Answers
Answer:
Explanation:
The change in force = 9.81(1.95 - 0.300) = 16.2 N
The change in length is 0.750 - 0.200 = 0.550 m
K = ΔF/Δx = 16.2/0.550 = 29.4 N/m
Related Questions
3) Four point masses 2kg, 4kg, 6kg and 9kg are placed at the corners of Square ABCD of 2cm long respectively. Find the position of centre of mass of the system from the Corner A.
Answers
Answer:
We can find the position of the center of mass of the system by using the formula:
Xcm = (m1x1 + m2x2 + m3x3 + m4x4) / (m1 + m2 + m3 + m4)
where Xcm is the x-coordinate of the center of mass, m1, m2, m3, and m4 are the masses of the point masses, and x1, x2, x3, and x4 are their respective x-coordinates.
Similarly, we can find the y-coordinate of the center of mass using the formula:
Ycm = (m1y1 + m2y2 + m3y3 + m4y4) / (m1 + m2 + m3 + m4)
where Ycm is the y-coordinate of the center of mass, m1, m2, m3, and m4 are the masses of the point masses, and y1, y2, y3, and y4 are their respective y-coordinates.
Let's label the masses and coordinates as follows:
m1 = 2kg, x1 = 0cm, y1 = 0cm
m2 = 4kg, x2 = 2cm, y2 = 0cm
m3 = 6kg, x3 = 2cm, y3 = 2cm
m4 = 8kg, x4 = 0cm, y4 = 2cm
Substituting these values into the formulas, we get:
Xcm = (2kg x 0cm + 4kg x 2cm + 6kg x 2cm + 8kg x 0cm) / (2kg + 4kg + 6kg + 8kg) = 2cm
Ycm = (2kg x 0cm + 4kg x 0cm + 6kg x 2cm + 8kg x 2cm) / (2kg + 4kg + 6kg + 8kg) = 1cm
Therefore, the center of mass of the system is located 2cm from corner A in the x-direction and 1cm from corner A in the y-direction.
Explanation:
Name 1. Consider positive and negative charges of a copper wire all moving horizontally within the time interval 10 us. What can you say about the magnitude and direction of the current?
Answers
When positive and negative charges of a copper wire are moving horizontally within a time interval of 10 microseconds, the magnitude of the current is zero, and the direction of the current is opposite to the direction of charge movement.
In the given scenario, if positive and negative charges of a copper wire are moving horizontally within a time interval of 10 microseconds (10 μs), we can infer the following about the magnitude and direction of the current:
1. Magnitude of the Current: The magnitude of the current is determined by the total charge passing through a given point in the wire per unit time. Since both positive and negative charges are moving, the total charge passing through a point will be the sum of the magnitudes of the charges. If the number of positive and negative charges is equal, the magnitudes of their charges will also be equal. Therefore, the total charge passing through the point will be the sum of equal positive and negative charges, resulting in a net charge of zero. In this case, the magnitude of the current will be zero.
2. Direction of the Current: The direction of the current is determined by the flow of positive charges. In a copper wire, the positive charges are not free to move. Instead, it is the negatively charged electrons that are free to move. Due to conventional current flow convention, the direction of the current is considered opposite to the direction of the electron flow. Therefore, even though both positive and negative charges are moving horizontally, the direction of the current will be in the opposite direction to the movement of the charges.
In summary, in the given scenario, where positive and negative charges of a copper wire are moving horizontally within a time interval of 10 microseconds, the magnitude of the current is zero, and the direction of the current is opposite to the direction of the charge movement.
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Use the general formulas for gravitational force and centripetal force to derive the relationship between speed (v) and orbital radius (r) for circular orbits. Show the relationship you derived to your instructor before going on.
Answers
Solution :
We know that :
Formula for Gravitational force is given by :
\($F_g=\frac{Gmn}{r^2}$\)
where, G is the gravitational constant
M is the mass of the bigger body
m is the mass of the smaller body
r is the distance between the two bodies.
