A bowling ball weighing 71.2 N is swinging like a pendulum at the end of a 3.8 m rope.
As the ball swings through its lowest point, its speed is measured at 4.2 m/s. What is
the magnitude and direction of the acceleration of the ball at this point?
A. 4.64 m/s, upward
B. 4.64 m/s, downward
C. 5.16 m/s, upward
D. 5.46 m/s, downward

Answer:

a) 0.60 kg cart has final velocity 3.0 m/s [E]

0.80 kg cart has final velocity 4.0 m/s [W]

b) 0.12 m

Explanation:

Take east to be positive.

a) Momentum is conserved.

m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂

(0.60) (-5.0) + (0.80) (2.0) = (0.60) v₁ + (0.80) v₂

-1.4 = 0.6 v₁ + 0.8 v₂

Kinetic energy is conserved in elastic collisions.

½ m₁u₁² + ½ m₂u₂² = ½ m₁v₁² + ½ m₂v₂²

m₁u₁² + m₂u₂² = m₁v₁² + m₂v₂²

(0.60) (-5.0)² + (0.80) (2.0)² = (0.60) v₁² + (0.80) v₂²

18.2 = 0.6 v₁² + 0.8 v₂²

Solve the system of equations.

-1.4 = 0.6 v₁ + 0.8 v₂

-1.4 − 0.6 v₁ = 0.8 v₂

-1.75 − 0.75 v₁ = v₂

18.2 = 0.6 v₁² + 0.8 (-1.75 − 0.75 v₁)²

18.2 = 0.6 v₁² + 0.8 (3.0625 +2.625 v₁ + 0.5625 v₁²)

182 = 6 v₁² + 8 (3.0625 + 2.625 v₁ + 0.5625 v₁²)

182 = 6 v₁² + 24.5 + 21 v₁ + 4.5 v₁²

0 = 10.5 v₁² + 21 v₁ − 157.5

0 = v₁² + 2 v₁ − 15

0 = (v₁ − 3) (v₁ + 5)

v₁ = 3 or -5

Since u₁ = -5.0 m/s, v₁ must be 3.0 m/s.

Solving for v₂:

v₂ = -0.75 v₁ − 1.75

v₂ = -4.0 m/s

b) The compression of the spring is a maximum when the carts have the same velocity.

Momentum is conserved.

m₁u₁ + m₂u₂ = (m₁ + m₂) v

(0.60) (-5.0) + (0.80) (2.0) = (0.60 + 0.80) v

-1.4 = 1.4 v

v = -1.0

Energy is conserved.

½ m₁u₁² + ½ m₂u₂² = ½ (m₁ + m₂) v² + ½ kx²

m₁u₁² + m₂u₂² = (m₁ + m₂) v² + kx²

(0.60) (-5.0)² + (0.80) (2.0)² = (0.60 + 0.80) (-1.0)² + (1200) x²

18.2 = 1.4 + 1200 x²

16.8 = 1200 x²

x² = 0.014

x = 0.12

Answer:

7 hours.

Explanation:

This is because you are traveling 5 kilometers per hour so 5 multiplied by 7= 35.

The refraction is the phenomena of bending of light towards or away from the normal when the light enter from one medium to another.

The light when travels from denser to rarer medium the light bends away from the normal and when the light enter from rarer to denser medium the light bends towards the normal. The common example of refraction that we see in our daily life is when the coin on the bottom of the bucket appears a little bit upwards than its actual position.

Also, the formation of a rainbow is also related to the phenomena of refraction.

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Answer:

thrust

Explanation:

Answer:

thrust

Explanation:

With a potential difference of 14 volts across it, the 10.0 ohm resistor dissipates 19.6 watts of electrical power.

Any equation connecting power to current, voltage, and resistance may be used to calculate the power wasted by each resistor.

The following formula must be used to determine the amount of electrical power a resistor dissipates in a parallel circuit:

P = V²/R

In this case, the resistance is 10.0 ohms and the potential difference is 14 volts.

These values are combined together to give us:

P = (14 V)²/ 10.0 Ω

P = 196 V²/ 10.0 Ω

P = 19.6 W

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Answer:

2nd and 4th statements.

Explanation

If voltage is constant ( k ) and I = V / R,

Then I is inversely proportional to R so if I increases R decreases and vice versa, according to that the second statement is correct not the first.

if current is constant, then v is directly proportional to R and vice versa..the 3rd statement is wrong

if resistance is constant v is directly proportional to I, then only the 4th is correct not the 5th

If something being dropped has a mass of 0.4 kg, and the height from the floor to the top is 15 m then 20J would be the change in PE.

