Time to reach target / s---> B4.1, Distance fallen / m,----> B4.2,
What is the connection between time and acceleration?The magnitude of the velocity change increases with lengthier acceleration. When acceleration is constant, the change in velocity is directly proportional to time. If velocity grows by a particular amount during a specific period of time, it ought to do so by an equal amount over an equal period of time.
What is the distance-time formula for acceleration?The equation a = v/t denotes acceleration (a), which is the change in velocity (v) over the change in time (t). This enables you to calculate the change in velocity in meters per second squared (m/s2).
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Could someone help me with this
Assuming a flat ground, and football thrown or dropped from the same height, the horizontally-thrown ball will hit the ground with the same vertical velocity as the dropped ball, but it will have most of its initial horizontal velocity, too. A simple vector addition, guarantees that that the horizontally-thrown ball will have a larger total velocity than the dropped ball.
What is Velocity.
Velocity is the directional velocity of a moving object as an indicator of the rate of change of position observed from a particular frame of reference and measured at a particular time standard.
Therefore, A simple vector addition, guarantees that that the horizontally-thrown ball will have a larger total velocity than the dropped ball.
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A certain quantity of a liquid has a volume of 10cm at 20°C. Calculate its volume at 50°C, if it’s cubic expansivity is 10^(-3) K^(-1)
Answer:
10.3 cm³
Explanation:
From the question given above, the following data were obtained:
Original volume (V₁) = 10 cm³
Initial temperature (θ₁) = 20 °C
Final temperature (θ₂) = 50 °C
Cubic expansivity (γ) = 10¯³ K¯¹
Final volume (V₂) =?
γ = V₂ – V₁ / V₁(θ₂ – θ₁)
10¯³ = V₂ – 10 / 10( 50 – 20)
10¯³ = V₂ – 10 / 10(30)
10¯³ = V₂ – 10 / 300
Cross multiply
10¯³ × 300 = V₂ – 10
0.3 = V₂ – 10
Collect like terms
0.3 + 10 = V₂
10.3 = V₂
V₂ = 10.3 cm³
Thus, the volume at 50 °C is 10.3 cm³
to explain the physical arrangement of place, an object, or an event, a speaker should be which pattern of arrangement?
a. topical
b. problem-solution
c. spatial
d. causal
A speaker should employ the spatial pattern of organisation to describe the physical arrangement of a location, an item, or an event.
Physical arrangement describes how things are laid out or organised spatially in the physical world. It can be used to describe the placement, tilt, and connections of various elements inside a given space. In a variety of professions, including architecture, urban planning, and interior design, it is crucial to comprehend how things are physically set up. A biological organism's physical structure or the arrangement of the planets in the solar system are two examples of how it might be useful in understanding or interpreting natural occurrences. In public speaking, the spatial pattern of arrangement can be used to describe the physical arrangement of a location, an item, or an event in order to aid the audience in visualising and comprehending it.
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All matter is made up of particles called
Answer:
atoms and molecules
Explanation:
as opposed to being continuous or just including particles). On the following page, the idea is stated as one of four concepts in Dalton's theory: “All matter is composed of tiny, indivisible particles called atoms”
Answer: atoms
Matter is made of atoms, the basic building blocks. Atoms are made of protons, neutrons and electrons. The answer is atoms.
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What force is required to move a 90.0 kg object in a circle of diameter = 85.0 meters at a constant speed of 8.10 m/s?
The force required to move the 90 Kg object at a constant speed of 8.10 m/s is 138.94 N
How to determine the force required?The force required to keep an object moving in a circle is called Centripetal force. This is defined according to the following equation:
F = mv²/r
F is the centripetal forcem is the massv is the velocityr is the radiusWith the above formula, we can obtain the force required to move the 90 Kg object. Details below:
Mass of object (m) = 90 KgDiameter = 85.0 metersRadius (r) = Diameter / 2 = 85 / 2 = 42.5 metersSpeed of object (v) = 8.10 m/sForce required (F) =?F = mv²/r
F = (90 × 8.10²) / 42.5
F = (90 × 65.1) / 42.5
F = 5904.9 / 42.5
F = 138.94 N
Thus, the force required is 138.94 N
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What are si units?explain.
