Given the wave described by y(x,t)=5cos[π(4x-3t)], in meters. Find the following. Giveexact answers with units.

Test tube holder

When a test tube is hot or need to be properly held to avoid the spillage of its contents, a test tube holder is the laboratory equipment that is used to grip or hold the test tube.

Therefore, the test tube holder is used for holding or gripping a test tube after it has been heated or cooled

b. insulator.

The others describe a type of transfer of energy

M = mass of the boy = 55kg

V = initial velocity of the boy = 12 m/s

m= mass of stationary skateboard = 15kg

v= velocity os stationary sketeboard= 0 m/s

V' = velocity of the boy on the skateboard after collision

Conservation of momentum:

MV + mv = (M + m) V'

Replacing:

55 kg * 12 m/s + 15 kg *0 = (55 kg+ 15 ) V'

Solve for V´'

660 = 70 V´'

660/70 = V'

V'= 9.42 m/s

ANSWER

EXPLANATION

We want to find the energy of the proton accelerated through the given potential.

To do this, apply the relationship between energy and potential:

where q = charge

V = potential

The charge of a proton is:

Therefore, we have that the energy of the proton is:

That is the answer.

The given statement 'Projections of a vector make up the components of that vector' is true. The direction of a vector

Option D

The law of conservation of charge states that the amount of charge in a system is constant

This means that as time changes, the amount of charge in a system does not change

By careful consideration of the options stated:

Each of options A to C either shows that charge is lost or gained

Only option D typifies the law of conservation of conservation of charges because charges are not lost or gained by the ballon so described.

Answer:Laboratory thermometer

Explanation:

For a convex lens to form a virtua

The true statement among the following is that the air is not affected by human movement. Hence, option C is correct.

Air relates to the atmosphere of the planet. Several gases and minute dust particles make up the air. Living organisms breathe and thrive in this pure gas. Its shape and volume are ill-defined. Considering that it is matter, it has mass and weight. Atmospheric pressure is generated by air weight. The space vacuum lacks air.

About 78% of the gas within air is nitrogen, 21% of the gas is oxygen, 0.9% of the gas is argon, 0.04% of the gas is co2, and very little other gas is present.

A typical amount of water vapor is around 1%.

Since respiration requires oxygen, animals must breathe it to survive. The lungs transfer back carbon dioxide back into the atmosphere when breathing, putting oxygen into the body.

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Conductor that carries electrons:

From the pic we can conclude that the conductor is the wire, in this case it would be A.

Load that transforms energy:

From the pic, it is the bulb which transform the electric energy into light and heat, so it would be B

Insulation that prevents electrons from flowing:

It is the cable sheath, from the pic it is C

Area of low potential energy for electrons:

It is the negative part of the battery, from the pic it is E

Area of high potential energy for electrons:

It is the positive part of the battery, it is D

Using kepler's law:

Where:

T1 = Planet's period of the first planet

T2 = Planet's period of the second planet

r1 = Average distance to Gliese of the first planet

r2 = Average distance to Gliese of the second planet

First, we need to do a conversion:

Now, solving for r2:

Answer:

62554858.93 km

Let's put the given values into the formula below and get the result;

We know the numerical value of speed. We also know the mass. We can jump straight to the conclusion.

The Kinetic Energy is 25J.

If we want to accelerate an object, we must apply force on it, after applying Force some work has to be done in which energy should be transferred to the object. The energy is known as kinetic energy. The kinetic energy always depends on the mass and the velocity. It is denoted as K and the Si unit is Joules (J).

To calculate the Kinetic Energy,

           K= 1/2 mv^2

m = mass  

v = velocity

K = kinetic energy

In solving the above equation,

K = 1/2 x2 x 5^2

K = 5x5

K = 25

The Kinetic Energy is 25J.

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Given,

The radius of the loop of the roller coaster, r=22.8 m

The forces that are acting on the roller coaster when it is at the top of the loop are the centripetal force directed upwards and the weight of the roller coaster including the passengers directed downwards.

For the passengers to stay in the seat, the centripetal force must be, at the least, equal to the weight of the passengers and the rollercoaster.

That is,

Where M is the combined mass of the rollercoaster and the passengers, v is the minimum speed of the roller coaster when it is at the top of the loop, and g is the acceleration due to gravity.

On simplifying the above equation,

On substituting the known values,

Thus the minimum speed that the roller coaster must have when it is at the top of the loop so that the passengers stay in contact with the seats is 14.95 m/s.

The net force on the canoe rowed northward with an average force of 19.1 N is 4.7 N North if the wind is blowing directly south with an average force of 14.4 N.