The force acting on the two objects affects the potential energy formula. The formula for gravitational force is P.E. = mgh, where g is the acceleration caused by gravity (9.8 m/s2 at the earth's surface) and h is the height in meters.

Potential energy is a form of stored energy that is dependent on the relationship between different system components. When a spring is compressed or stretched, its potential energy increases. If a steel ball is raised above the ground as opposed to falling to the ground, it has more potential energy.

Given :        

Mass of the object  M=0.4 kg

Height up to which it is raised  h=5 m

Potential energy P.E=Mgh

g = 10 m/s^2

P.E= 0.4×10×5=20J

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20J would be the change in PE for a drop with a mass of 0.4 kg and a height of 15 m from the ground to the top.

The potential energy formula is impacted by the force operating on the two objects.

P.E. = mgh, where g is the acceleration brought on by gravity, h is the height in metres, is the formula for gravitational force.

Potential energy is a type of stored energy that depends on how various system elements interact with one another. A spring's potential energy rises when it is crushed or stretched. A steel ball has higher potential energy if it is lifted above the ground as opposed to falling to the ground.

Given:

M=0.4 kg, the object's mass

It is raised to a height of h=5 m.

Powerful potential P.E=Mgh

g = 10 m/s^2

P.E= 0.4×10×5=20J.

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An electromagnetic wave with a wavelength about the same as the diameter of an apple, which is approximately 10 centimeters, would be a radio wave.

Radio waves are part of the electromagnetic spectrum, which includes a wide range of wavelengths and frequencies. The spectrum is divided into different categories, such as radio waves, microwaves, infrared, visible light, ultraviolet, X-rays, and gamma rays. Radio waves have the longest wavelengths and lowest frequencies among the categories of the electromagnetic spectrum. They are used for various purposes, such as communication, broadcasting, and navigation.

Radio waves with a wavelength of about 10 centimeters fall into the Ultra High Frequency (UHF) band, which ranges from 300 MHz to 3 GHz. UHF radio waves are utilized in television broadcasting, cell phone communication, and satellite systems. In summary, an electromagnetic wave with a wavelength comparable to the diameter of an apple would be classified as a radio wave, specifically within the UHF band. This type of radio wave is commonly used in modern communication and broadcasting technologies.

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Answer:

yes

Explanation:

When all of the molecules (or atoms) in a system stop moving completely, that's as cold as they can get

Answer:

2,500 watts

Explanation:

I got this answer right on a test. I hope it works for you to.

Answer:

2500 wats

Explanation:

When an airplane travels 640 miles from Topeka to Houston in 3. 2 hours, going against the wind. The return trip is with the wind and takes only 2 hours. Then the rate of the airplane with no wind is 260 miles/hr, and the rate of the wind is 100 miles/hr

Let Va is the velocity of the airplane

Va is the velocity of the wind

When flying against the wind then

(Va+Vw)*(3.2 hours) = 640

3.2Va + 3.2Vw = 640

3.2Vw = 640 - 3.2Va

Vw = 200 - Va----------------(1)

When flying with the wind:

(Va-V)*(2 hours) = 640km

2Va - 2Vw = 640

Va - Vw = 320 ----------------(2)

Putting the value of VW in equation (2) we get

Va - (200-Va) = 320

2Va = 320 +200

2Va = 520

Va = 260

Putting this value in equation (2)

Vw =Va - 360

Vw = 100

Therefore the rate of the airplane with no wind is 260 miles/hr, and the rate of the wind is 100 miles/hr

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Answer: the father of the nuclear physics is Ernest Rutherford

Explanation:

The average speed of gas molecules will increase by a factor of approximately 1.53 when the temperature is increased from 30°C to 160°C.

To determine the factor by which the average speed of gas molecules will increase, we can use the formula for the root-mean-square speed of gas molecules:
v_rms = √(3RT/M), where R is the gas constant, T is the temperature in Kelvin, and M is the molar mass of the gas.
First, we need to convert the temperatures to Kelvin:
30°C + 273.15 = 303.15 K
160°C + 273.15 = 433.15 K
We can now compare the ratios of the square roots of the temperatures:
Factor = √(T2/T1) = √(433.15/303.15) ≈ 1.53

When the temperature of a gas is increased from 30°C to 160°C, the average speed of its molecules will increase by a factor of approximately 1.53.

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Since the distance between them is 2.7 meters, the boat will also move a distance of 2.7 meters for Juliet to meet Romeo.

Displacement is the distance travelled in a specific direction. It is a vector quantity.

Given that Romeo (77kg) sings to Juliet (55kg) in the rear of a rowboat and he is 2.7 m away from Juliet. If after the song, Juliet carefully moves to the rear of the boat (away from the shore) to kiss Romeo which is 2.7 meters away, the distance covered by the 80 kg boat will also be equal to 2.7 m.

