A bucket of mass m is attached to a rope that is wound around the outside of a solid sphere (I = 2/5 M^2) of radius R. When the bucket is allowed to fall from rest, it falls with an acceleration of a down. What is the mass of the sphere in terms of m, R, a, and g?
Answer:
[tex]\displaystyle \sqrt{\frac{(5/2)\, (g - a)\, m\, R^{2}}{M^{2}\, a}}[/tex], assuming that the tension in the rope is the only tangential force on the sphere ([tex]g[/tex] denote the gravitational acceleration.)
Explanation:
The forces on the bucket are:
Weight of the bucket: [tex]m\, g[/tex] (downward.)Tension in the rope (upward.)Since the weight of the bucket and the tension from the rope are in opposite directions, the magnitude of the net force would be:
[tex]\begin{aligned} \|\text{Net Force}\| =\; & \|\text{Weight}\| - \|\text{Tension}\| \end{aligned}[/tex].
The upward tension in the rope prevents the bucket from accelerating at [tex]g[/tex] (free fall.) Rather, the bucket is accelerating at an acceleration of only [tex]a[/tex]. The net force on the bucket would be thus [tex]m\, a[/tex].
Rearrange the equation for the net force on the bucket to find the magnitude of the tension in the rope would be:
[tex]\begin{aligned} & \|\text{Tension}\| \\ =\; & \|\text{Weight}\| - \|\text{Net Force}\| \\ =\; & m\, g - m\, a \\ =\; & (g - a)\, m\end{aligned}[/tex].
At a distance of [tex]R[/tex] from the center of the sphere, the tension in the rope [tex](g - a)\, m[/tex] would exert a torque of [tex](g - a)\, m\, R[/tex] on the sphere. If this tension is the only tangential force on this sphere, the net torque on the sphere would be [tex](g - a)\, m\, R\![/tex].
Let [tex]M[/tex] denote the mass of this sphere. The moment of inertia of this filled sphere would be [tex]I = (2/5)\, M^{2}[/tex].
Therefore, the magnitude of the angular acceleration of this sphere would be:
[tex]\begin{aligned}& \|\text{Angular Acceleration}\| \\ =\; & \frac{\|\text{Net Torque}\|}{(\text{Moment of Inertia})} \\ =\; & \frac{(g - a)\, m\, R}{(2/5)\, M^{2}} \end{aligned}[/tex].
The bucket is accelerating at a magnutide of [tex]a[/tex] downwards. The rope around the sphere need to unroll at an acceleration of the same magnitude, [tex]a\![/tex]. The tangential acceleration of the sphere at the surface would also need to be [tex]\! a[/tex].
Since the surface of the sphere is at a distance of [tex]R[/tex] from the center, the angular acceleration of this sphere would be [tex](a / R)[/tex].
Hence the equation:
[tex]\begin{aligned}& \frac{(g - a)\, m\, R^{2}}{(2/5)\, M^{2}} = \|\text{Angular Acceleration}\| = \frac{a}{R} \end{aligned}[/tex].
Solve this equation for [tex]M[/tex], the mass of this sphere:
[tex]\begin{aligned}& \frac{(g - a)\, m\, R^{2}}{(2/5)\, M^{2}} = \frac{a}{R} \end{aligned}[/tex].
[tex]\begin{aligned}M^{2} &= \frac{(g - a)\, m\, R^{2}}{(2/5)\, a} \\ &= \frac{(5/2)\, (g - a)\, m\, R^{2}}{a}\end{aligned}[/tex].
[tex]\begin{aligned}M&= \sqrt{\frac{(5/2)\, (g - a)\, m\, R^{2}}{a}}\end{aligned}[/tex].
Draw free body diagrams for the following objects: (12pts)
1A) A coaster sitting under a cup of coffee.
1B) A car slowing down as it approaches a stop sign.
1C) Your test stuck to your fridge by a magnet.
1D) A baseball just before it leaves the bat.
(a) The force diagram of a coaster sitting under a cup of coffee includes the weight of the coater plus the weight of coffee acting downwards.
(b) The force diagram of a car slowing down as it approaches a stop sign includes force of the car and frictional force opposing the motion.
(c) The force diagram includes the force of the test and action of the fridge which are eqaul and opposite.
