Answer:
Explanation:
Writing out the Newton's Law pf Cooling:
dT/dt = -k * (T - A),
where T is the temperature of the coffee, A is the room temperature, and k is a positive constant.
If the coffee cools from 100°C to 90°C in 1 minute at a room temperature of 25°C,
T = 100
A = 25
dT = 100 - 90 = 10
dt = 1
Putting the figures into the equation:
10/1 = -k * (100 - 25)
k = -10/75°C
After 4 minutes, dT/4 = 10/75 (100 - 25) = 10
dT = 40
Temperature after 4 minutes = 100 - 40 = 60°C
The temperature of a cup of coffee varies according to Newton's Law of Cooling, the temperature of the coffee after 4 minutes is approximately 67°C.
To tackle this problem, we can apply Newton's Law of Cooling's differential equation and solve it using variable separation.
dT/dt = -k(T - A)
At t = 0 (initial condition): T = 100°C
At t = 1 minute: T = 90°C
dT/dt = -k(T - A)
At t = 0: dT/dt = -k(100 - 25)
So,
-10 = -k(75)
k = 10/75
Separating variables and integrating, we have:
1/(T - A) dT = -k dt
∫(1/(T - A)) dT = ∫(-k) dt
ln|T - A| = -kt + C
ln|100 - 25| = 0 + C
ln|75| = C
So, the equation will be:
ln|T - A| = -kt + ln|75|
ln|(T - 25)/(75)| = -kt
Now,
ln|((T - 25)/(75))| = -(10/75)(4)
|((T - 25)/(75))| = [tex]e^{(-40/75)[/tex]
T - 25 = ± 75 * [tex]e^{(-40/75)[/tex]
T = 25 ± 75 * [tex]e^{(-40/75)[/tex]
T ≈ 25 ± 42.42
Therefore, the temperature of the coffee after 4 minutes is approximately:
T ≈ 25 + 42.42 = 67.42°C
Thus, the temperature of the coffee after 4 minutes is approximately 67°C.
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According to Newton's First Law, what will an object in straight-line motion
tend to do?
O A. Slow down because of friction
B. Speed up
C. Stay in straight-line motion
D. Experience a force
Answer:
It will remain in straight-line motion at constant speed until acted on by an
external force. Moreover, it'll not only tend to do that ... it'll actually do it.
Explanation:
11. The measurement of an object's mass is a
a. physical change
b. physical property
c. chemical
d. chemical property
change
The isotope of an atom containing 40 protons and 51 neutrons suddenly has two neutrons added to it.
What isotope is created?
Answer:
91 :)
Explanation:
What are two differences and two similarities between applied force and tension force
Answer:
similarities: They are both members of an action reaction-pair and are produced by electromagnetic forces between the particles. In the case of tension a force is acting to separate the molecules from their equilibrium position, the tension is the resistance to this separatio; that is the electrical attraction among the charged particles that opposes the action of the applied force. In the case of the normal force when gravity pulls an object downward, the electrons of the two surfaces are pulled so close that they mutually reject each other. This rejection between the electrons of the 2 surfaces produces the normal force, acting in opposition to gravity.
Differences: The main difference between tension and force is the direction of force. ... Tension is a force pulling something apart, such as a force pulling apart on the ends of a rope. You often calculate tension in pulley problems. A force is a more general term applying to pushing or pulling on something.
Explanation:
i hope this helps you :)
Waste of points. Claim if you want.
long narrow uniform stick of length ! and mass m lies motionless on ice (assume the ice provides a frictionless surface). The center of mass of the stick is the same as the geometric center (at the midpoint of the stick). The moment of inertia of the stick about its center of mass is lcm . A puck (with putty on one side) has same mass m as the stick. The puck slides without spinning on the ice with a speed of v0 towards the stick, hits one end of the stick, and attaches to it. You may assume that the radius of the puck is much less than the length of the stick so that moment of inertia of the puck about its center of mass is negligible compared to Icm . (a) How far from the midpoint of the stick is the center of mass of the stick-puck combination after the collision?
Answer:
the answer would be 0 as known to the lengthExplanation:
0m x96 would put as an mass of 900 into 0 so there for your answer would be 0
I need to know the answer to this and I do not need an explanation
Answer:
3rd sentence
Explanation:
the center of mass is located a distance x from the less-dense end. Explain how Blake can determine the location of the center of mass
Blake can determine the center mass by dividing the product of less dense and its position by the sum of the two end densities.
What is center mass?The center mass of an object is the point on the object where the weighted relative position of the distributed mass sums to zero.