Net force = Force due to rowing - Force due to wind

Net force = 19.1 - 14.4

Net force = 4.7 N

The direction is towards North because the force due to rowing is greater than the force due to wind.

If two force act in opposite directions, the resultant force is the difference of these two forces and the resultant direction is the direction in which the greater force is applied.  

Therefore, the net force on the canoe is 4.7 N North

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The supplied puck is moving at a speed of v0x=+3.4m/s on an air hockey table at time t=0.

The direction of the movement of the body or the object is defined by its velocity. Most of the time, speed is a scalar quantity. In its purest form, velocity is a vector quantity. It measures how quickly a distance changes. It is the rate at which displacement is changing.

Any object traveling in a circular motion has a linear speed known as tangential velocity. On a turntable, a point in the center moves less distance in a full rotation than a point near the outside edge.

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The initial kinetic energy of the car = 312.5 kJ

The initial volume of the car, v = 25 m/s

The mass of the car, m = 1000 kg

The initial kinetic energy is given by the formula

Substitute m = 1000 kg, and v = 25 m/s into the formula

The initial kinetic energy of the car = 312.5 kJ

Given:

The mass of the ball is

The speed of the ball is

Required: calculate the kinetic energy of the baseball

Explanation: to calculate the kinetic energy of a body we will use the formula as

first, we convert velocity from mi/h into m/s.

we know that

and

then the velocity is

now plugging all the values in the above formula, we get

Thus, the kinetic energy of the baseball is

Ball A with diameter d and ball B with diameter 2d are dropped from the same height. When the two balls have the same speed, the ratio of the drag force on ball A to the drag force on ball B will be F1 : F2 = 1 : 4

When objects travel through fluids (a gas or a liquid), they will undoubtedly encounter resistive forces called drag forces.

The drag force always acts in the opposite direction to fluid flow. If the body’s motion exists in the fluid-like air, it is called aerodynamic drag.

formula to calculate drag force is = F(d) = 1/2 * C * rho*A * [tex]v^{2}[/tex]

C = drag coefficient

A = area of object

rho = density in which object is moving

v = velocity of object

A = area of the object

F1 ( drag force on ball A ) = 1/2 * C * rho * area of ball A *  [tex]v^{2}[/tex]

F2 (drag force on ball A ) = 1/2 * C * rho * area of ball B *  [tex]v^{2}[/tex]

since , both the balls have same speed and falling in same environment hence , density and speeds are the same , the only difference is in area of both the balls

F1/F2 = area of ball A / area of ball B  =  4 * pi * [tex]r1^{2}[/tex] / 4 * pi * [tex]r2^{2}[/tex]

         =  [tex]r1^{2}[/tex]  /  [tex]r2^{2}[/tex]

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

         = 1/4

F1 : F2 = 1 : 4

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If the car does not brake, its mechanical energy will be conserved along all its trajectory.

Then, the sum of the kinetic energy (K) of the car and its gravitational potential energy (U) will be the same for any two points in the trajectory:

The kinetic energy of an object with mass m and speed v is:

The gravitational potential energy of an object with mass m at a height h above a reference level, is:

Where g is the acceleration of gravity.

In the beginning, the car has a height of 10m and a speed of 10m/s. In the end, the car reaches the gas station at a height 15m and a unknown speed v.

Then, the initial speed and height are known, as well as the final height. Use the equation for the conservation of mechanical energy to isolate v_2, the unknown final speed of the car:

Replace v_1=10m/s, h_1=10m, h_2=15m and g=9.8m/s^2 to find the speed of the car as it reaches the gas station:

Therefore, the car's speed as it coasts into the gas station on the other side of the valley will be approximately 1.4 meters per second.

Given,

The kinetic energy of the car, E=2400 J

The speed of the car, v=20 m/s

Kinetic energy is the energy that is possessed by an object due to its motion.

It is given by,

Where m is the mass of the car.

On substituting the known values in the above equation,

Thus the mass of the car is 12 kg

The angle between the components x and y of a vector is given by:

once we know this we need to find in which quadrant the vector lies so we know how to calculate the correct direction.

Vector A lies in the fourth quadrant this means that we need to subtract theta to 360° in order to get the direction of the vector, then we have:

Therefore the direction of vector A is 343.61°

Vector B lies in the second quadrant, this means that we need to subtract theta (given by the first equation) to 180° in order to get the direction, then we have:

Therefore the direction of vector B is 105.26°

Let's find vector A+B:

Then we have that:

To find its magnitude we have to remember that the magnitude of any vector is given by:

Then for vector A+B we have:

Therefore the magnitude of vector A+B is 5.38 meters.

Vector A+B lies in the first quadrant, then its direction is given by the expression for theta, then we have:

Therefore the direction of vector A+B is 48.01°

The number converted to the standard notation as

Hence, the correct answer is 0.00193

The electric field charges, q₁, and q₂, which are each -6×10⁻⁶ μC, gives:

First part:

Second part:

An electric field is the field around a particle that is electrically charged and which exerts a force on charged particles within the field.

The given information are:

The electric charges, q₁ = q₂ = -6 μC

The location of the charge q₁ = y₁ = 3 cm on the y-axis

Location of the charge q₂ = y₂ = -3 cm

First part:

The required location of the point where the electric field magnitude and direction is required is x = 4 cm

The electric field formula is: [tex]\displaystyle{E = \frac{k\cdot q}{r^2}[/tex]

Where:

k = The electrostatic constant ≈ 9 × 10⁹ N·m²/C²

The distances, r, of the charges from the required point are therefore obtained using Pythagorean theorem as follows:

r = √(3² + 4²) = 5

r = 5 cm = 0.05 m

Which gives;

[tex]\displaystyle{E = \frac{9 \times 10^9\times (-6) \times 10^{-6}}{(0.05)^2} = -2.16\times 10^{7}[/tex]

Given that the magnitude of the electric field along the y-axis cancel out, the magnitude of the electric field along the x-axis is found as follows:

[tex]E_x = 2 \times -2.16\times 10^{7}\times \dfrac{4}{5} = -3.456 \times 10^7[/tex]

The magnitude of the electric field at x = 4 is -3.456 × 10⁷ N/C

Second part: The magnitude of the test charge is q₀  = 2 × 10⁻⁶ μC

The force of an electric field, F = E × q

The force experienced by the test charge is therefore:

F = -3.456 × 10⁷ × 2 × 10⁻⁶ = -69.12

The force the test charge experiences is 69.12 N acting towards the origin from the point x = 4 cm.

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The work done by a force can be calculated with the formula below:

Where W is the work in J, F is the force in N and d is the distance in meters.

Since in this case, the attempt was unsuccessful, the car didn't move, so the distance is zero.

Therefore the work is zero, and the correct option is 5 (work is zero).

Object Y has the greatest acceleration = 4m/s2

What is an acceleration ?

acceleration: the rate at which the speed and direction of a moving object vary over time. A point or object going straight ahead is accelerated when it accelerates or decelerates. Even if the speed is constant, motion on a circle accelerates because the direction is always shifting. Both effects contribute to the acceleration for all other motions.

Acceleration = (final velocity - initial velocity ) /time

For object W

Acceleration = ( 29-11)/6 = 3m/s2

For object X

Acceleration = (34-10)/12 = 2m/s2

For object Y

Acceleration = ( 40-12)/7 = 4m/s2

For object Z

Acceleration = (28-20)/8 = 1m/s2

Object Y has the greatest acceleration = 4m/s2

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First, let's convert the distance of 4 lightyears to miles:

Now, let's find the time required:

Then, we need to convert from hours to years:

Therefore it will take approximately 69727 years.

Kinetic energy = 1/2 * m * v^2

Potential energy = m*g*h

m = 15.9 kg

h= 113 m

Potential energy = 15.9 kg * 9.8 N * 113 m = 17,607.66 J

Kinetic energy right before it hits the ground

PE = KE

mgh = 1/2 m v^2

Masses cancel out

gh = 1/2v^2

9.8 N * 113m = 1/2 v^2

Solve for v

1,107.4 Nm = 1/2 v^2

1,107.4 Nm / (1/2) = v^2

2,214.8 Nm = v^2

√2,214 = v

47.06 m/s = V

Kinetic energy : 1/2 * m * v^2 = 1/2 * 15.9 * 47.06^2 = 17,606.41 J

Mechanical energy (ME) = Potential energy(PE) + kinetic energy (KE)

PE = mgh

m= mass

g= gravity

h= height

KE= 1/2 m v^2

v= speed

Point B

ME = KE + PE

PE = 0 (height = 0 )

KE = 1/2 (m) v^2

180,000 = 1/2 (m) (20)^2

m = 180,000 / (1/2 (20)^2 )

m= 900 kg

Point A.

ME = 180,000 J = PEa + KE a

PEa = m g h = 900 (9.8) (20) = 176,400J

MEa = PEa + KEa

KEa = MEa - PEa = 180,000 - 176,400 J = 3,600 J

A) mass = 900 kg

B) 176,400 J

C) 3,600 J