Answer:
Explanation:
The International System of Units (SI, abbreviated from the French Système international (d'unités)) is the modern form of the metric system. It is the only system of measurement with an official status in nearly every country in the world. It comprises a coherent system of units of measurement starting with seven base units, which are the second (the unit of time with the symbol s), metre (length, m), kilogram (mass, kg), ampere (electric current, A), kelvin (thermodynamic temperature, K), mole (amount of substance, mol), and candela (luminous intensity, cd).
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what are some features that you would expect to see in the design of a high-quality experiment?
Scientific experiments follow principles called the scientific method that ensure that accurate tests are performed, reliable results are collected, and reasonable conclusions are drawn. Scientific experiments must follow the basic principles of good research so that the final presented results can be believed to be reliable.
Observations of new physical processes or phenomena occur infrequently, but there are areas of science that are not fully understood. Scientists must verbalize their observations in order to formulate meaningful hypotheses.
It's not enough to just guess why something happens. Scientists must prove their theories to be correct. Predictions are made to test observations under different circumstances. The aim is to learn more about this phenomenon and prove its existence. One of his ways of improving the scientific method is by creating 'models'. Models can be used to infer difficult and unobservable concepts.
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23. Describe the objects or materials that
vibrated to produce three of the sounds
10 you've heard today
Answer: 1. flushing the toilet,
2. oil popping in a pan,
3. the clicking of a mouse on a computer,
Explanation: Lu-.v u
Complete the mechanism for the given decarboxylation by adding any missing atoms, bonds, charges, nonbonding electrons, and curved arrows
The decarboxylation reaction involves the removal and replacement of a carboxyl group with hydrogen.
What is a decarboxylation reaction?A decarboxylation reaction is one in which the carboxyl group in a carboxylic acid is replaced with hydrogen.
In living organisms, decarboxylation reactions are catalyzed by enzymes called decarboxylases or carboxy-lyases.
The decarboxylation of beta-carbonyl esters proceeds through a cyclic transition state giving an enol intermediate which then tautomerises to the carbonyl.
Therefore, a decarboxylation reaction involves the removal and replacement of a carboxyl group with hydrogen.
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The decarboxylation reaction is given with the removal of the carbon dioxide from the carboxyl group.
What is carboxyl group?The carboxyl group is the attachment of the OH and the =O functional group to the carbon atom.
In the decarboxylation reaction, there has been the removal of the carbon dioxide and the carboxyl group is replaces with the Hydrogen atom.
The decarboxylation reaction for the given reactant with the missing groups is given in the image attached.
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IA battery moves a charge of 60coloumbs around a circuit at a constant rate in 29seconds .Find the current in the circuit
The current in the circuit is ≈ 2.07 amperes (A)
What is current circuit?A current circuit is a closed path through which electric current can flow. It typically consists of a power source, such as a battery or generator, a load, such as a light bulb or motor, and conductive wires or other components that connect the power source and load to form a complete path for the current to flow.
The current in the circuit can be calculated using the formula:
current = charge / time
In this case, the charge moved around the circuit is 60 coulombs and the time taken is 29 seconds. Thus, the current in the circuit is:
current = 60 coulombs / 29 seconds
current ≈ 2.07 amperes (A)
Therefore, The current in the circuit is ≈ 2.07 amperes (A)
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One peice of evidence that the universe is expanding
if an object is accelerating does that mean the object is speeding up
Answer:
Yes.
Explanation:
Even though the initial and final speeds are the same, there has been a change in direction for the object. Thus, there is an acceleration. The object was moving rightward and slowed down to 0 m/s before changing directions and speeding up while traveling leftward.
A balloon-powered car rolls across the floor at a speed of 0.711 m/s. How long does it take to cover 8.25 m?
Answer:
Time = 11.60 seconds.
Explanation:
Speed can be defined as distance covered per unit time. Speed is a scalar quantity and as such it has magnitude but no direction.
Mathematically, speed is given by the equation;
\(Speed = \frac{distance}{time}\)
Given the following data;
Speed = 0.711m/s
Distance = 8.25m
To find the time;
Making time the subject of formula, we have;
\(Time = \frac{distance}{speed}\)
Substituting into the equation, we have;
\(Time = \frac{8.25}{0.711}\)
Time = 11.60 secs.
the actual underground location of an energy release that causes seismic waves is
The actual underground location of an energy release that causes seismic waves is known as the hypocenter or focus.