Blake can determine the location of the center mass as follows;
Let the end position of the high dense = 0Let the density of the "high dense end" = ρ₁Let the density of the "less dense end" = ρ₂[tex]C_{xm }= \frac{\rho_1 (0) + \rho(x)}{\rho_1 + \rho_2} \\\\C_{xm }= \frac{\rho(x)}{\rho_1 + \rho_2}[/tex]
Thus, Blake can determine the center mass by dividing the product of less dense and its position by the sum of the two end densities.
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Pls help me
What is the acceleration of a 10 kg mass pushed by a 5 N force?
Answer:
The answer is 0.5m/s²
Explanation:
Acceleration=Force ÷mass
= 5÷10=0.5m/s²
the filament of an electric lamp, which draws a current of 0.5 a is used for 2 hours. calculate the amount of charge flowing through the circuit
Answer:
I = 0.25 AND T= 4 HOURS, Q = ??
multiply both min and sec , 240 and 60
we get 1400 sec
the formula for current is I = Q/T
substitute the given data in the formula and simplify it
so , Q = 3600C
Describe the sequence of the formation of the solar system. Make sure you include these terms: solar nebula, planetesimals, protoplanets, protosun, condensation, accretion, differentiation, Jovians, terrestrials.
Answer:
Explanation:
e Sun and planets began to form in a rotating cloud of nebular gas and dust. These materials eventually clumped together with a hot protosun at the center and chunks of planetesimals rotating around it. Through repeated collisions, the planetesimals grew into protoplanets, and eventually the solar system came about.
The sequence of the solar system formation is started from sun and the planet's origination 4.6 billion years ago from the solar nebula, a cloud of gas and dust.
What is the solar system?The solar system consists of the planet's satellites, as well as numerous comets, asteroids, and meteoroids, as well as the interplanetary medium.
The Sun and planets formed in a revolving cloud of nebular gas and dust. These components finally clumped together, creating a hot proton in the middle with fragments of planetesimals orbiting around it.
Planetesimals developed into protoplanets as a result of repeated collisions, and the solar system finally formed.
Hence,the sequence of the solar system formation is started from sun and the planet's origination 4.6 billion years ago from the solar nebula, a cloud of gas and dust.
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Through an orbit what remains constant ?
a. Kinetic energy
B. Potential energy
C. Total energy
D. Work
Answer:
c. Total energy
Explanation:
An "orbit" is a path for an object to follow. An example of an object is the "satellite."
At certain points in the orbit, the satellite increases its speed and decreases its speed in relation to the gravity caused by the Earth. As it moves farther away from the Earth, its speed slows down. So, this means that the kinetic energy changes. It also gains and loses height which is responsible for the changes occurring regarding potential energy. This is true for elliptical motion of satellites.
However, the total mechanical energy (TME) of the satellite remains the same or is unchanged (elliptical/circular).
if i got rolled over and then survided and then i would go home then i died what happened
Answer:
you had probably died from the impact
Explanation:
because you got rolled over you would probably died due to your organs being damage and wouldn't function properly
In which soil layer do plant seeds germinate and plant roots thrive?
subsoil
organic
bedrock
topsoil
Answer: Topsoil
Explanation:
Bio
Answer:
topsoil
Explanation:
A baseball is batted. It's a long fly ball. 4 seconds later the ball reaches the outfield 100 meters away and returns to the height from which it left the bat. Determine the horizontal component of the ball's initial velocity in magnitude, in m/s,
Answer:
25 m/s
Explanation:
First we should define the variables
T=4
Dx = 100
ay=-9.8
ax=0
We can use formula 1 from the BIG 5
x=(v+v0)t/2
By plugging in our variables we can get 100=4(v+v0)/2
Which is 50=v+v0
v=v0 since horizontal acceleration always equals zero
so 2v0 = 50
v0 = 25
When a force of 50 newtons acts on a mass of 10 kilograms, what is the resulting
acceleration in m/s2?
Answer:
The answer is 5 m/s²Explanation:
The acceleration of an object given it's mass and the force acting on it can be found by using the formula
[tex]a = \frac{f}{m} \\ [/tex]
where
f is the force
m is the mass
From the question we have
[tex]a = \frac{50}{10} \\ [/tex]
We have the final answer as
5 m/s²Hope this helps you
A race starts and finishes a race that is 50,000m. (30miles). The time is 23 minutes. The final velocity is 67m/s. What is the average acceleration ?
Use acceleration formula
Answer:
a = 0.0505 [m/s^2]
Explanation:
In order to solve this formula we must use the following formula of kinematics.
[tex]x=(v_{o} *t)+(\frac{1}{2} )*a*t^{2}[/tex]
where:
x = distance = 50000 [m]
Vo = initial velocity = 0
a = acceleration [m/s^2]
t = time = 23 [min] = 1380 [s]
Note: the positive sign in the above equation shows that the car accelerates.
