The relationship that would be able to describe this is that the gas does not dissolve into the water at a temperature below -5.83 units.
What is a quantitative relationship?This is the term that is used to refer to the data types that includes Numbers such as weight, cost, and measurements
What is qualitative data?The descriptive and conceptual information gathered through surveys, interviews, or observation is referred to as qualitative data.
With a slope of 0.036, the volume v varies linearly with temperature T.
Volume v grows by 0.036 units for every unit increase in temperature as a result.
The volume of the gas dissolved in water is 0.21 units when the water's temperature is zero.
The smallest volume that is feasible is 0 because the volume cannot be negative. At a certain temperature, this occurs. This is the temperature at that time. Let's refer to it as Tc.
we have
Tc = -0.21 / 0.036
= -5.83
This means that the gas does not dissolve into the water below a temperature of -5.83 units.
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Honey is a technology company that provides online coupons to its subscribers. Honey's analytics staff has developed a classification method to predict whether a customer who has been sent a coupon will apply the coupon toward a purchase. For a sample of customers, the following table lists the classification model's estimated coupon usage probability for a customer. For this particular campaign, suppose that when a customer uses a coupon, Honey receives $1 in revenue from the product sponsor. To target the customer with the coupon offer, Honey incurs a cost of $0.05. Honey will offer a customer a coupon as long as the expected profit of doing so is positive. Using the equation
Expected Profit of Coupon Offer = P(coupon used) × Profit if coupon used + (1 - P(coupon used)) × Profit if coupon not used
determine which customers should be sent the coupon.
Customer Probability of Using Coupon
1 0.44
2 0.34
3 0.24
4 0.11
5 0.06
Determine the expected profit for each customer. Round your answers to the nearest cent. Enter negative value as negative number, if any.
Customer Expected Profit
1 $
2 $
3 $
4 $
5 $
The expected profit is positive for customers (Select your answer: 2 and 3, 4 and 5, 1, 2, and 33, 4, and 5, 1, 2, 3, and 4, 1, 2, 3, and 5, 2, 3, 4, and 5, 1, 2, 3, 4, and 5) so these customers (Select your answer: should be offered or should not be offered) the coupon.
The expected profit is positive for the customers 1, 2, 3, 4, 5.
What is expected profit?This is the term that is used to refer to the gain that would be expected to be gotten based on the fact that a person has engaged in a business.
We have 1 - 0.05 = 0.95 profit if the coupon is used
-0.05 is the profit if the coupon is not used
for consumer 1
the probability = 0.44
expected profit = 0.44 x 0.95 - 0.05 x 0.56
= 0.418 - 0.028
= 0.39
for consumer 2
the probability = 0.34
expected profit = 0.34 x 0.95 - 0.05 x 0.66
= 0.323 - 0.033
= 0.29
For consumer 3
the probability = 0.24
expected profit = 0.24 x 0.95 - 0.05 x 0.76
= 0.228 - 0.038
= 0.19
For consumer 4
the probability = 0.11
expected profit = 0.11 x 0.95 - 0.05 x 0.89
= 0.1045 - 0.0445
= 0.06
For consumer 5
the probability = 0.06
expected profit = 0.06 x 0.95 - 0.05 x 0.94
= 0.057 - 0.047
= 0.01
The expected profits can be listed as:
0.390.290.190.060.01The expected profits are positive for all of 1, 2, 3, 4, and 5, hence these customers can purchase the coupon.
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A 0.056 kg sample of an unknown substance is heated to 89.6 °C in a hot water tube. It is then quickly removed and placed into an insulated jar holding 188 ml of water initially at 132.8° F. The final equilibrium temperature of the system is 67° C. What is the specific heat of this unknown substance?
The specific heat of the unknown substance is 6.84 J/gºC
How do I determine the specific heat capacity?First, we shall convert 132.8° F to ° C. Thisis illustrated below:
Temperature (° F) = 132.8 ° FTemperature (° C) =?°C = (°F − 32) × 5/9
°C = (132.8 − 32) × 5/9
°C = 56 °C
Next, we shall determine the heat absorbed by the water. This is illustrated below:
Volume of water (V) = 188 mLDensity of water (d) = 1 g/mLMass of water (M) = dV = 1 × 188 = 188 gInitial temperature (T₁) = 56 °CFinal temperature (T₂) = 67 °CChange in temperature (ΔT) = 67 - 56 = 11 °CSpecific heat capacity of copper (C) = 4.184 J/gºC Heat absorbed (Q) =?Q = MCΔT
Q = 188 × 4.184 × 11
Q = 8652.512 J
Finally, we shall determine the specific heat capacity of the unknown metal. This can be obtained as follow:
Heat absorbed (Q) = 8652.512 JHeat released (Q) = -8652.512 JMass of unknown substance (M) = 0.056 kg = 56 gInitial temperature (T₁) = 89.6 °CFinal temperature (T₂) = 67 °CChange in temperature (ΔT) = 67 - 89.6 = -22.6 °CSpecific heat capacity of unknown substance (C) = ?Q = MCΔT
-8652.512 = 56 × C × -22.6
-8652.512 = C × -1265.6
Divide both sides by -1265.6
C = -8652.512 / -1265.6
C = 6.84 J/gºC
Thus, the specific heat capacity is 6.84 J/gºC
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How might these traits change from individual to individual? (Hint: Do you think the newts are all exactly the same color or size?)
Newts hatch in water, but they spend the most of their lives on land, returning to water only for mating.
They have rough skin, are 8 inches long, and have stubby legs and fangs. In the Pacific Northwest, some of them are toxic.
Rough-skinned newts have brown skin on their backs and bright orange skin on their bellies. When frightened by predators, these newts coil their bodies and show off their orange necks and tails. Predators are warned to stay clear from this orange tint.
It is to be noted that none of the newts are the same traits that is color or size.
What are traits?A phenotypic trait (simply trait or character state) is a distinct variety of an organism's feature that is visible and quantifiable and manifests itself in an observable manner.
For example, eye color (green, blue, brown, and hazel) is a phenotypic feature that is passed down by polygenetic inheritance.
Height, wing length, and hair color are all phenotypes. Phenotypes also include observable traits that may be evaluated in the lab, such as hormone levels or blood cell counts.
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Which one of the following is true of centrifugal force?
Centrifugal force is a fictional force.
Centrifugal force is a real force.
Centrifugal force pulls in a circular motion.
Centrifugal force causes objects moving in a circular path to move in.
Answer:
a is answer
Explanation:
centrifugal force, a fictitious force, peculiar to a particle moving on a circular path, that has the same magnitude and dimensions as the force that keeps the particle on its circular path (the centripetal force) but points in the opposite direction.
Please help! I don't understand how to do this!
A babysitter pushing a stroller starts from rest and accelerates uniformly at a rate of 0.778 m/s^2. What is the velocity of the stroller after it has traveled 5.54 m?
A babysitter pushing a stroller starts from rest and accelerates uniformly at a rate of 0.778 m/s^2. The velocity of the stroller after it has traveled 5.54 m will be 2.94 m/s
acceleration = 0.778 [tex]m/s^{2}[/tex]
distance = 5.54 m
initial velocity = 0
velocity of the stroller after it has traveled 5.54 m = ?
2as = [tex]v^{2} - u^{2}[/tex]
2 * 0.778 * 5.54 = [tex]v^{2}[/tex] - 0
v = 2.94 m/s
The velocity of the stroller after it has traveled 5.54 m will be 2.94 m/s
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A student is performing bomb calorimetry for a combustion reaction. The bomb calorimeter normally holds 5 L of water with a heat capacity of 4.184 J/g•°C. However, the student misread the directions and used 6 L of ethanol which has a heat capacity of 2.46 J/g•°C. If the student calculates the energy released by the reaction assuming it was 5 L of water, what will be the difference between the actual energy of the reaction and the calculated energy? Note: the densities of ethanol and water under normal conditions are 0.8 g/mL and 1.0 g/mL, respectively.
The difference between the actual heat energy of the reaction and the calculated heat energy is 9092ΔT.