The hypocenter is the point within the Earth where the rupture or movement of rocks occurs, releasing energy in the form of seismic waves. It is typically located along a fault line, which is a fracture in the Earth's crust where movement has taken place.
The depth of the hypocenter can vary, ranging from shallow depths near the Earth's surface to deeper depths within the Earth's interior. Seismic waves radiate outward from the hypocenter, propagating through the Earth and eventually reaching the surface, where they are detected and recorded by seismographs.
By studying the characteristics of seismic waves, scientists can determine important information about the nature of earthquakes and the properties of the Earth's interior.
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Water at the Antarctica usually exits as ice, making it very difficult to use the water or conduct experiment requiring the water to be in liquid state. A coffee addicted physicist stationed at a research base requires about 0.8 kg of ice for his coffee on the hour. a. How much heat is required to convert 0.8 kg of ice at -35 "C into steam at 100 C7 b. Plot the temperature - energy graph for the processes in (a). 5] [5] c. The surface tension of water was determined in a laboratory by using the drop weight method. 100 drops were released from a burette the inner diameter of whose opening is 1.8 mm. The mass of the droplets was 3.78 g. 1. Determine the surface tension of the water and comparing it with the tabulated value, i. Calculate the relative error of the measurements: [6] [4]
Answer:
water or conduct experiment requiring the water to be in liquid state. A coffee
addicted physicist stationed at a research base requires about 0.8 kg of ice for
his coffee on the hour.
a. How much heat is required to convert 0.8 kg of ice at -35 °C into steam
at 100°C?
[5]
b. Plot the temperature - energy graph for the processes in (a). [5]
C. The surface tension of water was determined in a laboratory by using
the drop weight method. 100 drops were released from a burette the
inner diameter of whose opening is 1.8 mm. The mass of the droplets
was 3.78 g.
i. Determine the surface tension of the water and, comparing it
with the tabulated value,
161
ii. Calculate the relative error of the measurements.
The mass of 9 m³ of mercury is 121770 kg. Find the density of mercury in kg/m³.
The density of 9 m³ of mercury is 13530 kg/m³.
Density is a characteristic of a substance that indicates how much mass it contains in a given volume. To calculate density, the mass of the substance is divided by its volume. The formula used to calculate density is:
Density = Mass / Volume
In this problem, the given mass of mercury is 121770 kg and its volume is 9 m³. To find the density of mercury, we can use the formula above and plug in the given values:
Density = Mass / Volume
= 121770 kg / 9 m³
= 13530 kg/m³
Therefore, the density of 9 m³ mercury is 13530 kg/m³.
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A 20.0g ball is attached to a 120cm long string and moves in a horizontal circle. The string exerts a force on the ball that is equal to 0.200N.
A particle starts to move in a straight line from
a point with velocity 10 m/s and acceleration - 20 m/s²? Find the position and velocity of the
particle at (i) t = 5s, (ii) t' = 10 s.
Answer: s(5) = -200, v(5) = -90
s(10) = -900, v(10) = -190
Explanation:
Position: s(t)
Velocity: s'(t) = v(t) ⇒ \(s(t)=\int {v(t)} \, dt\)
Acceleration v'(t) = a(t) ⇒ \(v(t)=\int {a(t)} \, dt\)
We are given that acceleration a(t) = -20 and velocity v(t) = 10
\(v(t)=\int {a(t)} \, dt\\\\v(t)=\int{-20}\, dt\\\\v(t)=-20t + C \\\\v(t)=10\quad \longrightarrow \quad C=10\\\\v(t)=-20t+10\)
\(s(t)=\int {v(t)} \, dt\\\\s(t)=\int {(-20t+10)} \, dt\\\\s(t)=-10t^2+10t\\\\\)
(a) Input t = 5 into the s(t) and v(t) equations
s(5) = -10(5)² + 10(5) v(5) = -20(5) + 10
= -250 + 50 = -100 + 10
= -200 = -90
(b) Input t = 10 into the s(t) and v(t) equations
s(10) = -10(10)² + 10(10) v(10) = -20(10) + 10
= -1000 + 100 = -200 + 10
= -900 = -190
Ineed of help with the units
A. The SI unit of force is the newton, symbol N.
b. The SI unit for distance is the meter (m)
c. The SI unit of work is joule (J).
or Sometimes, newton-metre (N-m) is also used for measuring work.
