Answer:
Option (d) is correct.
Explanation:
As the large mass M is found to just balance two of the small mass, m, so
[tex]M=2m\cdots(i)[/tex]
As both the masses M as well as m are forced to go around a bend of 1.0 m at a constant speed of 1.0 m/s.
So, the radius of curvature of the bend (curved path), R= 1.0 m
The speed both the masses, v= 1.0 m/s.
Naturally, without any restriction, all the masses have the tendency to move in a straight line due to its inertia, but here both the masses are moving on the curved path because of the application of the external force on them. This continuous change in the direction is due to the force by the wall of the curved path which is actually the normal reaction by the wall on both the masses.
This reaction force, [tex]F_R[/tex], balance the centrifugal force, F with which the masses have a tendency to go out of the path, the magnitude of this centrifugal force is,
[tex]F = \frac {mv^2}{R}[/tex]
Where m is the mass of the body, v is the speed at that instant, R is the radius of curvature of the path.
So, [tex]F_R=\frac {mv^2}{R}[/tex]
Now, for the small mass, m, the reaction force on it is
[tex]F_R1= \frac {mv^2}{R}[/tex]
[tex]\Rightarrow F_R1= \frac {m(1)^2}{1}[/tex]
[tex]\Rightarrow F_R1= m \cdots(ii)[/tex]
And for the bigger mass, M, the reaction force on it is
[tex]F_R2= \frac {Mv^2}{R}[/tex]
[tex]\Rightarrow F_R2= \frac {M(1)^2}{1}[/tex]
[tex]\Rightarrow F_R2= M[/tex]
By using equation (i), we have
[tex]F_R2= 2m[/tex]
[tex]\Rightarrow F_R2=2F_R1[/tex] [by using (ii)]
[tex]\Rightarrow F_R2 / F_R1 = 2/1[/tex]
So, the ratio of force acting on the bigger mass M to the magnitude of the force acting on the smaller mas m is 2:1.
Hence, option (d) is correct.
A car accelerates from rest. It reaches a velocity of 25m/s in 10 seconds. What was the cars acceleration
Answer:
a = 2.5 m/s^2
Explanation:
u = 0
v = 25
t = 10
(using first eq. of motion)
a = (v - u) /t
a = (25 - 0) /10
a = 25/10
a = 2.5 m/s^2
if a metal block has as a volume of .035 mL, and a mass of 765.0 mg, what is the density of the block in g/mL?
Given parameters:
Volume of metal block = 0.035mL
Mass of block = 765mg
Unknown:
Volume of metal block = ?
Solution:
Density is the mass per unit volume of a substance.
Density = [tex]\frac{mass}{volume}[/tex]
Mass is the amount of matter in a substance
Volume is space occupied by a substance
Mass of the block in g;
765mg = 765 x 10⁻³ g
= 0.765g
Density = [tex]\frac{0.765}{0.035}[/tex] = 21.86g/mL
The density of the metal block is 21.86g/mL
What is the correct definition of a circuit?
The temperature of a cup of coffee varies according to Newton's Law of Cooling: dT dt equals negative k times the quantity T minus 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, find the temperature, to the nearest degree Celsius of the coffee after 4 minutes.
74
67
60
42
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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What kind of nutrient comes from water and air?
mineral nutrients
non-mineral nutrients
Answer:
The answer is non-mineral nutrients.
Answer:
non-mineral nutrients.
Explanation:
During meiosis maternal and paternal chromosomes that occur in a gamete line up and exchange segments in a process called crossing over. Then they are randomly shuffled as the cell divides. This process results in
Explanation:
Crossing over is the swapping of genetic material that occurs in the germ line. During the formation of egg and sperm cells, also known as meiosis, paired chromosomes from each parent align so that similar DNA sequences from the paired chromosomes cross over one another.
Answer:
Explanation:
After cross-over, the chromosomes are randomly shuffled to the daughter cells as the cell divides. This process results in in gametes that with unique combinations of chromosomes and is called independent assortment.
A car driving down a street has a kinetic energy of 32,000 J. If the car has a mass of 1,600kg, at what velocity is the car moving?