50000 = (0*1380) + (0.5*a*1380^2)
a = 0.0525 [m/s^2]
But we can calculate the acceleration using the following formula:
[tex]v_{f} =v_{o} +a*t[/tex]
where:
Vf = final velocity = 67 [m/s]
67 = 0 + (a*1380)
a = 0.0485 [m/s^2]
We can see that by means of kinematics and with the given values we can find two values of accelerations, however, we can determine the average acceleration, by means of the mathematical average.
a = (0.0485 + 0.0525) / 2
a = 0.0505 [m/s^2]
A slingshot is used to shoot a BB at a velocity of 96 feet per second straight up from ground level. When will the BB reach its maximum height of 144 feet?
The time taken for the BB to reach its maximum height is 1.5 seconds.
What is time?Time can be defined as the measure of duration or period of past, present or future event.
To calculate the time it will take BB to reach the maximum height,
la we use the formula below
Formula:
v = d/t............ Equation 1Where:
v = velocityd = distance/heightt = timeMake t the subject of the equation
t = d/v............ Equation 2From the question,
Given:
d = 144 feetv = 96 feet/secondSubstitute these values into equation 2
t = 144/96t = 1.5 seconds.Hence, The time taken for the BB to reach its maximum height is 1.5 seconds.
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3. For a constant launch speed, what angle produces the same range
as a launch angle of
a) 30°?
b) 15°?
Answer:
A) 60 degrees B) 75 degrees
Explanation:
You use complementary angles to solve this. A complementary angle is when two angles add up to 90 degrees. For A), it says that the angle is 30 degrees. So you can do 90 minus 30 and you get 60. For B), it’s says the angle is 15 degrees. So you do 90 minus 15 and you get 75 degrees.
The less energy a wave has, the ________
Answer:
The less energy a wave has, the smaller the amplitude
Explanation:
Hope this helps!!!
The kinetic energy k of an object in joules is given by the formula k= 1 over 2mv^2 where m is the object’s mass in kilograms and v is it’s velocity in meters per second. An object’s velocity in meters per second, and it’s kinetic energy is 48,000 joules..If it speeds up to 40 meters per second, what is its new kinetic energy
Answer:
Ek = 192000 [J]
Explanation:
Originally missing speed data to solve this problem, we must assume that the original speed is 20 [m/s]. In this way, we can calculate the mass of the object.
48000 = (1/2)*m*(20)^2
m = 240 [kg]
The mass is conserved since it does not change only changes the speed of the body so we can calculate a new kinetic energy.
Ek = (1/2)*240*(40)^2
Ek = 192000 [J]
A cat, which mass 2.5 kg walks on a uniform plank of 4.0m long and mass 6.0kg. Two sawhorses at 0.3m and 2.4m from its right end to support the plank as shown in figure. The cat walks on it from right to the left until a certain position where the plank just begin to tip. Calculate the position of the cat from the left sawhorse when the plank just begin to tip .
Answer:
Explanation:
Let when cat reaches the point L distance from the right end , the plank starts turning about the left sawhorse.
The weight of the plank will at at middle point , ie at 2 m from the right end .
The plank will turn about the left sawhorse . Taking torque about this point of weight of the plank and weight of the cat , we have
2.5 g x ( L - 2.4 ) = 6 x g x ( 2.4 - 2.0 )
2.5 L - 6 = 14.4 - 12
2.5 L = 8.4
L = 3.36
position from left sawhorse = 3.36 - 2.4 = .96 m to the left of left sawhorse.
A student is investigating magnetic fields. The student places four different objects near identical magnets and observes what happens. The student records her observations in the table below. Using data from the table, which argument can the student make about magnetic fields?
a. The effect that a magnetic field has on an object depends on the mass of the object.
b. The effect that a magnetic field has on an object depends on the material of the object.
c. The effect that a magnetic field has on an object depends on the type of magnet used.
d. The effect that a magnetic field has on an object depends on the distance to the object.
Answer:
B. The effect that a magnetic field has on an object depends on the material of the object.
Explanation:
Just makes sense
Based on the data given in the table, the best argument the student can make about magnetic fields is that b. The effect that a magnetic field has on an object depends on the material of the object.
Why can this argument be made?Certain objects have properties that make them easier to be magnetizable than other materials. Crayons and wooden toothpicks for instance, are not magnetizable.
The conclusion that can be made therefore is that the effect of a magnet on an object depends on the material of the object.
In conclusion, option B is correct.
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Object A has a charge of -1 C. Object A has a charge of -1 C. At a given distance, the object with which
charge would be most strongly attracted by object A?*
+1 C
-1 C
+2 C
-2 C
The positive charge with the highest magnitude is +2 C and this charge would be most strongly attracted by object A.
Attraction of opposite charges
Opposite charges have the ability to attract each other while, similar charges repel each other.
The given charge of object A is negative, and it will be strongly attracted to a positive charge.
The greater the positive charge, the greater the force of attraction of object A.
From the given options, the positive charge with the highest magnitude is +2 C and this charge would be most strongly attracted by object A.
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1-1 A carpet is to be installed in a room whose length is measured to be 12.71 m and whose width is measured to be 5.46 m. Find the area and error in the area of the room. (∆L=0.01)
Answer:
Explanation:
Area of the room = Length × Width
Given
Length = 12.71m
Width = 5.46m
Area of the room = 12.71m×5.46m
Area of the room = 69.3966m²
To get the area of the error, we will use the relationship;
∆A/A = {∆L/L + ∆W/W}
∆A/A = {0.01/12.71 + 0.01/5.46}
∆A/A = {0.0007868+ 0.001832}
∆A/A = 0.0026182
∆A = 0.0026182A
Since Area A = 69.3966m²
∆A = 0.0026182(69.3966)
∆A ≈ 0.1817m²
Hence error in the area of the room is 0.1817m²
A 20 ohm lamp and a 5 ohm lamp are connected in series and placed across a potential difference of 50 V.
1. What is the equivalent resistance of the circuit?
2. What is the voltage drop across each lamp?
3. What is the power dissipated in each lamp
Hi there!
1.
Since the two resistors are in series, we can simply add:
[tex]R_T = R_1 + R_2 + ... R_n[/tex]
[tex]R_T = 20 + 5 = \boxed{25 \Omega}[/tex]
2.
In series, the potential difference of each resistor (lamp) ADDS UP. We can begin by finding the current through the circuit using Ohm's law:
[tex]V = IR\\\\I = \frac{V}{R_T}[/tex]
Plug in the values:
[tex]I = \frac{50}{25} = 2 A[/tex]
Now,
we can use Ohm's law to find the individual voltage for each lamp.
20 Ohm lamp:
[tex]V = 2 * 20 = \boxed{40 V}[/tex]
5 Ohm lamp:
[tex]V = 2 * 5 = \boxed{10 V}[/tex]
3.
To solve, we can use the power equation.
[tex]P (\text{Watts})= IV[/tex]
Plug in the values for each.
20 Ohm lamp:
[tex]P = 2 * 40 = \boxed{80 W}[/tex]
5 Ohm lamp:
[tex]P = 2 * 10 = \boxed{100 W}[/tex]
the force F is given in terms of time 'y'all and displacement 'X' by the equation F=AsinBx+CsinDt. what is the dimension of D/B?
Answer:
D/B ahs units of Length over Time
Explanation:
Notice that B is multiplying "x" (displacement) as argument of the sine function, therefore it has to have units of the reciprocal of Length.
Also the constant D is multiplying "t" as argument of the sine function, and as such, it must have units of the reciprocal of time.
Therefore, the quantity D/B must have units of Length over Time.
What is the name of the area around a charged object where the object can exert a force on other charged objects?
A) electric field
B) electric charge
C) electric induction
D) electric force
The name of the area around a charged object where the object can exert a force on other charged objects will be the electric field. Option A is correct.
What is an electric field?An electric field is an electric property that is connected with any location in space where a charge exists in any form. The electric force per unit charge is another term for an electric field.
The electric field formula is as follows:
E = F /Q
Where,
The electric field is denoted by the letter E.
F is the electric force
The charge is Q.
The name of the area around a charged object where the object can exert a force on other charged objects will be the electric field.
Hence option A is correct.
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Speed and velocity are not the same thing.How?
Explanation:
speed only have magnitude whereas velocity have magnitude and direction
100 POINTS QUESTION. PLEASE PROVIDE EXPLANATION
Answer:
t = 0, p = 12.0, v = 6.00
t = 20, p = 112, v = 56.0
t = 25, p = 62.0, v = 31.0
Explanation:
Impulse = change in momentum
J = Δp
FΔt = mΔv
The impulse equals the area under the F vs t graph.
At t = 0 s, the initial velocity is 6.00 m/s, so the momentum is:
p = (2.00 kg) (6.00 m/s)
p = 12.0 kg m/s
From t=0 s to t=20 s, the impulse is:
J = (20 N) (5 s) + ½ (20 N) (5 s) + ½ (-10 N) (10 s)
J = 100 Ns
So the new momentum is:
p = 12.0 kg m/s + 100 kg m/s
p = 112 kg m/s
And the new velocity is:
v = (112 kg m/s) / (2.00 kg)
v = 56.0 m/s
From t=20 s to t=25 s, the impulse is:
J = (-10 N) (5 s)
J = -50 Ns
So the new momentum is:
p = 112 kg m/s − 50 kg m/s
p = 62.0 kg m/s
And the new velocity is:
v = (62.0 kg m/s) / (2.00 kg)
v = 31.0 m/s