What do you predict will happen when a charged foam cup is brought near an uncharged, aluminum foil-covered cup?
When a charged foam cup is brought near an uncharged, aluminum foil-covered cup, a transfer of electrons is likely to occur.
This is because the foam cup has a net charge, which will induce a charge separation in the aluminum foil of the uncharged cup. The negatively charged electrons in the foil will be repelled by the negatively charged foam cup and will move towards the opposite end of the foil.
As a result, the foil will become polarized, with one end carrying a positive charge and the other carrying a negative charge. This can lead to a flow of electrons from the negatively charged end of the foil towards the positively charged end,
resulting in a transfer of charge from the foam cup to the foil. The magnitude and direction of this charge transfer will depend on the distance between the cups and the strength of the charge on the foam cup.
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During the dilemma what are the thoughts of your mind? What are 2 alternative solutions you implemented to solve the dilemma?
During dilemma, a person may experience conflicting thoughts and emotions, uncertainty, anxiety, and stress. Two alternative solutions you implemented to solve the dilemma are the Pros and cons list and Seeking advice.
They may struggle to make a decision, as each option has its pros and cons. To solve a dilemma, one can consider alternative solutions, weigh their potential outcomes, and decide which one aligns better with their values, beliefs, and goals. Here are two examples of alternative solutions:
Pros and cons list: One way to solve a dilemma is by making a list of pros and cons for each option. This can help to clarify the potential benefits and drawbacks of each choice, which can help in making a more informed decision.
Seeking advice: Another way to solve a dilemma is to seek advice from a trusted friend, family member, or professional. Talking through the situation with someone else can help to gain a different perspective and see the situation from a new angle.
Ultimately, the solution to a dilemma will depend on the specific situation and the individual's unique circumstances. It's important to take the time to consider all options and their potential outcomes before making a decision.
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In the absence of air resistance, from what height should the diver
jump so he hits the water at a speed of 24 m/s? (Set the air resistance
slider to none. Adjust the height slider so the diver hits the water with
a speed of 24 m/s. )
The height at which the diver must jump in other to hit the water with a speed of 24 m/s is 29.4 m.
The height of the player above the ground can be calculated using the formula below.
v² = u²+2gs................. Equation 1Where:
v = final velocity of the diveru = initial velocity of the divers = height from where the diver will fallg = acceleration due to gravity.From the question,
⇒ Given:
v = 24 m/su = 0 m/sg = 9.8 m/s².⇒ Substitute these values into equation 1
24² = 0²+(2×9.8×s)⇒ Solve for s.
s = 24²/(2×9.8)s = 29.4 mHence, The height at which the diver must jump in other to hit the water with a speed of 24 m/s is 29.4 m.
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A +35 µC point charge is placed 46 cm from an identical +35 µC charge. How much work would be required to move a +0.50 µC test charge from a point midway between them to a point 12 cm closer to either of the charges?
Answer:
512.5 mJ
Explanation:
Let the two identical charges be q = +35 µC and distance between them be r₁ = 46 cm. A charge q' = +0.50 µC located mid-point between them is at r₂ = 46 cm/2 = 23 cm = 0.23 m.
The electric potential at this point due to the two charges q is thus
V = kq/r₂ + kq/r₂
= 2kq/r₂
= 2 × 9 × 10⁹ Nm²/C² × 35 × 10⁻⁶ C/0.23 m
= 630/0.23 × 10³ V
= 2739.13 × 10³ V
= 2.739 MV
When the charge q' is moved 12 cm closer to either of the two charges, its distance from each charge is now r₃ = r₂ + 12 cm = 23 cm + 12 = 35 cm = 0.35 m and r₄ = r₂ - 12 cm = 23 cm - 12 cm = 11 cm = 0.11 cm.