Explanation:
The mechanical energy can be expressed as kinetic and potential energy, given by the equation;
ME=KE+PE
but since the car isn't elevated off the ground nor is it subjected to the restoring force of a spring, we can then say PE=0
ME=KE
The equation of KE=0.5mv²
ME=0.5mv²
32 000=0.5(1600)v²
[tex]v {}^{2} = \frac{32 \: 000}{1600 \times 0.5} [/tex]
[tex]v {}^{2} = \frac{32 \: 000}{800} [/tex]
[tex] {v}^{2} = 40[/tex]
[tex]v = \sqrt{40} = 6.324[/tex]
v=6.324 m/s :)
which types of star cluster is shown
Open star clusters tend to orbit within the disk. Globular star clusters contain hundreds of thousands of stars, and some – like Omega Centauri, shown above – contain millions of stars. Open star clusters tend to contain only hundreds of stars.
A balloon with a negative charge of -2.0×10-8 C is held 2 cm (0.02 m) below a rod with a positive charge of 2.0×10-8 C. What is the force between the balloon and the rod?
The force of attraction between the balloon and the rod is 9 x 10⁻³ N.
Force of attraction between the balloon and the rodThe force of attraction between the balloon and the rod is calculated by applying Coulomb's law as shown below;
[tex]F = \frac{kq_1 q_2}{r^2}[/tex]
where;
r is the distance between the chargesk is Coulomb's constant = 9 x 10⁹ Nm²/C²F = (9 x 10⁹) x (2.0 x 10⁻⁸)²/(0.02)²
F = 9 x 10⁻³ N
Thus, the force of attraction between the balloon and the rod is 9 x 10⁻³ N.
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[tex]\:\:\:\:\:\:\:\:\:\:\star [/tex]We can calculate the force between the balloon and the rod applying "Coulomb's Law". Which states-
[tex]\:\:\:\:\:\:\:\:\:\:\star\:\sf \underline{F_{(air)} = K\times \dfrac{ q_1 q_2}{r^2}} \\ [/tex]
[tex] \:\:\:\:\:\:\:\:\:\:\star\:\sf\underline{F_{(air)} = \dfrac{1}{4\pi \epsilon_{0} } \dfrac{q_1q_2}{r^2} }\\ [/tex]
Where-
q₁ and q₂ are the two cahrges.r is the distance between the charges.[tex]\sf \epsilon_{0} [/tex] is the permittivity of free space.K is the Coulomb's Constant.k = 9×10⁹ Nm²/C²As per question, we are given that -
q₁= 2.0 x 10⁻⁸Cq₂= -2.0 x 10⁻⁸CDistance,r = 0.02 mNow that required values are given, so we can substitute the values into the formula and solve for Force -
[tex] \:\:\:\:\:\:\:\:\:\:\star\:\sf\underline{F_{(air)} = \dfrac{1}{4\pi \epsilon_{0} } \dfrac{q_1q_2}{r^2} }\\ [/tex]
[tex] \:\:\:\:\:\:\:\longrightarrow \sf Force_{(air)}= 9\times 10^9 \times \dfrac{-2\times 10^{-8}\times 2\times 10^{-8} }{(0.02)^2}\\ [/tex]
[tex] \:\:\:\:\:\:\:\longrightarrow \sf Force_{(air)}= -9\times 10^9 \times\dfrac{4\times10^{-16}}{4\times 10^{-4}}\\ [/tex]
[tex] \:\:\:\:\:\:\:\longrightarrow \sf Force_{(air)}= -9\times 10^9 \times\dfrac{\cancel{4}\times10^{-16}}{\cancel{4}\times 10^{-4}}\\ [/tex]
[tex] \:\:\:\:\:\:\:\longrightarrow \sf Force_{(air)} = -9\times 10^9 \times 10^{-16} \times 10^{4}\\ [/tex]
[tex] \:\:\:\:\:\:\:\longrightarrow \sf Force_{(air)} = -9\times 10^9 \times 10^{-16+4} \\ [/tex]
[tex] \:\:\:\:\:\:\:\longrightarrow \sf Force_{(air)} = -9\times 10^9 \times 10^{-12} \\ [/tex]
[tex] \:\:\:\:\:\:\:\longrightarrow \sf Force_{(air)} = -9\times 10^{9-12}\\ [/tex]
[tex] \:\:\:\:\:\:\:\longrightarrow \sf Force_{(air)} = -9\times 10^{-3}\\ [/tex]
[tex] \:\:\:\:\:\:\:\longrightarrow \sf \underline{Force_{(air)} = -9\times 10^{-3}\:N}\\ [/tex]
Therefore,the force between the balloon and the rod is -9 x 10⁻³ N.The space station Babylon 5 has a diameter of 1 miles, and rotated around its long axis to produce artificial gravity for its inhabitants. It completes 1 revolutions/min. Calculate the effective gravitational strength at the outer rim of the station, in units of g. (use g = 9.81 m/s^2)
This question involves the concept of artificial gravity.