(d) The force diagram of baseball before it leaves the bat incudes only the weight of the baseball acting downwards.
Force diagram of coaster sitting under a cup of coffeeThe force diagram of a coaster sitting under a cup of coffee includes the weight of the coater plus the weight of coffee acting downwards.
↑ Fn
Ф Fn = W
↓ W
Where;
W is weight of the coaster plus weight of coffeFn is the normal reactionForce diagram of a car slowing down as it approaches a stop signThe force diagram inlcudes the applied force and frictional force opposing the motion.
Ff ← Ф → F
where;
Ff is the kinetic frictional forceF is force of the carForce diagram of test stuck to your fridgeThe force diagram includes the force of the test and action of the fridge which are eqaul and opposite.
Fb ← Ф → Fa
where;
Fa is the force of the testFb is the force of the fridgeForce diagram of baseball before it leaves the batThe force diagram includes only the weight of the baseball acting downwards.
Ф
↓
W = mg
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Terry is walking down the street at 3 m/s. If he
has a mass of 70 kg, what is his momentum?
[tex]\text{Given that, mass m = 70 kg and velocity v = 3 m/s}\\\\\text{Momentum,}~ p = mv = 70 \times 3 = 210~ kg ~ms^{-1}[/tex]
A combination of two identical resistors connected in series has an equivalent resistance of 12. ohms. What is the equivalent resistance of the combination of these same two resistors when connected in parallel?
Answer:
R1 + R2 = R = 12 for resistors in series - so R1 = R2 if they are identical
2 R1 = 12 and R1 = R2 = 6 ohms
1 / R = 1 / R1 + 1 / R2 for resistors in parallel
R = R1 * R2 / (R1 + R2) = 6 * 6 / (6 + 6) = 3
The equivalent resistance would be 3 ohms if connected in parallel
A student is standing at a distance of 45 m from a wall. He gives a loud clap at the echo is heard 0.3a later. Calculate the speed of sound.
Answer:
300 m/s
Explanation:
2d = vt
v = 2d/t
v = 2×90/.3
v=300 m/s
d = distance
t = time
v = velocity/speed of sound
WHO WANTS BRAINLY?? ANSWER THESE 3 PHYSICS QUESTION!!!
1. What velocity must a car with a mass of 1210 kg have in order to have the same momentum as a pickup truck which has a momentum of 5.6 x 10^4 kg m/s to the east?
2. A 0.50 kg football is thrown with a velocity of 15 m/s to the right. A stationary receiver catches the ball and brings it to rest in 0.020s. What is the force exerted on the receiver?
3. A 0.40 kg soccer ball approaches a player horizontally with a velocity of 18 m/s to the north. The player strikes the ball and cases it to move in the opposite direction with a velocity of 22 m/s. What impulse was delivered to the ball by the player?
1. The car should move with velocity of 46.28 m/s
2. The force exerted on the receiver is 375 N
3. The player delivered an impulse of !.6 N s to the ball
What is Impulse?In Physics, Impulse is the product of mass and change in velocity. from Newtons law change in momentum is equal to impulse
m ( v - u ) = f * t = impulse = momentum
m = mass
v = final velocity
u = initial velocity
f = force
t = time
1.
Given:
mass = 1210 kg
momentum = 5.6 x 10^4 kg m/s
change in velocity = v - u = ?
u = 0 so change in velocity = v
momentum = mass * velocity
velocity = momentum / mass
velocity = 5.6 x 10^4 / 1210
velocity = 46.28 m/s
2.
Given:
m = 0.50 kg
u = 15 m/s
v = 0
t = 0.020 s
m ( v - u ) = f * t
f = 0.50 * ( 0 - 15 ) / 0.02
f = -375 N (the negative sign indicates the direction of the stoppage force as against the force that produces the motion )
force = 375 N
3.
Given:
m = 0.40 kg
u = 18 m/s to the North
v = 22 m/s
m ( v - u ) = impulse
impulse = 0.4 (22 - 18 )
impulse = 1.6 N s
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Fill in the blank with the correct response.
Light striking a mirror at a 45° angle will be reflected at a
list out the use of simple machine
Explanation:
simple machine can multiplayer of speed and force
A student in the Biomechanics class has decided that she would like to make her arms
stronger. She has a mass of 63 kg, She chooses to complete some elbow flexion exercises
using a kettlebell. For this problem, consider the hand and forearm to be a single segment.