Since the distance between them is 2.7 meters, the boat will also move a distance of 2.7 meters for Juliet to meet Romeo.

Therefore, the answer will be 2.7 m

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646 N  is the strength of the gravitational force on the satellite

F=GmM/r²

satellite mass= 718 kg

mass of triton=1.35x10*23 kg

r= 352500m

F=GmM/r²

F=6.67×10^-11×718 kg×1.35x10*23 kg ÷(352500m)²

F=646 N

The gravitational subject has course, much as other electromagnetic fields just like the electric powered and magnetic fields. it's far a vector subject as a end result. The gravitational discipline power, which has the unit Newtons consistent with kilogram, is used to degree the gravitational discipline. This area force has a endless range and is constantly attracting.

The electromagnetic area, or the electrical and magnetic fields for charged debris and magnets, is comparable to the gravitational discipline. due to the fact electromagnetic discipline forces are stronger than gravitational field forces, they take priority over them.

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There are different types of square guides that can be used, including T-square guides and miter guides.

When using a portable circular saw, it is recommended to use a square guide. A square guide can be used to ensure that the cut is straight and accurate, which is important when working with wood or other materials. A square guide is a tool that is used to guide the saw blade in a straight line, and it can be used to make cuts at a variety of angles.

There are different types of square guides that can be used with a portable circular saw. One type is a T-square guide, which consists of a long, straight edge that is attached to a T-shaped handle. The handle is used to guide the saw blade along the edge of the material being cut, ensuring that the cut is straight and accurate.

Another type of square guide is a miter guide, which is used to make cuts at a specific angle. A miter guide consists of a piece of metal or plastic that is attached to the saw and can be adjusted to the desired angle. This type of guide is useful when making cuts for frames, molding, or other angled cuts.

In conclusion, a square guide is an essential tool when using a portable circular saw. It helps to ensure that the cut is straight and accurate, which is important when working with wood or other materials. There are different types of square guides that can be used, including T-square guides and miter guides.

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Answer:

10 seconds

Explanation:

because the cat is moving one m/s slower than the dog, the dog has a relative speed of 1 m/s. 10 meters would take 10 seconds for the dog to cover

According to given information, the potential energy of the box is 439.04 kg m²/s². The potential energy of an object is given by the formula PE = mgh

The potential energy of an object is given by the formula PE = mgh, where PE represents potential energy, m represents mass, g represents the acceleration due to gravity, and h represents the height.

In this case, the mass of the box is 14 kg and the height of the shelf is 3.2 meters. The acceleration due to gravity is approximately 9.8 m/s².

To find the potential energy of the box, we can substitute the given values into the formula:

PE = (14 kg)(9.8 m/s²)(3.2 m)

Multiplying these values together, we find:

PE = 439.04 kg x m²/s²

Simplifying, we can conclude that the potential energy of the box is 439.04 kg x m²/s².

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Answer:

A) R = 190.42 Ω

B) P = 5.325 W

Explanation:

We are given;

Total power;P_tot = 7.1 W

Voltage;V = 26 V

A)We are told that while the battery is still connected, one of the resistors is heated, so that its resistance doubles.

Thus, the power is doubled.

Now, formula for power is;

P = IV

Thus, since power is doubled, we have;

P = 2(IV)

Now, formula for current is; I = V/R

So, P = 2V²/R

Making R the subject, we have;

R = 2V²/P

In this question, P is p_total = 7.1 W

Thus;

R = (2 × 26²)/7.1

R = 190.42 Ω

B) Now, the resistance of the resistors are R and 2R.

Formula for power in this context is;

P = V²/R

Thus,

Total power delivered to the resistors is;

P = V²/R + V²/2R

P = 3V²/2R

P = (3 × 26²)/(2 × 190.42)

P = 5.325 W

The statement "Both qualitative and quantitative data should be used in decision making" is True.

Qualitative data refers to the data that can’t be measured or counted with the help of numbers, such as interviews, observations, and open-ended survey responses.

Quantitative data refers to the data that can be measured and expressed with the help of numerical values, such as market research, statistical analysis, and financial reports.

Qualitative data can add depth and insight into the reasoning behind a particular situation, while quantitative data can provide concrete evidence and numerical information. Both qualitative and quantitative data play a critical role in decision-making, and both types of data should be used in the decision-making process to make informed and well-rounded decisions.

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Answer:

Approx 50 atm

Explanation:

See graph below:

Answer:

12.267 seconds approximately.

Explanation:

The units can be simplified into m/s, in which case you would have 61000/3600. Simplify that to 16 and 17/18. This is your meters per second, so multiply that by .724 to get the answer.