The effective gravitational strength at outer rims is "0.9 g".
Artificial GravityThe effective gravitational strength at the outer rims can be given by the following formula:
[tex]v=\frac{1}{2\pi}\sqrt{\frac{a_c}{r}}\\\\a_c=4\pi^2v^2r[/tex]
where,
[tex]a_c[/tex] = effective gravitational strength = ?v = rotational speed = 1 rev/min = 0.0167 rev/sr = radius = diameter/2 = 1 mile/2 = 0.5 miles = 804.672 mTherefore,
[tex]a_c = 4\pi^2(0.0167\ rev/s)^2(804.672\ m)\\a_c =8.82\ m/s^2\\\\In\ terms\ of\ g:\\\\a_c=(8.82\ m/s^2)(\frac{g}{9.81\ m/s^2})\\\\a_c = 0.9g[/tex]
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What happens to pressure if temperature increases?
what were formed after the big bang theory?
Answer:
neutrons protons electrons
Explanation:
after the Big Bang, the universe was filled with neutrons, protons, electrons, anti-electrons, photons and neutrinos.
The current is 0.720 A in a circuit in which a battery of emf 12.0 V is connected to a resistor of resistance 14.5 Ω. Find the potential difference across the terminals of the battery.
Answer:
explain the meaning of the term work done and give an example of where work is done
What do you need to do before you can make a hypothesis?
Can someone help me please :( ASAP. Also I’m sorry if it’s small
Answer:
Graph #2
Explanation:
Notice, on the position time graph, there is a constant rate of change. This means that there is a constant velocity, meaning it's a straight line. The line is decreasing so the velocity will be negative.
it is more difficult to climb a vertical staircasethan a slanted one
Answer:
it's because of friction
Explanation:
In slanted one the friction will be less so it would be more difficult to climb
the density of gold is 19kg/cm³ find the volume of a) 38g b)0.095kg. solve this question and give explanation i will mark you as brainlist
Answer:
a) 0.002 cm³
b) 0.005 cm³
Explanation:
density d = 19 kg/cm³
Given mass m, find volume V
The definition of density is
d = m/V
so V = m/d
a) m = 38 g = 0.038 kg
so V = 0.038/19 = 0.002 cm³
b) m = 0.095 kg
V = 0.095/19 = 0.005 cm³
Select the correct answer.
What is proper technique for lifting?
A.
Bend your back
B.
Bend at your knees and lift with your legs.
C.
Focus your power from your back.
D.
None of the above
Answer:
B
Explanation:
Answer:
i think it's either B or C
Explanation:
A Home Depot worker pushes a lumber cart loaded with a mass of 115 kilograms of lumber. If he accelerates the cart with an acceleration 5.6m/s^2 what is the amount of force the worker applied.
Answer:
use math.way
Explanation:
i solved it.
will there be a mega tsunami like in the movie tidal wave from 2009?
A 400 N student climbs up a 3.0 m ladder in 4.0s.
a)How much work does the student do?
b)What is the student’s power output?