The distance from her elbow to her wrist is 22.86 cm.
The force from the kettlebell is applied to her hand, which is 30.48 cm from her elbow joint.
She knows that the moment arm of the elbow extensor muscles about the elbow axis is
Answer:
what is heat and transfer
Which of the following is an arithmetic sequence? A. 2, 1, 4, 3, 6, 5, …
Explanation:
it is not a arithmetic sequence
3,0,-3,-6 is the correct arithmetic sequence. So, the correct option is C.
What is Arithmetic sequence?An arithmetic sequence is defined as a sequence where the common difference between any two consecutive terms is constant. A sequence is explained as a collection of numbers that follow a pattern such as the sequence 2, 7, 12, 17, ... is an arithmetic sequence as there is a pattern where each number is obtained by adding 5 to its previous term. Is performed.
For above given information,
3,0,-3,-6 is the correct arithmetic sequence.
as, d is called as the common difference of the series
d=0 - 3= - 3 - 0 = -6 - (-3)
d= - 3
An arithmetic sequence is called as the equal common difference in each progressive term.
Thus, 3,0,-3,-6 is the correct arithmetic sequence. So, the correct option is C.
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Your question is incomplete, most probably the complete question is:
Which of the following is an arithmetic sequence?
a.2,4,16,32
b.2,3,7,1,
c.3,0,-3,-6
d.5,-5,5,-5
What is the magnitude of the electric field at the dot in the figure?
The magnitude of the electric field at the dot is : 10⁴ v/m
Given that there are three equipotential lines with equal spacing,we will apply the the relationship between P.D and electric field
Determine the magnitude of the electric field at the dotchange in voltage = E .d
100 - 0 = E * ( 1 * 10⁻² m ) ----- ( 1 )
From equation ( 1 )
The magnitude of E = 100 v / ( 1 * 10⁻² m )
= 10⁴ v/m
Hence we can conclude that The magnitude of the electric field at the dot is : 10⁴ v/m
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A spring-loaded ballistic cart measuring 0.68 kg is in contact with a second 0.80 kg
cart. The carts are initially at rest on a level surface. The spring is released and the
lighter cart is observed to move at +0.52 m/s afterward. What is the velocity of the
other cart?
Answer:
wait in comments.................
The Ice and steam points of a certain thermometer are found to be 20 cm apart. What temperatureis recorded in Celsius when the length of mercury theard is 5cm above the ice point mark?
A capacitor of cylindrical shape as shown in the red outline, few cm long carries a uniformly distributed charge of 7.2 uC per meter of length. By constructing a suitable Gaussian surface around the wire, Find the magnitude and direction of the electric field at points (a) 5.5 m and (b) 2.5 m perpendicular from the center of the wire. Show your detailed calculations and comment on the results.
Hi there!
Begin by using Gauss' Law to find the electric field.
[tex]\oint {E \cdot} \, dA = \frac{Q_{encl}}{\epsilon_0}[/tex]
E = Electric field (N/C)
dA = differential area element
Q = enclosed charge (C)
ε₀ = Permittivity of free space (8.85 * 10⁻¹² C²/Nm²)
We can construct a large cylinder around the wire in order to determine the electric flux. The electric field lines will pass through the LATERAL surface area of the cylinder, so:
[tex]A = 2\pi rL[/tex]
Where 'L' is the length of the cylinder and 'r' is the distance from the capacitor.
The enclosed charge is equivalent to the charge per meter length (λ) multiplied by the length, so:
[tex]\oint {E \cdot} \, dA = \frac{\lambda L}{\epsilon_0}[/tex]
We can rewrite the dot product as EA (where cosθ = 1 since the normal vector points in the direction of the field).
A = the lateral surface area of a cylinder, so:
[tex]E * 2\pi rL = \frac{\lambda L}{\epsilon_0}[/tex]
Rearrange to solve for 'E'.
[tex]E = \frac{\lambda L }{2\pi r L \epsilon _0}\\\\E = \frac{\lambda }{2\pi r \epsilon_0}[/tex]
a)
Plug in the distance into 'r'.