The speed of a wave is its wavelength multiplied by its frequency.

Wave speed and wavelength are related by the wave speed equation (Speed = Wavelength x Frequency). The wave speed can be determined using this equation if the wavelength and frequency are known.

The quantity of waves that move in a wave's frequency is measured in waves per second.

A periodic wave's wavelength is its spatial period or the length over which its shape repeats.  It is a property of both traveling waves and standing waves as well as other spatial wave patterns.

It is the distance between two successive corresponding locations of the same phase on the wave, such as two nearby crests, troughs, or zero crossings.

Therefore, The speed of a wave is its wavelength multiplied by its frequency.

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Stopping distance of the car, as measured from the point where the driver first sees the red light, is 43.95 meters We can use distance-time formula.

To calculate the stopping distance of the car, we need to determine the distance traveled during the driver's reaction time and the distance traveled while the car is decelerating.

During the driver's reaction time, the car will continue to move forward at its initial speed of 15.5 m/s. The distance traveled during this time is:

\(d_reaction = v_initial * t_reaction = 15.5 m/s * 0.321 s = 4.98 m\)

After the driver reacts, the car begins to decelerate at a rate of \(6.2 m/s^2\). Use equation:

d =\(v_initial * t + (1/2) * a * t^2\)

where d: distance traveled, v_initial: initial velocity, t: time, a: acceleration, and final velocity = 0 (since car stops).

We need to find the distance traveled during the deceleration period, so we can rearrange the equation to solve for d:

d = \((v_initial^2) / (2a)\)

Put values:

\(d_deceleration = (15.5 m/s)^2 / (2 * -6.2 m/s^2) = 38.97 m\)

Note that we used a negative value for acceleration, since the car is decelerating (slowing down) rather than accelerating (speeding up).

The total stopping distance is the sum of the distance traveled during the driver's reaction time and the distance traveled while decelerating:

\(d_total = d_reaction + d_deceleration = 4.98 m + 38.97 m = 43.95 m\)

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One cycle corresponds to a complete revolution of 360 degrees or 2π radians.

The number of cycles a wheel completes in 1 minute, we need to understand the relationship between angular velocity and cycles. Angular velocity is measured in radians per second, while cycles are typically measured in revolutions per minute (rpm).

One cycle corresponds to a complete revolution of 360 degrees or 2π radians. In this case, the angular velocity is π/3 radians per second. To convert this to cycles per minute, we need to calculate how many cycles are completed in one second and then multiply by 60 to get the cycles per minute.

Since one cycle is equal to 2π radians, the number of cycles per second can be found by dividing the angular velocity (π/3 radians/second) by 2π radians/cycle, which simplifies to 1/6 cycles/second.

To find the number of cycles in one minute, we multiply the cycles per second (1/6 cycles/second) by 60 seconds/minute, which gives us a total of 10 cycles in one minute.

The wheel will complete 10 cycles in 1 minute.

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Answer:

-6500N

Explanation:

F = ma

Note:  1N = 1 kg⋅m⋅s−2

a = (0-6.5m/s)/3s

a = -6.5m/s^2

F = 1000kg(-6.5m/s^2)

F = -6500kgm/s^2

F = -6500 N

In problem #1, the temperature of a bolt cooling in a room is given by the differential equation T'' = -10/10(T - 23), with an initial condition T(0) = 30. Part (a) asks to use Euler's method with a step size of h = 0.5 to approximate the value of T(3). Part (b) asks to repeat the approximation with a step size of h = 0.2. Problem #2 involves solving the initial value problem analytically.

(a) To approximate T(3) using Euler's method with h = 0.5, we start with the initial condition T(0) = 30 and iteratively calculate the values of T using the formula T(n+1) = T(n) + h * T'(n), where T'(n) is the derivative of T at time n. By performing the calculations for n = 0, 1, 2, and 3, we obtain an approximation for T(3).

(b) Similar to part (a), we use Euler's method with h = 0.2 to approximate T(3). We repeat the iterative process and calculate T(n+1) using the formula T(n+1) = T(n) + h * T'(n) for n = 0, 0.2, 0.4, ..., 3.

Problem #2 asks to solve the initial value problem analytically. This involves finding the general solution to the given differential equation T'' = -10/10(T - 23) and applying the initial condition T(0) = 30. The solution will be a function of t, denoted as T(t), without including T'' in the answer. The exact solution will provide a more precise result compared to the approximations obtained using Euler's method.

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Answer:

v =2.02

Explanation:

v^2=0.05-4.9

v^2=-4.85

square root both side

v=2.02

^^^^this is a not a perfect square