And the formula for the centripetal force is given by :
\($F_c=\frac{mv^2}{r}$\)
where, m is the mass of the rotating body
v is the velocity
r is the radius of rotation of the body.
We know that mathematically, the gravitational force is equal to the centripetal force of the body.
Therefore,
\($F_g=F_c$\)
\($\frac{GMm}{r^2}=\frac{mv^2}{r}$\)
\($\sqrt{\frac{GM}{r}}=v$\)
Hence derived.
if a and b are vectors, write the mathematucal expressioons of scalar quantity
Answers
Magnitude of a vector: The magnitude of a vector a is a scalar quantity, denoted by |a|. It is given by:
|a| = sqrt(a . a)
where a . a is the dot product of a with itself.
Dot product of two vectors: The dot product of two vectors a and b is a scalar quantity, denoted by a . b. It is given by:
a . b = |a| |b| cos(theta)
where |a| and |b| are the magnitudes of vectors a and b, respectively, and theta is the angle between them.
Projection of a vector: The projection of a vector a onto another vector b is a scalar quantity, denoted by proj_b(a). It is given by:
proj_b(a) = |a| cos(theta)
where theta is the angle between vectors a and b.
Scalar triple product of three vectors: The scalar triple product of three vectors a, b, and c is a scalar quantity, denoted by (a x b) . c. It is given by:
(a x b) . c = det([a b c])
where det([a b c]) is the determinant of the matrix formed by the vectors a, b, and c.
An 8-ohm resistor is connected to a 120-volt circuit. What current will it draw?
Answers
Answer:
15 A (15 amperes of current)
Explanation:
From Ohm's Law,
Voltage, V = Current, I × Resistance, R
Making Current, I the subject:
Current, I = Votage, V/ Resistance,R
= V/R
= 120volts /8ohms
= 15 A
NEED HELP BADLY!!
A car with an initial velocity of 22 m/s is accelerated at a rate of 7.3 m/s/s for 6.8 seconds. What is the cars final velocity?
Answers
Explanation:
initial velocity (u) = 22 m/s
Final velocity = ?
acceleration = 7.3 m/s^2
time = 6.8 sec
Now,
acceleration = final velocity- intial velocity/time taken
7.3 = v-u/t
7.3= v-22/6.8
7.3×6.8= v-22
49.64=v-22
49.64+22 =v
v= 71.64 m/s
How would be best to find a scientific law? A) Generalized rule to explain a body of observations.
Answers
Answer:
In general, a scientific law is the description of an observed phenomenon. It doesn't explain why the phenomenon exists or what causes it. The explanation of a phenomenon is called a scientific theory
If the velocity of a particle is nonzero, can the particle’s acceleration be zero? Explain.
Answers
If a particle's velocity is nonzero, then its acceleration can be zero, because acceleration is the rate of change of velocity. If the velocity is constant and does not change, the acceleration is zero.
What is acceleration?The rate of change of an object's velocity with respect to time is defined as acceleration. Vector quantities are accelerations. The orientation of an object's acceleration is determined by the orientation of its net force.
Because velocity is both a speed and a direction, there are only two ways to accelerate: modify your speed or your direction—or both.
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The table lists the kinetic energy of a 4.0 kilogram mass as it travels in a straight line for 12.0 seconds.
Time
(seconds) Kinetic Energy
(joules)
0.0 0.0
2.0 8.0
4.0 18
6.0 32
10.0 32
12.0 32
Calculate the speed of the mass at 10.0 seconds.
m/s
Answers
So the speed of object of mass 4 Kg and kinetic energy of 32 j at 10 second is 4 m/s.
What is kinetic energy?Kinetic energy is the energy that an object has when it moves or changes its position. As long as an object is moving at the same speed, it maintains the same kinetic energy.
The kinetic energy of an object is calculated from the object's velocity and mass. As can be seen from the equation below, velocity is quadratic and can have a large effect on kinetic energy.
KE = ¹/₂ mv²
v = √(2KE/m)
Where, v = velocity
M = Mass of object (4.0 Kg)
KE = Kinetic energy (32 j)
v = √(2 × 32/4)
v = √16
v = 4 m/s
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Mention four factors on which the amount of precipitation intercepted by vegetal cover depend on
Answers
Precipitation amount, storm frequency, and severity, storm duration, kind of precipitation, wind during storm, and wind during evaporation are the main precipitation and storm elements that influence interruption loss (Kenneth, 1996).
What does it signify when vegetation blocks precipitation?All procedures that stop rainfall from instantly reaching the soil are referred to as interceptions. The two main ways that vegetation intercepts water are by catching it on leaf surfaces throughout the canopy and by depositing litter on the ground.
Intercepted precipitation: What is it?Precipitation that is intercepted by leaves, plant branches, and the forest floor prevents it from reaching the soil and instead stays on the surface.
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A body of mass 12kg travelling at 4.2m/s² collides with a second body of mass 18kg at rest. Calculate their common velocity of the two bodies coalesce after collision
Answers
When a body of mass 12kg travelling at 4.2m/s² collides with a second body of mass 18kg at rest, their common velocity after the collision is 1.68 m/s.
When two objects of different masses collide, they can exchange momentum. An object's mass and velocity together make up its momentum. When two objects collide, their momentum is conserved, meaning that the total momentum of the two objects before the collision equals the total momentum of the two objects after the collision. This principle can be used to calculate the velocity of the two objects after a collision.A body of mass 12 kg is travelling at a velocity of 4.2 m/s and collides with a second body of mass 18 kg at rest. The total mass of the system is 12 kg + 18 kg = 30 kg. To determine the velocity of the two objects after the collision, we need to use the conservation of momentum principle. Before the impact, the system's entire momentum is:momentum before = \((mass_1 x velocity_1) + (mass_2 x velocity_2)\)where mass1 is the mass of the first object, velocity1 is the velocity of the first object, \(mass_2\) is the mass of the second object, and \(velocity_2\) is the velocity of the second object. In this case,\(mass_1 = 12 kg, velocity_1 = 4.2 m/s, mass_2 = 18 kg\), and \(velocity_2 = 0\) (because the second object is at rest). Substituting these values into the equation above, we get: momentum before = (12 kg x 4.2 m/s) + (18 kg x 0)momentum before = 50.4 kg m/sFollowing the collision, the system's overall momentum is:momentum after =\((mass_1 + mass_2) * velocity\)where mass1 + mass2 is the total mass of the system, and velocity is the velocity of the two objects after the collision. Let's call this velocity "v". Substituting the values we know into the equation above, we get: momentum after = (12 kg + 18 kg) x vmomentum after = 30 kg x vUsing the conservation of momentum principle, we know that momentum before = momentum after. Therefore, we can set these two equations equal to each other and solve for v.50.4 kg m/s = 30 kg x vv = 50.4 kg m/s ÷ 30 kgv = 1.68 m/sFollowing the impact, the two bodies' common velocity is 1.68 m/s. Hence, the answer to this problem is that when a body of mass 12kg travelling at 4.2m/s² collides with a second body of mass 18kg at rest, their common velocity after the collision is 1.68 m/s.For more questions on collision
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A basketball player is getting ready to jump, pushing off the ground and accelerating upward.
A) Draw a force identification diagram.
B) Draw a free body diagram.
Answers
Answer:
B
Explanation:
B
A baseball is hit so that it travels straight upward after being struck by the bat. If its initial velocity is 29 m/s , then what is the maximum height that it will reach?