Answer:
We are given that the student has a weight of 400N
So, the force applied by the boy has to be added to 400 since he has to apply force to keep his body on the stairs
We are given:
u = 0 m/s
v = v m/s
t = 4 s
a = a m/s/s
s = 3 m
w = 400 N
Converting to Mass
w = m * g (where m is the actual mass and g is the value of gravity)
letting g = 10m/s/s
400 = 10 * m
m = 40 kg
Finding Acceleration:
From the second equation of motion:
s = ut + (a*t*t) / 2
3 = (0)(4) + (a)(4)(4)/2
3 = 8a
a = 3/8 m/s/s
Force Applied by the Student:
Now that we have the acceleration, we can find the force applied by the student to go up the stairs
F = ma (Newton's second law of motion)
F = (40)(3/8)
F = 15 N
Hence, the student is applying 15N to climb up the stairs and another 400 N to support his mass
Total Force applied by the Student:
F(total) = F(climbing) + F(weight)
F(total) = 15 + 400
F(total) = 415 N
Work done by the Student:
Work done = F.S (dot product of force applied and displacement)
Work done = (415)(3)
Work done = 1245 Joules
Power Output of the Student:
power output is the amount of work done per second
Power = Work Done / t
Power = 1245 / 4
Power = 311.25 Watt
**note that the this is just the power consumed by the student to climb the stairs**
An object on the surface of the earth weighs 90 lb. At two earth radii above the surface, It will welgh:
270 lb.
10 lb.
90 lb.
30 lb.
An unbalanced force of 20 N is applied to a 10 kg mass. What is the acceleration of the mass?
Answer:
2 m/s2
Explanation:
Newton's 2nd law:
F=ma
20 N= (10 kg)a
a= 2 m/s2
Time management skills include
A. A personal mission statement, prioritizing, and deep breathing.
B. Setting objectives, knowing your limits, and reviewing.
C. Avoiding distractions, setting dreams, and budgeting time.
D. Budgeting time, avoiding stress, and prioritizing.
Answer:
D.
Explanation:
Budgeting time, avoiding stress, and prioritizing.
An experiment is set up to determine the speed of charged particles as they move through a region that is traversed by a constant electric and a constant magnetic field. The particles are moving toward the right of the page when they encounter the region. The electric field points toward the top of the page, and the magnetic field points out of the page. Required:
Predict how the positively and negatively charged particles of various speeds will behave in this experiment
The deflection will be toward the backside for bad cost and closer to the pinnacle of the spread page for the high-quality charge.
What are charged particles?Charged particles are simply defined as particles with an electric charge on them. This may sometimes result in being an ion, as a molecule with excess or a reduced amount of electrons relative to protons.
Generally, the Magnetic area points internal the airplane so through fleming left hand rule is
F = q ( V x B). Ie
hence
qVB = qE
V= E/B then no deflection.
V > E/B then magnetic pressure is dominant over electric powered force.
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The projectile motion of an object can
be described by two independent
vector components that are
______
Answer:
perpendicular
Explanation:
The projectile motion of an object can be described by two independent vector components that are horizontal and vertical motion.
What is projectile motion?The motion of an item hurled or projected into the air, subject only to gravity's acceleration, is known as projectile motion.
The item is known as a projectile, and the course it takes is known as a trajectory. Falling object motion is a simple one-dimensional kind of projectile motion with no horizontal movement.
The projectile's motion is divided into two parts: horizontal and vertical motion.
Because perpendicular motion components are independent of one another, these two motion components may be treated individually.
Hence two independent vector components are horizontal and vertical motion.
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What does it mean to say that mass is conserved during a physical change
Answer: When there is no change in chemical composition of a substance then it is known as physical change. When we say that mass is conserved during a physical change then it means that total mass of the substance or object will remain the same from beginning till the end
Answer:
Sample Response: When a physical change occurs, the mass of the substance is conserved. This means that the total mass of the substance remains the same from beginning to end. The physical properties of the substance, such as size and shape, may change, but the amount of matter in the substance does not change.
Explanation:
median of 18 24 17 21 24 16 29 18
Answer:
19.5
Explanation:
16,17,18,18,21,24,24,29
(fourth (18) and fifth(21)) ÷2=
(18+21)÷2=
39÷2=
19.5 is median
the refractive index is the blank of the speed of light in a medium to the speed of light in a vacuum
Answer:
ratio
Explanation:
Apex Verified
A rock weighing 250N falls from a height of 16 m and falls towards the ground. Determine the momentum of the rock prior to striking the ground.
Answer: I'm not very good at all. I need help with determine the velocity of an object just before it hits the ground, given the object's mass and the distance it falls. For example, a .060 kg (or 60 g) ball falls from a 12 meter building. Also, assume it is free falling (no air resistance) and the average time it takes to hit the ground it 1.16 seconds.
Explanation: