A light, inextensible cord passes over alight, frictionless pulley with a radius of15 cm. It has a(n) 18 kg mass on the left and a(n) 2.6 kg mass on the right, both hanging freely. Initially their center of masses are a vertical distance 1.5 m apart.The acceleration of gravity is 9.8 m/s².

At what rate are the two masses accelerating when they pass each other answer in units of m/s^2

The shortest distance in which you can stop, after the breaks are applied is 80.38 m.

The shortest distance in which you can stop is calculated by applying the principle of conservation of energy and work energy principle.

K.E = ¹/₂mv²

where;

K.E is your kinetic energy

m is your mass

v is your speed

The work done by force of friction before you stop is calculated as follows;

W = Ffx

where;

W = (μmg)x

where;

W = K.E

(μmg)x = ¹/₂mv²

(μg)x = ¹/₂v²

x = (v²) / (2μg)

x = (32²) / (2 x 0.65 x 9.8)

x = 80.38 m

Thus, the shortest distance in which you can stop, after the breaks are applied is determined by applying the principle of conservation of energy.

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The complete question is below:

Your are driving at 32 m/s, what is the shortest distance in which you can stop, after the brakes are applied, without the groceries sliding off the seat? The static and kinetic coefficients of friction are, respectively, 0.65 and 0.45. Assume that the surface of the seat is horizontal.

Until 1897, atom was thought as the fundemental particle. But in 1897 J.J Thompson discovered that the atoms contains electrons. He discovered during his experiment with cathod ray tube.

Thus the correct answer is option C.

According to Newton's law of gravitation, any particle of matter in the universe attracts any other with a force varying directly as the product of their masses and inversely as the square of the distance between them. It is expressed as

F = Gm1m2/r^2

where

G = gravitational constant and its value is G = 6.673 x 10^-11 Nm^2/kg^2

m1 and m2 are the masses of the bodies

r is the distance between the bodies

From the information given,

m1 = 1

m2 = 2

r = 2

By substituting these values into the formula,

F = (6.7 x 10^-11 x 1 x 2)/2^2

F = 33.5 x 10^- 12

F = 3.35 x 10^-11

The second option is correct

There are 3 types of energy:

Kinetic energy(KE): energy of moving objects

Potential energy(PE): energy that an object has stored, position energy

Mechanical energy: The sum of both. PE+KE

ANSWER

1.61 m/s

EXPLANATION

Given:

• The distance the Slinky is stretched, d = 4 m

• The time it takes for the wave to travel the length mentioned before and back, t = 4.97 s

Find:

• The speed of the wave, v

We know that the wave takes 4.97 seconds to travel the 4 meters the Slinky was stretched and back, so it travels a total of 8 meters in that time. This means that the speed of the wave is,

Hence, the speed of the wave is 1.61 m/s.

Due to the car goes around the trajectory without sliding, then. it is necessary that centripetal force equals the friction force.

Then, we have:

Fc = Fr

where,

Fc = m(v^2/R) centripetal force

Fr = μN = μ*m*g friction force

Then, by replacing the precious expressions we obtain:

m(v^2/R) = μ*m*g

And by solving for v:

where,

μ = 1.00

g = 9.8 m/s^2

R = 70.0 m

By replacing we get:

Given data

*A construction worker pushes a wheelbarrow at a distance is d = 5.0 m

*The given horizontal force is F = 250.0 N

The formula for the work is done by the worker on the wheelbarrow is given as

Substitute the known values in the above expression as

Hence, the work done by the worker on the wheelbarrow is W = 1250 J

ANSWER

• I(toaster) = 15.08 A

• I(pan) = 11.17 A

• I(lamp) = 0.71 A

EXPLANATION

Given:

• The toaster's power, P(toaster) = 1810 W

• The frying pan's power, P(pan) = 1340 W

• The lamp's power, P(lamp) = 85 W

• The total current supported by the circuit, I = 15 A

• The voltage of the circuit, V = 120 V

Find:

• The current across each device

Power is the product of current and voltage,

We know that all three devices are connected in parallel, which means that they all have the same voltage, 120 V.

Solving the equation above for I,

So, for each device,

Hence, the current drawn by each device is:

• I(toaster) = 15.08 A

• I(pan) = 11.17 A

• I(lamp) = 0.71 A

For a sine or cosine function of the form:

the perfiod is given by:

In this case we have that:

Then we have:

Therefore, the period is 10 ms

The distance between them remain the same over time both of them are accelerating - because of gravity

What is 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.

Both of them are accelerating - because of gravity - and the one that you dropped first has been accelerating for longer - and is therefore going faster than they one that you dropped later.

