A 200 g blob of clay moves with a speed of 10 m/s towards a 300 g cart that is initially at rest.

a. What is the momentum of the system before the blob of clay strikes the cart?

b. What must be the momentum of the system after they come together?

c. If the blob of clay sticks to the cart, with what speed will the clay and cart move after they come together?

Answers

Answer 1

Answer:

a. 2 kg*m/s

b. \(p_{T_{f}} = 0.5v_{f} = 2 kg*m/s\)

c. 4 m/s

Explanation:

a. The momentum of the system (\(p_{Ti}\)) before the blob of clay strikes the cart is:

\( p_{Ti} = p_{b} + p_{c} \)

Where:

\(p_{b}\) is the momentum of the blob clay

\(p_{c}\) is the momentum of the car      

\( p_{Ti} = m_{b}v_{b} + m_{c}v_{c} \)

Since the car is initially at rest, \(v_{c}\) = 0

\( p_{Ti} = 200 g*\frac{1 kg}{1000 g}*10 m/s + 0 = 2 kg*m/s \)

b. The momentum of the system after they come together:

\(p_{T_{f}} = m_{b}v_{b} + m_{c}v_{c}\)

Since they come together, \(v_{b}\) =

\(p_{T_{f}} = v_{f}(m_{b} + m_{c}) = v_{f}(0.2 kg + 0.3 kg) = 0.5v_{f}\)   (1)

Because we do not have the final speed we can not calculate the final momentum.

                   

c. We can find the speed of the clay and car by conservation of the momentum:

\( p_{i} = p_{f} \)

The initial momentum of the system was founded in part "a" (p = 2 kg*m/s), so we have:

\( 2 kg*m/s = m_{b}v_{b_{f}} + m_{c}v_{c_{f}} \)

Again, when they come together, the final speed is the same:

\( 2 kg*m/s = v_{f}(m_{b} + m_{c}) \)                

\( v_{f} = \frac{2 kg*m/s}{0.2 kg + 0.3 kg} = 4 m/s \)

Now, since we found the final speed we can calculate the momentum of the system after they come together (equation 1):        

\( p_{T} = 0.5v_{f} = 0.5 kg*4m/s = 2 kg*m/s \)

I hope it helps you!                  


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Answers

The final speed of both playdoughs which stick together after the collision is 0.5 m/s

The mass of the first playdough = 0.5 kg

The mass of the second playdough = 0.25 kg

The initial speed of the first playdough =  1.5 m/s

The initial speed of the second playdough = 2 m/s

The final speed of both playdoughs can be found using the formula,

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where m₁,m₂ is the mass of the first and second playdough respectively

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           v is the final speed of both playdough

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Answer:

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Given that the object has an excess of 2.15 x 10²⁰ protons, we can calculate the total charge by multiplying the number of protons by the charge of each proton:

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To perform this calculation, we can use scientific notation. When multiplying numbers in scientific notation, we add the exponents and multiply the coefficients:

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Now, let's simplify the multiplication:

Total charge = 3.44 x 10 C

The next charge on the object with an excess of 2.15 x 10²⁰ protons is 3.44 C (coulombs).

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A moving police car plays a sound with constant frequency fo. The police
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Choose 1 answer:
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B. fL < fR
C. fL = fR

Answers

The frequency observed by the observer on the left (fL) is higher than the frequency observed by the observer on the right (fR). Here option A is the correct answer.

The observed frequency, fL, of the sound heard by the observer on the left is higher than the observed frequency, fR, heard by the observer on the right. This phenomenon is known as the Doppler effect.

When a source of sound is moving towards an observer, the sound waves are compressed, resulting in a higher frequency. Conversely, when the source of sound is moving away from an observer, the sound waves are stretched, leading to a lower frequency.

In this case, as the police car is moving towards the observer on the left, the sound waves are compressed, causing an increase in frequency. Therefore, the observer on the left hears a higher frequency, fL. On the other hand, the observer on the right experiences the sound waves stretching due to the car moving away, resulting in a lower frequency, fR. Thus, the correct answer is A. fL > fR.

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What is hydrogens outer most energy level

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Answer:

Students should realize that each atom in a group has the same number of electrons in its outermost energy level. For instance, hydrogen, lithium, sodium, and potassium all have 1 electron on their outer energy level. Let students know that these electrons in the outermost energy level are called valence electrons.

a spring has a relaxed length of 5 cm and a stiffness of 150 n/m. how much work must you do to change its length from 7 cm to 12 cm? n·m

Answers

The amount of work you must do to change the length of the spring from 7 cm to 12 cm is 0.3375 N·m.