So, the new electric potential at this point is
V' = kq/r₃ + kq/r₄
= kq(1/r₃ + 1/r₄)
= 9 × 10⁹ Nm²/C² × 35 × 10⁻⁶ C(1/0.35 m + 1/0.11 m)
= 315 × 10³(2.857 + 9.091) V
= 315 × 10³ (11.948) V
= 3763.62 × 10³ V
= 3.764 MV
Now, the work done in moving the charge q' to the point 12 cm from either charge is
W = q'(V' - V)
= 0.5 × 10⁻⁶ C(3.764 MV - 2.739 MV)
= 0.5 × 10⁻⁶ C(1.025 × 10⁶) V
= 0.5125 J
= 512.5 mJ
Work done will be: \(512.5 \mu J\).
Given:
q = +35 µC
q' = +0.50 µC
r₁ = 46 cm
r₂ = 46 cm/2 = 23 cm = 0.23 m
The electric potential at this point due to the two charges q is thus
\(V = \frac{kq}{r_2}+\frac{kq}{r_2}\\\\ V= \frac{2kq}{r_2}\\\\V= \frac{2 * 9 * 10^9Nm^2/C^2 * 35 * 10^{-6} C}{0.23 m}\\\\V= \frac{630}{0.23*10^3}V\\\\V= 2739.13 * 10^3 V\\\\V= 2.739 \mu V\)
When the charge q' is moved 12 cm closer to either of the two charges, its distance from each charge is now;
r₃ = r₂ + 12 cm = 23 cm + 12 = 35 cm = 0.35 m and
r₄ = r₂ - 12 cm = 23 cm - 12 cm = 11 cm = 0.11 cm.
Thus, the new electric potential at this point is
\(V' = \frac{kq}{r_3} + \frac{kq}{r_4}\\\\V= kq(\frac{1}{r_3}+\frac{1}{r_4})\\\\V= 9 * 10^9 Nm^2/C^2 * 35 * 10^{-6} C (\frac{1}{0.35m}+\frac{1}{0.11m})\\\\V= 315 * 10^3(2.857 + 9.091) V\\\\V= 315 * 10^3 (11.948) V\\\\V= 3763.62 * 10^3 V\\\\V= 3.764 \mu V\)
Now, the work done in moving the charge q' to the point 12 cm from either charge is:
\(W = q'(V' - V)\\\\W= 0.5 * 10^{-6} C(3.764 MV - 2.739 MV)\\\\W= 0.5 *10^{-6} C(1.025 * 10^6) V\\\\W= 0.5125 J\\\\W= 512.5 \mu J\)
Thus, the work done will be: \(512.5 \mu J\).
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A sales clerk at a local hardware store sells you a hammer with a mechanical advantage of 10 when used to pry up nails. You are able to create a force of 60 N. Using the hammer, what would be the maximum force that could be generated to remove a nail?
Answer:
W = 600 N
Explanation:
The mechanical advantage of any machine is the ratio of the load or weight to the effort applied. Hence, the general formula for mechanical advantage is as follows:
M.A = W/P
where,
M.A =Mechanical Advantage of Hammer = 10
W = Maximum force that could be generated = ?
P = Force created by me = 60 N
Therefore,
10 = W/60 N
W = 10*60 N
W = 600 N
the apparent backward motion of a planet as seen against the background of stars is called
The apparent backward motion of a planet as seen against the background of stars is called "retrograde motion." This occurs when a planet appears to move in the opposite direction of its usual motion, due to the relative positions and motion of both the observed planet and Earth.
Retrograde motion was a major mystery to ancient astronomers. They believed that the planets were perfect spheres that moved in perfect circles. They could not explain why the planets sometimes appeared to move backwards.
The Greek astronomer Ptolemy proposed a model of the universe that could explain retrograde motion. His model was based on the idea that the Earth was at the center of the universe and that the planets, Sun, and stars all revolved around the Earth. Ptolemy's model was very successful in explaining the motion of the planets, and it was used for over 1,500 years.In the 16th century, Nicolas Copernicus proposed a new model of the universe that placed the Sun at the center. Copernicus's model could also explain retrograde motion, and it eventually replaced Ptolemy's model.
Today, we know that the planets revolve around the Sun in elliptical orbits. This means that their motion is not always in the same direction. When a planet is on the opposite side of the Sun from the Earth, it appears to move backwards in the sky. This is what causes retrograde motion.
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A 600 nm laser illuminates a double-slit apparatus with a slit separation distance of 3.55 μm. The viewing screen is 1.50 meters behind the double slits. What is the distance, in cm, between the 2nd and 3rd dark fringes?
The distance between the 2nd and 3rd dark fringes will be 0.09 cm.
In a double-slit interference pattern, the distance between the dark fringes can be determined using the following formula:
Y = (λ × L) / d
where:
Y is the distance between the dark fringes,
λ is the wavelength of the light,
L is the distance from the double slits to the viewing screen (also known as the slit-to-screen distance), and
d is the slit separation distance.
Given:
λ = 600 nm = 600 × 10⁻⁹m (since 1 nm = 10⁻⁹ m)
L = 1.50 m
d = 3.55 μm = 3.55 × 10⁻⁶ m (since 1 μm = 10⁻⁶m)
Plugging these values into the formula, we get:
Y = (600 × 10⁻⁹ m) ×(1.50 m) / (3.55 × 10⁻⁶m)
Simplifying, we get:
Y = 0.0009 m
To convert this to centimeters, we multiply by 100 (since 1 m = 100 cm):
Y = 0.0009 m× 100 cm/m = 0.09 cm
So, the distance between the 2nd and 3rd dark fringes is 0.09 cm.
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average method and it reports the tollowing unit data tor the rorming department. Units completed in the torming department are transferred to the painting department. Production cost information for the forming department follows. . Calculate the equivalent units of production for both direct materials and conversion for the Forming department. o. Calculate the costs per equivalent unit of production for both direct materials and conversion for the Forming department c. Using the weighted average method, assign costs to the forming department's output-specifically, its units transferred to painting and its endina work in brocess inventorv. Calculate the costs per equivalent unit of production for both direct materials and conversion for the For Jsing the weighted average method, assign costs to the forming department's output-specifically, its 4 d its ending work in process inventory. Complete this question by entering your answers in the tabs below. Calculate the equivalent units of production for both direct materials and conversion for the forming department. a. Calculate the equivalent units of production for both direct materials and conversion for the Forming departm b. Calculate the costs per equivalent unit of production for both direct materials and conversion for the Forming c. Using the weighted average method, assign costs to the forming department's output-specifically, its units tra and its ending work in process inventory. Complete this question by entering your answers in the tabs below. Calculate the costs per equivalent unit of production for both direct materials and conversion for the forming department Required information Using the weighted average method, assign costs to the forming department's output-specifically, its units trar painting and its ending work in process inventory.
Given information: The average method reports the following unit data for the forming department. Units completed in the forming department are transferred to the painting department. Production cost information for the forming department follows.
Direct materials:
Units completed during the period = 45,000 units
Ending work in process inventory = 5,000 units
Direct materials cost = $202,500
Conversion costs:
Units completed during the period = 45,000 units
Ending work in process inventory = 5,000 units
Conversion cost = $189,000
a. Calculation of equivalent units of production for both direct materials and conversion for the forming department:
Equivalent units of production = Units completed during the period + (Ending work in process inventory * Degree of completion)
Direct materials:
Equivalent units of production = 45,000 + (5,000 * 50%) = 47,500 units
Conversion costs:
Equivalent units of production = 45,000 + (5,000 * 60%) = 48,000 units
b. Calculation of the cost per equivalent unit of production for both direct materials and conversion for the forming department:
Cost per equivalent unit of production = Total cost for the period / Equivalent units of production
Direct materials:
Cost per equivalent unit of production = $202,500 / 47,500 units = $4.26 per unit
Conversion costs:
Cost per equivalent unit of production = $189,000 / 48,000 units = $3.94 per unit
c. Calculation of the cost assigned to the forming department's output using the weighted average method:
Total cost = Cost of units transferred out + Cost of ending work in process inventory
Cost of units transferred out = Number of units transferred out * Cost per equivalent unit of production
Cost of ending work in process inventory = Number of units in ending work in process inventory * Cost per equivalent unit of production
Direct materials:
Cost of units transferred out = 40,000 * $4.26 per unit = $170,400
Cost of ending work in process inventory = 5,000 * $4.26 per unit = $21,300
Total cost = $170,400 + $21,300 = $191,700
Conversion costs:
Cost of units transferred out = 40,000 * $3.94 per unit = $157,600
Cost of ending work in process inventory = 5,000 * $3.94 per unit = $19,700
Total cost = $157,600 + $19,700 = $177,300
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A point charge q1=5. 00μC is held fixed in space. From a horizontal distance of 8. 00 cm, a small sphere with mass 4. 00×10−3kg and charge q2=+2. 00μC is fired toward the fixed charge with an initial speed of 35. 0 m/s. Gravity can be neglected.
