washing.

The air all around us is constantly filled with the vapour of water. It is not visible. When water is boiled, it transforms from a liquid to a gas or water. At ambient temperature, water is a liquid; however, when cold, it solidifies to form ice. If heated, the same water transforms into a gas known as water vapour. Only when the substance reaches a specific temperature do the modifications take place. Ice formation occurs at 32°F (0°C). It requires more energy to raise and lower the temperature of water because a large body of water has a higher heat capacity than land. As a result, cities near water typically have a more limited range of temperatures throughout the year.

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10 kg sack of bread flour is given a horizontal force (2 N) and move about 35 cm distance.

Kinetic energy is formed and the speed is changed. The value of kinetic energy and the speed after pushed is calculated as follows :

Change the unit of distance (s = 35 cm = 0,35 m)

• Work = Δ EK

F × s = EK (after pushed) – EK (before pushed)

2 × 0,35 = EK (after pushed) – 0

0,7 Joule = EK (after pushed)

*EK before pushed is zero because the sack does not move*

• Speed after pushed

EK (After pushed) = ½ × m × v²

0,7 = ½ × 10 × v²

0,7 = 5 × v²

v² = 0,7/5 = 0,14

v (after pushed) = 0,37 m/s

So, kinetic energy after pushed is 0,7 joule and the speed is changed to 0,37 m/s.

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As the temperature across the lamp increases, the

resistance of the lamp increases.

This is because the temperature is proportional to resistance.

The current through a diode flows in one direction only.

The resistance is flowing in the reverse direction.

Resistance is described as a measure of the opposition to current flow in an electrical circuit. Resistance is known to be measured in ohms, symbolized by the Greek letter omega (Ω) which is named after Georg Simon Ohm (1784-1854), a German physicist who studied the relationship between voltage, current and resistance.

The relationship between temperature and resistance is that the resistance increases as the temperature increases in conductors and decreases with the increasing temperature in insulators.

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Answer:

Work performed=57.14 NM

Power= 22.86 J/s

Explanation:

Work done= Force/distance

W=F/d

we don't have the force but weight and force is the same thing so to find weight we have to use the formula

Weight= mass × gravitational field strength

W=mg

W= 10.0×10. (please remember that g has a constant value of 10)

W=100 N

Therefore the force is 100 N

Going back to the original equation

W= 100/1.75

W= 57.14 NM

Power=Work done/time

P= W/t

P= 57.14/2.5

P= 22.86 J/s

With the use of a magnetometer, the magnetism or magnetic field of the human body can be measured or demonstrated.

A magnetometer is a device used to measure the magnetic field or the magnetic dipole moment. Magnetometers of various sorts measure the direction, intensity, or relative change of a magnetic field at a specific area.

A magnetometer is a scientific tool that measures the intensity of magnetic fields. Magnetometers may be used on land to locate iron ore reserves for mining.

Magnetometers are instruments that can detect the amount or direction of a magnetic field. They may be found practically anywhere in electronics. They might be as basic as the one used by your smartphone to identify whether it is upright or as complicated as the one used by NASA to assess Mars' magnetic field.

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The mass of the other object is 18.11 kg and their acceleration  will be respectively 5.8 × 10⁻⁸ m/s² and 17.66× 10⁻⁸ m/s².

Given parameter:

The gravitational force between two objects : F = 3.2×10⁻⁶ N.

Distance between two objects : r =  2.1x10⁻¹ m.

The mass of one object m₁ = 55 kg.

The mass of other object m₂ =?

From universal gravitational law, we know that, force acting between two objects of mass m₁ and m₂ separated by a distance r is:

F = G m₁ m₂ / r²

Where, G = universal gravitational constant = 6.67 × 10⁻¹¹ N m⁻² kg⁻².

So, we can write,

 3.2×10⁻⁶ N = (6.67 × 10⁻¹¹ N m⁻² kg⁻²) (55 kg) m₂/( 2.1x10⁻¹ m)

⇒ m₂ = (3.2×10⁻⁶ N ×  2.1x10⁻¹ m )/ { (6.67 × 10⁻¹¹ N m⁻² kg⁻²) (55 kg)}

= 18.11 kg.

Hence, the mass of the other object is 18.11 kg.

So, acceleration of the object of mass 55 kg is:

a₁ = F/m₁ = 3.2×10⁻⁶/55  m/s² = 5.8 × 10⁻⁸ m/s².

The acceleration of the object of mass 18.11 kg is:

a₂ = F/m₂ = 3.2×10⁻⁶/18.11 m/s² =  17.66× 10⁻⁸ m/s².

Hence, their acceleration if they are released from their position will be respectively 5.8 × 10⁻⁸ m/s² and 17.66× 10⁻⁸ m/s².

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