To find the work required to change the spring's length from 7 cm to 12 cm, we'll use the formula for work done on a spring, which is W = (1/2)k(x₂² - x₁²), where W is the work, k is the stiffness or spring constant, x₂ is the final length, and x₁ is the initial length.

In this case, the stiffness (k) is 150 N/m, the initial length (x₁) is 7 cm - 5 cm = 2 cm (0.02 m), and the final length (x₂) is 12 cm - 5 cm = 7 cm (0.07 m).

Plug these values into the formula: W = (1/2)(150)(0.07² - 0.02²) = (1/2)(150)(0.0049 - 0.0004) = 75(0.0045) = 0.3375 N·m

So, you must do 0.3375 N·m of work to change the spring's length from 7 cm to 12 cm.

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what is the voltage at the node indicated by the red dot (at the inverting input of the op-amp) in volts?

Answers

The voltage at the node indicated by the red dot (at the inverting input of the op-amp) is 0 volts.

In an ideal operational amplifier (op-amp) configuration with negative feedback, the voltage at the inverting input (red dot) is equal to the voltage at the non-inverting input. Assuming the non-inverting input is grounded (connected to a 0V reference), the voltage at the inverting input will also be 0 volts. This is known as the virtual short circuit concept, which is a fundamental property of op-amps in negative feedback configurations.


Based on the virtual short circuit concept, the voltage at the red dot (inverting input) of the op-amp is 0 volts.

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Would a bottleneck event of the plants in an area from the video at the top of this page result in the need for primary or secondary succession?

A: Primary Succession

B: Secondary Succession

subject: Environmental Science

Answers

The bottleneck event of the plants in an area results in secondary succession.

What is bottleneck event?

A bottleneck is an event that drastically reduces the population size of an organism. The bottleneck may be caused by various events, such as an environmental disaster, the hunting or habitat destruction that results in the deaths of organisms.

Secondary succession

Secondary succession is a type of ecological succession in which plants and animals recolonize a habitat after a major disturbance such as a devastating flood, wildfire, landslide, lava flow, or human activity e.g., farming or road or building construction.

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An electron is accelerated from rest to 4.0×106m/s in 9.0×10−8s.
A. What distance did the electron travel in this time interval?
B.What is its average acceleration? The direction of the unit vector ı^ is the direction of motion of the electron.

Answers

The electron traveled 17.9 meters and the average acceleration of the electron is 4.44 x 10^13 m/s^2 in the direction of the unit vector ı^, which is along the direction of motion of the electron.

What is the distance traveled and average acceleration of an electron accelerated from rest to 4.0×10^6 m/s in 9.0×10^-8 s in the direction of the unit vector ı^?

A. To find the distance traveled by the electron, we can use the equation:

d = (1/2)at^2

where:

a = acceleration of the electron

t = time interval

Initially, the electron is at rest, so its initial velocity, u=0 m/s

The final velocity of the electron is v = 4.0 x 10^6 m/s

Therefore, the acceleration of the electron can be found using the equation:

a = (v-u)/t

where:

u = initial velocity

v = final velocity

t = time interval

Substituting the given values, we get:

a = (4.0 x 10^6 m/s - 0 m/s) / (9.0 x 10^-8 s)

 = 4.44 x 10^13 m/s^2

Now, substituting this value for 'a' and the given value of 't', we get:

d = (1/2)at^2

 = (1/2)(4.44 x 10^13 m/s^2)(9.0 x 10^-8 s)^2

 = 17.9 m

Therefore, the electron traveled a distance of 17.9 meters in this time interval.

B. The average acceleration of the electron can be found using the equation:

average acceleration = change in velocity / time taken

We know that the initial velocity (u) of the electron is 0 m/s and the final velocity (v) is 4.0 x 10^6 m/s. Therefore, the change in velocity is:

change in velocity = v - u = 4.0 x 10^6 m/s - 0 m/s

                  = 4.0 x 10^6 m/s

Substituting this value and the given value of 't', we get:

average acceleration = change in velocity / time taken

                    = (4.0 x 10^6 m/s) / (9.0 x 10^-8 s)

                    = 4.44 x 10^13 m/s^2

Therefore, the average acceleration of the electron is 4.44 x 10^13 m/s^2 in the direction of the unit vector ı^ which is along the direction of motion of the electron.

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