What is the acceleration of the sphere at the instant when its speed is 27. 0 m/s
According to the given statement , the acceleration of the sphere at the instant when its speed is 27.0 m/s.
We can use the principles of electrostatics and kinematics. a = [(9.00 x 10⁹ N * m² / C²) * |5.00 μC * 2.00 μC| / (0.08 m)²] / (4.00 x 10⁻³ kg).
1. Determine the electric force between the two charges:
- The electric force between two charges can be calculated using Coulomb's Law:
F = k * |q1 * q2| / r².
- In this case, q1 = 5.00 μC and q2 = +2.00 μC. The distance between them, r, is the horizontal distance of 8.00 cm (which is 0.08 m).
- The constant k is 9.00 x 10⁹ N * m^2 / C².
- Plugging in the values, we get F = (9.00 x 10^9 N * m² / C²) * |5.00 μC * 2.00 μC| / (0.08 m)².
2. Calculate the net force acting on the sphere:
- At any instant, the net force acting on the sphere is the sum of the electric force and the force due to gravity.
- However, in this case, gravity can be neglected, as stated in the question.
- Therefore, the net force acting on the sphere is equal to the electric force between the two charges.
3. Calculate the mass of the sphere:
- The mass of the sphere is given as 4.00 x 10⁻³ kg.
4. Apply Newton's second law:
- Newton's second law states that the net force acting on an object is equal to the product of its mass and acceleration: Fnet = m * a.
- In this case, the net force acting on the sphere is the electric force between the charges.
- Plugging in the values, we get (9.00 x 10⁹ N * m^2 / C²) * |5.00 μC * 2.00 μC| / (0.08 m)² = (4.00 x 10⁻³ kg) * a.
5. Solve for the acceleration:
- Rearranging the equation, we have a = [(9.00 x 10⁹ N * m² / C²) * |5.00 μC * 2.00 μC| / (0.08 m)²] / (4.00 x 10⁻³ kg).
- Evaluating the expression, we find the value of acceleration.
By following these steps, you can find the acceleration of the sphere at the instant when its speed is 27.0 m/s.
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What is the resultant of the vectors shown?
Answer:
b
Explanation:
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A go cart with a mass of 60 kg is moving at a rate of 10 m/s. How much Kinetic Energy does the go cart have?
Answer:
3000 JExplanation:
The kinetic energy of an object can be found by using the formula
\(k = \frac{1}{2} m {v}^{2} \\ \)
m is the mass in kg
v is the velocity in m/s
From the question
m = 60 kg
v = 10 m/s
We have
\(k = \frac{1}{2} \times 60 \times {10}^{2} \\ = 30 \times 100 \\ = 3000\)
We have the final answer as
3000 JHope this helps you
Answer:
\(\boxed {\boxed {\sf 3000 \ J}}\)
Explanation:
Kinetic energy is the energy an object has due to motion. It is calculated using the following formula:
\(KE=\frac{1}{2} mv^2\)
The mass of the go-cart is 60 kilograms and the velocity is 10 meters per second.
m= 60 kg v= 10 m/sSubstitute the values into the formula.
\(KE= \frac{1}{2} (60 \ kg)(10 \ m/s)^2\)
Solve the exponent.
(10 m/s)² = 10 m/s * 10 m/s = 100 m²/s²\(KE = \frac{ 1}{2} (60 \ kg)(100 \ m^2/s^2)\)
Multiply the numbers together.
\(KE= 30 \ kg * 100 \ m^2/s^2\)
\(KE= 3000 \ kg*m^2/s^2\)
Convert the units. 1 kilogram meter squared per second squared is equal to 1 Joule, so our answer of 3000 kg*m²/s² equals 3000 Joules.
\(KE= 3000 \ J\)
The go-cart has 3000 Joules of kinetic energy.