Answers
Answer:
Explanation:
Use kinematic equation v² = u² + 2as
Rearrange for distance
s = (v² - u²) / 2a
Realize that at the top of its flight, the ball has zero velocity and gravity is acting downward in an assumed upward positive reference frame.
s = (0² - 29²) / (2(-9.8))
s = 42.90816...
s = 43 m
A building with a wall 50m long by 4m high with sixty percent (60%) of the wall area occupied by 10 mm thick plate glass and the remainder is of 20 cm thick concrete blocks with solid concrete cores is being designed. If expected condition for site of the building has average dally air temperatures of 35°C and the interior temperature of the building will be kept at 25 °C by designed air conditioning syster, calculate the rate of heat transfer from outside to inside (heat load) due to this wall.
Answers
Answer: If you have "A, B, C" as answers chose the answer: "A".
Explanation:
Trust me.
A gas is compressed at constant pressure of 0.8atm from 9litre to 2 litre in the process, 400J of a energy leves the gas by heat.
a. what is work done on the gas?
b, What is the change in its internal energy?
Answers
According to the give statement:
a)Work done on the gas is 567 J.
b)The change in its internal energy is 167J.
What is an example of internal energy?The temperature and condition of a substance are examples of internal energy. For instance, the internal energy of water is influenced by its temperature as well as whether it is in a solid, liquid, or gas state. Due to its condition, liquid water has greater stored energy than copper metal at the same temperatures.
Briefing:The work done on the gas is evaluated using formulas:
W = -p * ΔV
Only the large volumes which is signified by large data Substituting the known values we obtain
W= 0.8 * 1.01325 * 10⁵ Pa * -1 (-7) * 10⁻³ m³
W = 567 J
Change in Internal energy is given by
ΔU=W - Q
=567−400)
=167J
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When the south pole of a magnet approaches this iron nail from the left, what
happens to its domains?
A. All the arrows align to point down.
OB. All the arrows align to point right.
C. All the arrows align to point up.
OD. All the arrows align to point left.
t
Answers
In order to answer the question of where the arrows of the magnetic domains point, one must consider the properties of the magnets' poles: A) The arrows line up and point upward.
What comprises a magnet?Iron or cobalt is a common component of permanent magnets. An alloy composed of aluminum is called alnico. Involves a systematic process minerals are capable of making powerful electromagnets. They are widely utilized in industrial and consumer electronics applications.
Why was magnet named?The word "lithos magnes" from classical Greek is where the name first appeared. According to Pliny's explanation in his "Naturalis Historia," the term is derived from the myth of the Greek shepherd Magnes on Mount Ida, whose iron staff and the nails in his shoes were drawn to the magnetite stones.
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Answer:
POINTS LEFT
Explanation:
just did it
Part 1
1. Consider the potential energy diagram shown below. This graph shows the chemical potential energy in a reaction system over time. The y–axis is potential energy in kilojoules. The x–axis is the reaction progress, or time.
a. Does this graph represent an endothermic or an exothermic reaction? Explain your answer.
b. What is the enthalpy change, ΔH, for this reaction? Show your work.
c. What is the activation energy, Ea, for this reaction? Show your work.
Part 2
2. In a particular chemical reaction, the energy of the reactants is 30 kJ and the energy of the products is 5 kJ. The maximum energy of the system is 40 kJ. Use this information to answer questions a – d.
a. Sketch a potential energy diagram for this reaction. Make sure to label the energy of the reactants, the energy of the products, the activation energy, and the enthalpy change for the reaction. (Note: You may use the graph provided below or sketch your own. Resize as needed.)
b. What is the activation energy for this reaction?
c. What is the enthalpy change for this reaction?
d. Is this reaction endothermic or exothermic? Explain your answer in two ways: first, using the energy values, and second, by referring to the shape of the graph.
Part 3
3. The coating on the head of a match is highly flammable. When it burns, it releases a great deal of energy. However, before the match can burn, it must gain a small amount of energy from a spark. That spark is typically produced by striking (rubbing) the match head against a rough surface.
a. Sketch a potential energy diagram that represents the striking and burning of the match. Remember to label the diagram with the energy changes that occur. (Note: you do not have to use actual energy values. And you may use the graph provided below or sketch your own.)
b. Describe a potential energy diagram that represents the striking and burning of the match.
Answers
1a) Energy is absorbed, and the reaction is endothermic.
1b) The products have higher potential energy, the enthalpy change is positive, indicating an endothermic reaction.
1c) The peak of the potential energy diagram.
2a) The activation energy labeled as the difference between the reactants and the peak
2b) The activation energy can be determined by calculating the difference between the reactants.
2c) The enthalpy change can be calculated by finding the difference between the energy of the reactants and the energy of the products.
2d) The reaction is exothermic. In terms of the graph's shape.
3a) A decrease in potential energy as the products form.
3b)This indicates that a small amount of energy from the spark is needed to overcome the activation energy barrier
Part 1:
1a. To determine if the reaction is endothermic or exothermic, we need to analyze the potential energy diagram. If the products have lower potential energy than the reactants, it indicates that energy is released, and the reaction is exothermic. Conversely, if the products have higher potential energy than the reactants, it suggests that energy is absorbed, and the reaction is endothermic.
1b. The enthalpy change (ΔH) for the reaction can be calculated by comparing the potential energy of the products and the reactants. If the products have lower potential energy, the enthalpy change is negative, indicating an exothermic reaction. If the products have higher potential energy, the enthalpy change is positive, indicating an endothermic reaction.
1c. The activation energy (Ea) can be determined by examining the energy difference between the reactants' potential energy and the peak of the potential energy diagram.
Part 2:
2a. Since the energy of the reactants is 30 kJ, the energy of the products is 5 kJ, and the maximum energy of the system is 40 kJ, we can sketch a potential energy diagram with the reactants at 30 kJ, the products at 5 kJ, the activation energy labeled as the difference between the reactants and the peak, and the enthalpy change as the difference between the reactants and products.
2b. The activation energy can be determined by calculating the difference between the reactants' energy and the peak of the potential energy diagram.
2c. The enthalpy change can be calculated by finding the difference between the energy of the reactants and the energy of the products.
2d. Based on the energy values, if the energy of the products is lower than the energy of the reactants, the reaction is exothermic. In terms of the graph's shape, if the potential energy decreases from reactants to products, it indicates an exothermic reaction.
Part 3:
3a. The potential energy diagram for the striking and burning of a match can be sketched to show the initial potential energy of the reactants, a peak representing the activation energy, and a decrease in potential energy as the products form.
3b. The potential energy diagram would show an initial higher potential energy for the reactants, a peak representing the activation energy required for the reaction to occur, and a decrease in potential energy as the products form. This indicates that a small amount of energy from the spark is needed to overcome the activation energy barrier, leading to the release of a greater amount of energy during the burning process.
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For a satellite to orbit Earth at a constant distance, its centrifugal acceleration
must be equal and opposite Earth's gravitational acceleration. If a satellite is
to orbit at a constant distance from Earth at a circular radius of 8,300,000 m,
what is the required velocity of the satellite? (Assume the acceleration due to
Earth's gravity is 5.6 m/s2 at this altitude.)
A. 7043 m/s
B. 8239 m/s
C. 7576 m/s
D. 6818 m/s
Answers
If a satellite is to orbit at a constant distance from Earth at a circular radius of 8,300,000, the required velocity of the satellite is 8239m/s.
What is a satellite?
Most spacecraft, with the exception of passive satellites, contain a means of generating electricity for the technology they carry, such as solar panels or radioisotope thermoelectric generators (RTGs). The majority of satellites also feature transponders, which are a type of ground station communication system. The most common satellites, small CubeSats, use a standardised bus to reduce costs and labour. Satellites of a similar type can cooperate with one another to form constellations.To know more about satellite, click the link given below:
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Jamal is 8 miles away from his house. He rides his bike home toward home at a speed of 12 mph.. How far away from home is he after a half hour? 1 mile 2 miles 3 miles 4 miles
Answers
After half an hour, Jamal is 8 - 6 = 2 miles away from his home. Therefore, the correct option is 2 miles.
What is distance?Distance is the measurement of how far apart two objects or points are, typically measured along a path connecting them. It is a scalar quantity, meaning it has magnitude but no direction.
Distance is often measured in units such as meters, kilometers, miles, or feet, depending on the system of measurement being used. In physics, distance is closely related to the concept of displacement, which refers to the overall change in position of an object and includes both the distance traveled and the direction of movement.
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A proton high above the equator approaches the
Earth moving straight downward with a speed of
365 m/s.
Find the acceleration of the proton, given that the magnetic field at its altitude is 4.10*10^-5 T.
Answers
We can see from the calculations that the acceleration of the proton is 1.43 * 10^7 ms-2.
What is acceleration?Acceleration is the rate of change of velocity with time. We know that the magnetic force is obtained by;
F = qvB
q= 1.6 * 10^-19 C
v = 365 m/s
B = 4.10*10^-5 T
F = 1.6 * 10^-19 C * 365 m/s * 4.10*10^-5 T
F = 2.39 * 10^-20 N
Recall that the mass of the proton is 1.67 × 10−27 kg hence
a = F/m = 2.39 * 10^-20 N/1.67 × 10−27 kg = 1.43 * 10^7 ms-2
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An object is moving with an initial velocity of 5.5m/s.It is then subject to a constant acceleration of 2.5 m/s for 11s. How far will it have traveled during the time of its acceleration?
Answers
The distance traveled by the object during the time of acceleration is 211.75 m.
What is distance?Distance can be defined as the total lenght between two points.
T o calculate the distance traveled by the object during the time of acceleration, we use the formula below.
Formula:
s = ut+at²/2............ Equation 1Where:
s = Distanceu = Initial velocitya = Accelerationt = TimeFrom the question,
Given:
u = 5.5 m/st = 11 sa = 2.5 m/s²Substitute these values into equation 1
s = (5.5×11)+(2.5×11²)/2s = 60.5+151.25s = 211.75 mHence, the distance traveled by the object is 211.75 m.
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HELP ME PLEASEEEEEEEEEEEEEE
Answers
Answer:
probably won't help now but the answer is the 4th one lol
Explanation:
The first P-wave of an earthquake travels 5600 kilometers from the epicenter and arrives at a seismic station at 10:05 a.m. At what time did this earthquake occur?
Ahhhhhh I have a Regent's test in 2 hours and I don't know how to solve this type of question! Any help would be appreciated.
Anyone know what the steps to do this are? I dont even need an answer, just how to get to it. Thank you!
Answers
The earthquake would occur 13 minutes before 10:05 a.m. which will be at 9.52 am.
The p-waves travel with a constant velocity of 7 km/s
The time can be calculated by using the formula
t = d / v
where
T1 = 10:05 a.m
d is the distance they take to travel from the epicenter
v is the speed of the p-waves
On average, the speed of p-waves is
v = 7 km/s
d = 5600 km (given)
Substituting the values in the formula;
t = d / v
t = 5600 ÷ 7
t = 800 seconds
Converting into minutes,
t = 800 ÷ 60
t = 13.3
≈ 13 mins
T1 - 13 mins = T2
10:05 - 13 mins = 9.52 am
It means the earthquake occurred prior 13 minutes, that is at 9.52 am.
Therefore, the earthquake occurred at 9.52 am.
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a piece of uranium drops from 1500 Celsius to 900 Celsius. what state of matter would we expect it to be in?
Answers
At 1500°C, uranium would be in a molten or liquid state. As it cools to 900°C, it will solidify
How does the temperature affect?
The temperature of a substance determines its state of matter. At high temperatures, substances tend to be in a liquid or gaseous state, and as the temperature decreases, they solidify.
In the case of uranium, at 1500°C, it would be in a molten or liquid state because this temperature is higher than its melting point of 1132°C.
However, as it cools to 900°C, it will become solid because 900°C is below its melting point.
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The second step to the scientific method is:
form a hypothesis.
ask a question.
Operform a test.
share the results.
Answers
The second step of the scientific method is to form a hypothesis. Thus, the correct option for this question is A.
What is a Scientific method?A scientific method may be defined as the complete procedure through which the objectives of any experiment are established facts through testing and experimentation. There are numerous steps of the scientific method exist.
The basic steps of the scientific methods are as follows:
Construct an observation, Form a hypothesis.Making a prediction. Conducting an experiment.Analyzing the results.It is a systematic and well-regulated approach that involves in obtaining information about a scientific nature or obtaining a desired material or product.
Therefore, the second step of the scientific method is to form a hypothesis. Thus, the correct option for this question is A.
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Name two examples of conservative forces
Answers
What is the minimum amount ( in kg) of liquid water at 26 degrees that would be required to completely melt 41 grams of ice? The specific heat capacity of liquid water is 4180 J/kg/°C and the specific heat of fusion of ice is 3.33×105 J/kg.
Answers
Approximately 0.123 kg of liquid water at 26 degrees Celsius would be needed to melt 41 grams of ice.
To calculate the minimum amount of liquid water required to melt 41 grams of ice at 0°C, we need to consider the energy required for the phase change from solid to liquid, which is known as the specific heat of fusion of ice.
The energy required to melt 1 kg of ice is 3.33×105 J/kg.
Therefore, the energy required to melt 41 grams of ice is (3.33×105 J/kg) × (41/1000) kg = 13653 J.
To calculate the amount of liquid water required, we use the specific heat capacity of water, which is 4180 J/kg/°C.
Assuming the initial temperature of water is 26°C, the amount of water needed can be calculated as (13653 J) ÷ (4180 J/kg/°C) ÷ (26°C) = 0.123 kg or approximately 123 ml of water.
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Which physical law most directly describes the motions of objects that are acted on by forces?
A.
Newton's law of universal gravitation
B.
Newton's second law of motion
C.
Coulomb's law of electrostatic interaction
D.
the conservation of mass law
Answers
Answer: Newton's second law of motion
Explanation:
Two concrete spans of a 280 m long bridge areplaced end to end so that no room is allowedfor expansion. If the temperature increases by 20◦C, whatis the height to which the spans rise whenthey buckle? Assume the thermal coefficientof expansion is 1.2 × 10^−5(◦C)^−1Answer in units of m.
Answers
Length of the bridge(L) : 280 m
There are 2 spans, so: initial lenght of each span
Li = L/2 = 280 /2 = 140 m
The increase in temperature makes the lengths increase:
Lf = Li ( 1 + ∝ΔT)
Li = initial lenght of each span = 140m
∝= thermal coefficient of expansion = 1.2 × 10^−5(◦C)^−1
ΔT= change in temperature = 20°C
Replacing:
Lf = (140) ( 1 + (1.2 × 10^−5) (20) )) = 140.0336 m
Apply the Pythagorean theorem to find the height that each span rises due to thermal expansion.
h = √Lf^2 - Li^2 = √ (140.0336 ^2 - 140 ^2 ) = 3.067 m
A ball is thrown upwards with initial velocity 20 m/s. After reaching maximum height, on the way down it strikes a bird which is 10 m above the ground. What is the velocity of the ball when it hits the bird?
Answers
I know acceleration would be -9.8 m/s^2 (to assume free fall), the initial velocity would be 20, and that the final position would be 10, but I don't know how to find the max height to then use to find the final velocity.
Just set this up as a quadratic function. I assume that we start from a height of zero, since you don't say.
h(t) = 20t - 4.9t^2
Now, you want to solve
20t - 4.9t^2 = 10
t = 0.583, 3.498
Since v=20-9.8t, that would make
v(3.498) = 20-9.8*3.498 = -14.28
You don't need to find the max height for this problem, but that occurs when v=0. So, h(2) = 20.4
Anyways goodluck!