Until the two objects both reach their terminal velocities - assuming the objects are identical - their speeds will eventually be the same - and from that point onwards - the distance between them won’t change

The distance between them remain the same over time both of them are accelerating - because of gravity

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If an object is following a curve, it means that it is changing direction. This change in direction will cause a change in velocity. Change in velocity causes acceleration. Since the velocity keeps changing, the acceleration is not zero. This also means that the net force is not zero. Therefore, you can safely assume:

There is a net force being applied

ANSWER:

5th option: sometimes come very close to Earth

STEP-BY-STEP EXPLANATION:

Asteroids are small rocky objects that orbit the Sun. Although asteroids orbit the Sun like planets, they are much smaller.

Therefore, of the options the only totally true option is "sometimes come very close to Earth"

So the correct answer is 5th option: sometimes come very close to Earth

To determine whether the given statement is true/false.

Explanation:

In nuclear reactors, after nuclear fission, energy is generated in the form of heat. This heat is used convert water steam.

In coal plant, burning coal produces steam.

Thus, the statement is true.

Explanation

The beat frequency is equal to the complete value of the alteration in the frequency of the two waves,it can be calculated by using the expression

so

Step 1

a)let

b) replace and calculate

so

the beat frequency is 10 HZ

Step 2

the frequency yuo will detect is the difference of the frequency, so , teh frequency beat, so

the frequency you hear will be 10 Hz

I hope this helps you

Answer: For downwind sailing, with the sail oriented perpendicular to the wind direction, the pressure increase on the upwind side is greater than the pressure decrease.

Explanation: this is all i know

Given:

The current is,

The resistance is,

To find:

The potential across the battery

Explanation:

Using Ohm's law, we can write the potential across the battery is,

Hence, the potential across the battery is 10 V.

After solving each problem to correct the number of significant figures :

(a) 76330

(b) 8199 × 10⁻³

(c) 74.81 dm.

(d) 13.8 cm

(e) 8.09 km

Equations are mathematical expressions that have two algebraic expressions on either side of an equals (=) sign. The expressions on the left and right are shown to be equal to one another, demonstrating this relationship. L.H.S. = R.H.S. (left hand side = right hand side) is a fundamental mathematical formula.

According to the question,

(a) (7.31 × 10⁴) + (3.23 × 10³)

(73100) + (3230) = 76330

(b) (8.54 × 10⁻³) – (3.41 × 10⁻⁴)

= 8199 × 10⁻³

(c) 4.35 dm × 2.34 dm × 7.35 dm

= 74.81 dm.

(d) 4.78 cm+3.218 cm+5.82 cm

= 13.8 cm

(e) 38,736 km ÷ 4784 km

= 8.09 km

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Given:

The mass of the Darin is m = 75.5 kg

The air resistance is

Required: Darin's acceleration.

Explanation:

According to Newton's second law, the downward force will be

Here, g = -9.8 m/s^2 is the acceleration due to gravity.

On substituting the values, the downward force will be

The net force will be

Final Answer: Darin's acceleration is -611.9 N

Given,

The initial velocity of the car, u=10 m/s

The final velocity of the car, v=30 m/s

The acceleration of the car, a= 4.0 m/s²

From one of the equations of the motion, we have

Where t is the time duration.

On rearranging the above equation,

On substituting the known values,

Therefore the time that the car takes to accelerate is 5 s

The force (r) on one atom as a function of r is  a/r¹³ - b/r⁷.

The electric force between charged molecules is determined by applying Coulomb's law, which states that the electric force between tow charged molecules is directly proportional to the product of their charges and inversely proportional to the square of their distance.

F = kq²/r²

where;

The electric potential energy of the atoms is given as;

U = Fr

From the given parameters;

Fr = a/r¹² − b/r⁶

F = 1/r( a/r¹² − b/r⁶)

F = a/r¹³ - b/r⁷

Thus, the force on one atom as a function of r is determined by applying Coulomb's law of electrostatic force. The force is also expressed in terms of the variables a , b , and r .

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Isothermal process: Temperature remains constant

Adiabatic process: No heat is exchanged to or from the system.

Isochoric process : Change in volume is zero.

ISobaric process : Pressure remains constant .

Answer:

If the triangle representing the 3 non-colinear forces is closed

then then (C) the body is in equilibrium:

Adding vectors  A + B + C = 0 means that the resultant of adding the three vectors A, B, and C is zero

Given:

The mass of the child and the sled is,

The child acquires a speed at the bottom of the hill is,

To find:

The height of the hill

Explanation:

The potential energy at the top of the hill will be converted to the potential energy at the bottom of the hill. So for the hill of height 'h', we can write, the potential energy as

The kinetic energy is

So,

Hence, the height of the hill is 1.84 m.

The final speed (in meters per second), given that the coefficient of friction between her skis and the snow is 0.38 is 14.65 m/s

First, we shall obtain the force. This can be obatined as follow:

F = μKN

F = 0.38 × 588

F = 223.44 N

Next, we shall obtain the acceleration of the skier. This can be obtained as follow:

a = F / m

a = 223.44 / 61

a = 3.724 m/s²

Finally, we shall determine the final velocity. This can be obtained as follow:

v² = u² + 2as

v² = 14² + (2 × 3.724 × 50)

v² = 196 + 18.62

v² = 214.62

Take the square root of both sides

v = √214.62

v = 14.65 m/s

Thus, the the final speed is 14.65 m/s

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The final speed right at the top will be 14.65 m/s and the coefficient of friction between her skis and the snow is 0.38.

The ratio between displacement to time is referred to as the velocity of the object. It is a vector quantity with SI unit meter per second (m/s).

According to the question, the given information is :

Skier's mass, m = 60 kg

The acceleration due to gravity, g = 9.8 m/s²

Initial Speed, u = 14 m/s

Distance, s = 2.5 m

Deceleration is given as, a = 3.724 m/s².

Normal reaction force (N) will be equal to mg.

N = 60 × 9.8

N = 588 N

The coefficient of kinetic friction is given as, μ = 0.38

By using the formula,

F = μKN

F = 0.38 × 588

F = 223.44 N

Now, let's calculate the acceleration of the skier :

f = ma

a = f/m

a = 223.44/60

a =  3.724 m/s².

Now, calculate the velocity,

v² = u² + 2as

v² = 14² + 2 (3.724) (50)

v² = 196 + 18.62

v² = 214.62

v = 14.65 m/s.

Hence, the final speed right at the top will be 14.65 m/s.

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ANSWER

A. 9600 kg

EXPLANATION

Given:

• The volume of the substance, V = 12m³

• The relative density of the substance, 0.8

• The density of water, 1000 kg/m³

Unknown:

• The mass of the substance, m

The relative density of a substance is defined as,

And the density of a substance is,

Let's solve the first formula for the density of the substance,

Then, solve the second formula for m,

Hence, the mass of this substance is 9600 kg

Explanation:

When the temperature is increasing, the kinetic energy change, and when the graph is horizontal (the water is changing phases), the potential energy changes.

So at A, C, and E, there is a change in kinetic energy and at B and D there is a change in potential energy.

Then, we use a specific heat capacity of 4.2 J/g°C when the water is at A, C, and E. We use latent heat of 334 J/g for melting and latent heat of 2260 J/g for evaporation.

Answer:

Therefore, the complete table is

Given:

Different kinds of forces

To find:

Identify the contact forces and non-contact forces

Explanation:

A force that acts between two surfaces in contact is a contact force, while the force that acts between the two surfaces, not in contact, is a non-contact force.

The contact forces here are:

Sitting on a chair (friction)

Skateboard slows down on a rough surface (friction)

Slamming the door (friction)

Non-contact forces:

Magnet attracting paper clips (magnetic force)

Two like charges repel each other (electrostatic force)

When A peach falls from a tree (gravitational force)

Given

Every 5 seconds

One wave travel 25m

Speed of waves

Explanation

The answer would be 5 m/s

Given:

The mass when fully loaded with passengers is m =2078.1 kg

The height is h = 107.1 m

To find the potential energy of the roller coaster.

Explanation:

The potential energy of the roller coaster is given by the formula

Here, g= 9.8 m/s^2 is the acceleration due to gravity.

Substituting the values, the potential energy of the roller coaster will be

Final Answer: The potential energy of the roller coaster is 2181132.198 N

Answer:

Angle:

α =  - 62°

Explanation:

 Given:

Nₓ = 12.6 m

Ny = - 22.2 m

_________

α -  ?

The direction of  vector:

tg α = Ny / Nₓ

tg α = ( - 22.2 ) / 12.0 ≈ - 1.85

Angle:

α = arctg ( - 1.85) ≈ - 62°

The direction of the vector is [tex]\alpha=-62^o[/tex]. Given Components: Nₓ = 12.6 m and Ny = -22.2 m. The negative sign indicates that the angle is measured clockwise from the positive x-axis.

Finding the Tangent of Angle α:

  - The tangent of an angle α can be calculated using the formula: tan(α) = opposite/adjacent. In this case, the opposite side is Ny, and the adjacent side is Nₓ. So, you have:

    tan(α) = Ny / Nₓ

    tan(α) = (-22.2) / 12.6 ≈ -1.85

Finding the Angle α:

  - To find the angle α, you need to take the arctangent (inverse tangent) of the value you calculated above. This will give you the angle whose tangent is approximately -1.85:

    α = arctan(-1.85)

    α ≈ -62°

So, based on the given vector components Nₓ and Ny, the angle α is approximately -62 degrees.

The negative sign indicates that the angle is measured clockwise from the positive x-axis.

The angle obtained is in degrees. If you need the angle in radians, you could convert it using the relationship: radians = degrees × (π / 180).

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