What is the heat energy released if 6 L of are used for a combustion reaction?The heat energy released if 6 L is used for a combustion reaction is calculated as follows:
Heat change = mcΔTwhere;
m is massc is the specific heat capacity ΔT is temperature changewhen 6.0 L of ethanol was used;
Mass of ethanol = volume * density
The volume of ethanol = 6.0 L or 6000 mL
Mass of ethanol = 6000 * 0.8
Mass of ethanol = 4800 g
Heat change = 4800 * 2.46 * ΔT
Heat change = 11808ΔT
If 5.0 L of water was used:
Mass of ethanol = volume * density
The volume of ethanol = 5.0 L or 6000 mL
Mass of water = 5000 * 1.0
Mass of ethanol = 5000 g
Heat change = 5000 * 4.18 * ΔT
Heat change = 20900ΔT
Heat difference = 20900ΔT - 11808ΔT
Heat difference = 9092ΔT
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Two forces, F1=(1.65i−0.90j+1.15k) N F2=(−1.00i+1.20j) N are applied on a moving object of mass 0.20 kg. The displacement vector produced by the two forces is d=(10.0i+8.8j+5.1k)m. What is the work done by the two forces?
I need help with this question. please
Answer:
I don't Know espero que le entiendas
I have three energy levels, with 10 electrons in my outer energy level. What am I?
I have three energy levels, with 10 electrons in my outer energy level. I am calcium.
What are energy levels?Energy levels refer to the regions around an atom where electrons can be found.
The energy levels are given by the principal quantum number, n.
Electrons in an atom are arranged in energy levels.
An atom that has three energy levels belong to period 3 of the periodic table.
The outermost energy level for an atom that has three energy levels is energy level 3.
The atom that has 10 electrons in the outermost energy level of 3 will have 10 + 8 + 2 electrons = 20 electrons.
The element is calcium.
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Motor oil, axle grease, and other lubricants are slippery. Why do you
think people spend the money to put these lubricants in their cars? Answer ASAP
Because there is less resistance, it is simpler to maneuver their vehicle and requires less effort.
How should we define force?The definition of force is physics states that when a mass-containing object is pushed or pulled, it alters its velocity. The ability to change a body's resting and moving state is actually possessed by force, an external agent. It moves and has a certain size.
What role does force play?Things move and, more precisely, change their motion as a result of force. The forces of magnetic forces and gravity are two examples of natural forces that humans have encountered. These two forces don't need to be in close proximity to each other to work because they act at a distance.
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a sample of cube X is shown above. If it’s mass is 244.4 mg, what is its density in g/cm^3
The density of the cube is 1.1 g/cm³
What is density?Density is described as the substance's mass per unit of volume. Mathematically, density is defined as mass divided by volume: density (rho) =mass/ Volume where ρ is the density, m is the mass, and V is the volume.
mass of cube= 244.4mg
volume of cube = 222.2 cm³
density = mass/ volume
density = 244.4/ 222.2 cm³
density = 1.1 g/cm³
Density is essentially a measurement of how tightly matter is packed together. density is a unique physical property of a particular object.
In conclusion, the principle of density was discovered by the Greek scientist Archimedes.
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Three masses are connected as shown on a smooth horizontal surface.
(Take acceleration due to gravity as 9.8ms^-2)
a)Calculate the acceleration of the mass M3.
b)Calculate the tension in each string.
c)If the surface was not smooth describe how:
1.the acceleration of the system would be affected.
2.the tension in each string would be affected.
a) The acceleration of the mass M3 is 14.42 m/s².
b) The tension in each string. is : T₁ = 5119 N.
T₂= 7714 N.
And T₃ . = 12833 N.
c) If the surface was not smooth, there will be a frictional force which lessen both tension and acceleration of the system.
What is acceleration?Acceleration is rate of change of velocity with time. Due to having both direction and magnitude, it is a vector quantity. Si unit of acceleration is meter/second² (m/s²).
Let the acceleration of the system = a.
And the tension in each string is T₁ , T₂ and T₃ respectively.
Then for M₁ mass;
tension in string T₁ = M₁a
For M₂ mass:
tension in string T₂ = M₂ a
For M₃ mass:
tension in string T₃ - M₃g = M₃ a.
⇒T₃ = M₃g + M₃ a.
And T₃ = T₁ + T₂.
⇒M₃g + M₃ a. = M₂ a + M₁a
⇒ a = M₃g/( M₁ +M₂ -M₃)
= 530× 9.8/ (355+535-530)
= 14.42 m/s².
Then, the tension in each string is T₁ = 355 * 14.42 N = 5119 N.
T₂ = 535×9.8 N = 7714 N.
And T₃ = T₁ + T₂ = 5119 N +7714 N. = 12833 N.
If the surface was not smooth, there will be a frictional force which lessen both tension and acceleration of the system.
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A 32.0 kg crate is initially moving with a velocity that has magnitude 3.58 m/s in a direction 37.0 ∘ west of north. How much work must be done on the crate to change its velocity to 5.10 m/s in a direction 63.0 ∘ south of east?
The amount of work done on the crate to change its velocity is 211.1 J.
What is the work done on the crate to change its velocity?
The work done on the crate to change its velocity is calculated by applying the principle of conservation of energy as shown below.
Applying work-energy theorem, the work done in changing the velocity of the crate is equal to the change in kinetic energy of the crate as shown below;
W = ΔK.E
W = ¹/₂m(v₂² - v₁²)
where;
m is mass of the cratev₁ is the initial velocity of the cratev₂ is the final velocity of the crateW = ¹/₂m(v₂² - v₁²)
W = ¹/₂(32)(5.1² - 3.58²)
W = 211.1 J
Thus, the amount of work done on the crate to change its velocity from 3.58 m/s at 37.0 ∘ west of north to 5.10 m/s in a direction 63.0 ∘ south of east, is based on the principle of conservation of energy.
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two vehicle are moving in same direction the first one has velocity of 24m/s another has 18m/s find their relative velocity & also their relative velocity when they are moving in opposite direction
The relative velocity of two vehicles moving in the same direction will be 42 m/s, whereas the relative velocity of two vehicles moving in different directions will be 8 m/s.
Let the velocities of the two vehicles be, v1 and v2, respectively.
Given,
The velocity of the first vehicle (v1) = 24 m/s
The velocity of the second vehicle (v2) = 18 m/s
Case-1
When they are moving in a same direction,
The relative velocity (V) of the two vehicles will be the sum of their velocities, i.e.,
V = v1 + v2
=> V = 24 + 18
=> V = 42 m/s.
Case-2
When the vehicles are moving in different directions,
The relative velocity (V) of the two vehicles will be the difference between the velocities, i.e.,
V = v1 - v2
=> V = 24 - 18
=> V = 6 m/s.
Therefore, The relative velocity of two vehicles moving in the same direction will be 42 m/s, whereas the relative velocity of two vehicles moving in different directions will be 8 m/s.
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Mendeleev arranged elements in order for increasing?
Answer: Relative Atomic Mass
Explanation: The closer the element is to the bottom-right corner, the higher the relative atomic mass. Hydrogen has the lowest relative atomic number at 1, whereas Lawrencium has the highest relative atomic mass at 262.
Pls draw me what a velocity time graph would look like : moving at a positive constant speed to then at rest? Thank you!!!
Answer:
See below
Explanation:
Here are a couple of options..... one where the object slows to a rest and the other where the object stops to a rest instantaneously
An object with a mass of 33g and a volume of 39cm^3 is placed in a liquid with a density of 1.25 g/cm^3. Find the volume of the part of the object that is NOT submerged in the liquid. Give your answer in cm^3 and with 3 significant figures.
Answer:
V₂ = 12.6 cm³ - volume of the NOT immersed part:
Explanation:
Given:
m = 33 g
V = 39 cm³
ρ = 1.25 g/cm³
____________
V₂ - ?
Gravity:
F = m·g
Strength of Archimedes:
Fa = ρ·g·V₁
V1 - the volume of the submerged
The object is floating, so:
F = Fa
m·g = ρ·g·V₁
m = ρ·V₁
V₁ = m / ρ = 33 / 1.25 ≈ 26,4 cm³
V₂ - volume of the NOT immersed part:
V₂ = V - V₁ = 39 - 26.4 = 12.6 cm³
Brooke is learning about electronic devices that use electric current to encode information. She learns that when a person speaks into the microphone of a telephone, the sound wave generated by the person’s voice is changed into an electronic signal. This electronic signal is then transmitted to another telephone where it is converted back to a sound wave so the other person can hear the voice. The sound wave is encoded by varying the voltage of the electronic signal. Brooke learns that the voltage can be changed in two ways, resulting in two types of electronic signals: analog and digital. Figure 1 and Figure 2 represent these two types of signals.
Identify the type of signal represented by each figure. Explain your reasoning.
The signals in this problem are classified as follows:
Figure 1: Digital signal.Figure 2: Analog signal.What are analog and digital signals?Analog signals are signals that are continuous in both domain and range, meaning that it can assume decimal values, hence it's graph is represented by a continuous curve.
Digital signals are signals that are discrete in both domain and range, meaning that it assumes only integer values, hence it's graph is composed by pulses.
Hence the classification of the signals for each figure in this problem are given as follows:
Figure 1: Digital signal, as the graph is composed only by pulses.Figure 2: Analog signal, as the graph is represented by the continuous and oscillating curve.More can be learned about analog and digital signals at https://brainly.com/question/22858440
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A 50.0-kilogram cheetah has a kinetic energy of 18000J How fast is the cheetah running ? ( Hint : Rearrange the equation to solve for v .)
I found that people say it’s 36 but there is no explanation for it
Answer:
Explanation:
here take kinetic energy =1/2×m×v²
m=50.0-kilogram (given)
kinetic energy=18000J (given)
now by taking the given values we get v²=(2×18000)/50
⇒v²=720
⇒v=26.8328m/s
done!
Move over Jeff Bezos, this invention is about to make you the richest person in the world. You have just invented the OyOy (that's YoYo spelled backwards). It is the very latest in home safety and so easy to use!
If your building is on fire, simply reach out and grab the cord on the OyOy and you will be lowered safely toward the ground at a low velocity. The OyOy has a total mass M = 95.0 kg and is shaped like a cylinder of radius R = 0.940 meters. The secret to the operation of the OyOy is its patented shaft whose radius is only r = 0.0900 meters. The cord is wound around the small shaft and this is the secret to your low velocity.
We will use the approximation that the shaft is of negligible mass compared to the total. This means that you can treat the entire OyOy as though it is a solid cylinder with mass M and radius R. Imagine that a customer of mass m = 78.5 kg is using the OyOy and begins his decent from an initial height of y0 = 12.55 meters.
Find velocity of customer at ground.
Answer: The correct answer is 144.716
Explanation: This is the correct answer because the velocity of the customer at ground is higher than it should be
A person is falling from the top of a building. If they hit the ground they will die. A superhero swoops in from the side at high speed and catches them just before they reach the ground. The person is saved from harm.
Why does this defy physics? Give Equations/Laws to justify your answer.
This situation defies the laws of physics because the force required to stop the person from touching the ground would be too great that it would be equally fatal.
What laws should be considered in this situation?The first law to be considered is that an object will continue moving at a constant acceleration unless there is an unbalanced force that interrupts this. In other words the person will fall unless the supehero force is equally strong to the accelaration.
What is the problem with this?The main problem is that the superhero's speed and force would have to be about 160 miles per hour or even more to "save" the person. However, this would be even more dangerous than being hitted by a car and the person would immediately die due to the impact.
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does the current stays the same throughout in a parallel circuit
Answer:
When the current splits, the current in each branch after the split adds up to the same as the current just before the split.
No, the current is not constant across the entire parallel circuit.
The circuit is known to be divided into branches by the parallel connection. Consequently, those branches are formed from the total current.
A parallel circuit may have one or more branches. The total current splits into its corresponding branches as soon as it enters one. Less current flows through the branches than across the entire system. The branch resistance affects the branch current values. In parallel circuits, the current is therefore different. All components in a parallel arrangement share the same voltage.
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Three miles of an ideal gas kept at constant temperature 300K are compressed from volume of 4L to 1L. Calculate work done in the process where R = 8.31 J/mol/K
[tex]{ \boxed{ \red{ \sf{W = 10370.652 \: J}}}}[/tex]
Explanation:
Given,
[tex]{ \blue{ \sf{μ = 3}}}[/tex]
[tex]{ \blue{ \sf{ T= 300K}}}[/tex]
[tex]{ \blue{ \sf{ V_{1} = 4L}}}[/tex]
[tex]{ \blue{ \sf{ V_{2} = 1L}}} [/tex]
[tex]{ \blue{ \sf{W = \: ?}}}[/tex]
[tex]{ \blue{ \sf{R = 8.31 \: J/mol/K}}}[/tex]
[tex]{ \purple{ \sf{W = μRT \: l_{n}[ \frac{ V_{2}}{ V_{1} }}]}} [/tex]
[tex]{ \purple{ \sf{W = μRT[ l_{n} V_{2} - l_{n}V _{1}}]}}[/tex]
[tex]{ \purple{ \sf{W = 2.303μRT[ log_{1} - log_{4}]}}}[/tex]
[tex]{ \purple{ \sf{W = 2.303 \times 3 \times 8.31 \times 300(0 - 0.6021)}}}[/tex]
[tex]{ \purple{ \boxed{ \green{ \sf{W = 10370.652 \: J}}}}}[/tex]
A falling object with a mass of 2.55 kg encounters 4.0 N of air resistance. What is the acceleration of the object? (Choose up to be the positive direction, and remember the definition of weight).
The acceleration of the falling object with a mass of 2.55 kg that encounters 4.0 N of air resistance is 1.57m/s².
How to calculate acceleration?Acceleration is change of velocity with respect to time (can include deceleration or changing direction).
The acceleration of a body can be calculated by using the following expression;
a = F/m
Where;
a = acceleration (m/s²)F = force (N)m = mass (kg)According to this question, a mass of 2.55 kg encounters 4.0 N of air resistance. The acceleration of the object can be calculated as follows:
a = 4N ÷ 2.55kg
a = 1.57m/s²
Therefore, 1.57m/s² is the acceleration of the object.
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If I wanted to increase the current, but maintain the voltage in a USB 3.1 port that provides a current of 0.9 A and a voltage of 5 V, to which I have connected a device with 4 ohms of resistance, how would I have to associate several USB ports to achieve this?
To achieve an increase in the current delivered in the USB 3.1 port, at a constant voltage, the several USB ports must be connect in parallel to each other. This will ensure an increase in current and constant voltage.
What is the relationship between current and resistance?According to ohms Law the current flowing through an ohmic conductor is directly proportional to the voltage across the conductor.
V = IR
where;
I is the current in the circuitR is the resistance across the circuitV is the voltage across the circuitI = V/R
To increase the current at a constant voltage, the resistance must decrease.
In a parallel circuit, the current flowing in each circuit component is different while the voltage drop in each circuit component is the same.
Thus, to increase the current delivered in the USB port, and maintain the initial voltage, the several USB ports must be connect in parallel to each other.
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In Graph C above, which line(s) shows an object that has a constant
velocity?
Answer:
it's D that has a constant velocity
A cap 6.000 cm in diameter plugs an opening in a spherical container 1.000 m in diameter at atmospheric pressure. The container is submerged to a depth of 10.00 ft in water. Assume the plug is planar and the pressure over the container is equalized. The force needed to remove the plug is closest to?
The force needed to remove the plug that is 6.000 cm in diameter which plugs an opening in a spherical container 1.000 m in diameter at atmospheric pressure is 85 N
P = F / A
P = ρ g h
P = Pressure
F = Force
A = Area
ρ = Density
g = Acceleration due to gravity
h = Height
ρ = 1000 kg / m³
g = 9.8 m / s²
h = 10 ft = 3.048 m
A = π r²
d = 6 cm = 0.06 m
r = d / 2 = 0.06 / 2
r = 0.03 m
A = 3.14 * 0.03 * 0.03
A = 0.002826 m²
Equating both formulae of P,
F / A = ρ g h
F = 1000 * 9.8 * 3.048 * 0.002826
F = 85 N
Therefore, the force needed to remove the plug is closest to 85 N
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A soccer coach is working with a device that measures the velocity of a soccer ball after it has
been kicked.
Which units should the coach use for velocity?
Choose 1 answer:
meters per second
kilograms
meters
meters per second
What is Velocity?
The pace at which an object's position changes in relation to a frame of reference and time is what is meant by velocity. Although it may appear sophisticated, velocity is just the act of moving quickly in one direction. Since it is a vector quantity, the definition of velocity requires both magnitude (speed) and direction. Its SI equivalent is the meter per second (ms-1). A body is considered to be accelerating if the magnitude or direction of its velocity changes.
Therefore, it will measured in meters per second.
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Which has the most momentum?
C: 150 g object at 5 m/s
D: 200 kg object at 2 m/s
A: 50 kg object at 5 m/s
B: 100 kg object at 10 m/s
Option D) 200 kg object at 2 m/s has the highest momentum.
What is momentum?
Momentum is calculated using Newtonian mechanics by multiplying an object's mass by its velocity.As a vector quantity with both a magnitude and a direction, it has both. Considering that an object's mass is m and its speed is v (also a vector quantity),Momentum formula, P = mv
p = momentum
m = mass \ velocity
The newton-second is a unit of measurement for momentum in the International System of Units (SI), and the kilogram metre per second (kg m/s) is its SI counterpart.
A) 50 kg object at 5 m/s
m = 50 kg
v = 5 m/s
Momentum, p = m x v
= 50 x 5
= 250 kg m/s
B) 100 kg object at 10 m/s
m = 100 kg
v = 10 m/s
Momentum, p = m x v
= 100 x 10
= 1000 kg m/s
C) 150 g object at 5 m/s
m = 150 g
= 0.15 kg
v = 5 m/s
Momentum, p = m x v
= 0.15 x 5
= 0.75 kg m/s
D) 200 kg object at 2 m/s
m = 200 kg
v = 2 m/s
Momentum, p = m x v
= 200 x 2
= 400 kg m/s
Hence, Option B has the highest momentum.
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A tennis ball with a mass of 0.2 kg is thrown upwards from the ground at a velocity of 30 m/s. What
is the height of the ball when it has a velocity of 20 m/s?
The height of the ball when it has a velocity of 20 m/s is 45m.
What is mass?
It is the most fundamental feature of matter and one of the fundamental quantities in Physics. Mass can be defined as the amount of matter in a body. Kilogram is the SI unit of mass (kg).
It should be noted that a body's mass does not alter with time. Only in severe instances where a massive amount of energy is provided or removed from the body. In a nuclear reaction, for example, a tiny bit of matter is turned into a massive amount of energy, reducing the mass of the substance.
Given Initial velocity of ball, u=30 m/s
Let the maximum height reached and time taken to reach that height be H and t respectively.
Assumption: g=9.8 m/s2
holds true (maximum height reached is small compared to the radius of earth)
30/g=30/9.8=3 seconds
as the time taken to reach max height.
h(3)=-4.9(3²)+30(3)
=90–45
=45m
The height of the ball when it has a velocity of 20 m/s is 45m.
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A car is initially moving at 10.5 m/s and accelerates uniformly to reach a speed of 21.7 m/s in 4.34 s. How far did the car move during this
acceleration?
The care travelled a distance of 69.87 m.
What is acceleration?Acceleration is rate of change of velocity with time. Due to having both direction and magnitude, it is a vector quantity. SI unit of acceleration is meter/second² (m/s²).
Given parameters:
Initial velocity of the car; u = 10.5 m/s.
Final velocity of the car; v = 21.7 m/s.
Time; t = 4.34 s.
The acceleration of the moving car; a = (Final velocity of the car - Initial velocity of the car)/time
= ( 21.7 m/s - 10.5 m/s)/4.34 s.
= 2.58 m/s².
Hence, the car move a distance during this acceleration; s = ut +1/2 at²
= 10.5×4.34 + 1/2 × 2.58×4.34² m.
= 69.87 m.
Hence, the car move a distance of 69.87 m during this acceleration.
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