[tex]E = \frac{\lambda }{2\pi r \epsilon_0} \\\\E = \frac{0.0000072}{2\pi * 5.5 * (8.85 * 10^{-12})} = \boxed{23542.18 \frac{N}{C}}[/tex]
b)
Repeat:
[tex]E = \frac{\lambda }{2\pi r \epsilon_0}\\\\E = \frac{0.0000072}{2\pi * 2.5 * (8.85 * 10^{-12})} = \boxed{51792.8 \frac{N}{C}}[/tex]
We can see that the distance from the wire is INVERSELY related to the electric field strength by a power of r⁻¹. The field strength DECREASES as the distance INCREASES.
give the mathematical expression for coulombs force if q1,q2 are the magnitude of charges and r is the distance between them.
Give the mathematical expression for coulomb's force if q1, q2 are the magnitude of charges and r is the distance between them.
F=K q1q2/r2
Describe gravitational force in your own words. Which two factors affect the gravitational force between two objects?
Answer:
Gravitational force is the force that attracts objects towards each other. Two factors that affect the gravitational force between objects are the mass of the two objects and the distance between
Explanation:
Gravity is what pulls us towards the Earth if we were to jump into the air, so it is the force that pulls things towards other things. The bigger the objects are the more gravity they have, so a planet has more gravity than say, an apple. Distance between objects also makes their gravity change, so the Earth's pull on the moon is different than the Earth's pull on the sun.
Hopefully this helps- let me know if you have any questions!
Describe gravitational force in your own words. Which two factors affect the gravitational force between two objects?
Answer :-Gravitational Force :- It is the attractive force between the two body having some mass.Example of gravitational force :- attraction between the human and earth . earth pulls the body towards it with the help of this This force helps the celestial bodies to revolve in there orbits Factors effecting Gravitational force:- Mass :- gravitational force directly proportional on the masses of the body between which it is acting [tex]gravitational \: force ∝m{ \tiny1}m{ \tiny2}[/tex]Distance between the masses :- Gravitational force is inversely proportional to the square of the distance between the masses [tex]gravitational \: force∝ \frac{1}{ {r}^{2} } [/tex]Formula of the Gravitational force :-[tex]F = \frac{G m{ \tiny1}m{ \tiny2} }{ {r}^{2} } [/tex]
where
F is gravitational force G is gravitational constant ( universal constant ) m 1 is mass of first body m2 is mass of second body r is the distance between the two bodiesdefine briefly what is second conditionofequilibrium with examples
Which of the following can only be a situation of increasing temperature?
1. The phase change of the material is going from water to solid
2. The height of the object is increasing
3. The objects speed in increasing at a constant rate
4. The average kinetic energy of the particles of a material is increasing
Increasing the temperature causes an increase in the average kinetic energy of the particles of a material.
What is average kinetic energy of particles?The average kinetic energy of particles is the energy possessed by particles due to their constant motion.
The constant motion of particles occurs due to the energy acquired by the particles, when the temperature of the particles increases, the average kinetic energy increases which in turn increases the speed of the particles.
Thus, we can conclude that, increasing the temperature causes an increase in the average kinetic energy of the particles of a material.
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How can you describe the relationship between height and pressure?
Answer:
p = rho× g × h
Explanation:
p: pressure
rho : density
g : gravity acceleration
h : height
A block of mass m = 8.40 kg, moving on a horizontal frictionless surface with a speed 4.20 m/s makes a perfectly elastic collision with a block of mass M at rest. After the collision, the 8.40 block recoils with a speed of 0.400 m/s. In the figure; the blocks are in contact for 0.200 s.
For A block of mass m = 8.40 kg, moving on a horizontal frictionless surface with a speed of 4.20 m/s is mathematically given as
F = 193.2N
What is the magnitude of the average force on the 8.40-kg block, while the two blocks are in contact, is closest to?
Generally, the equation for the magnitude of the average force mathematically given as
F = m(v1+v2)/t
F = 8.40(4.2+O.4)/t
F = 193.2N
In conclusion magnitude of the average force is
F = 193.2N
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When a penny is dropped, it takes 16 seconds. What is its height
A man of mass 70 kg climbs stairs of vertical height 2.5m. Calculate the work done against the force of gravity. (Take g = 9.81 ms?)
Answer:
1716.75 J
Explanation:
Step 1: First check what we are provided with. As per given question we have:
mass (m) = 70 kg, height (h) = 2.5 m and acceleration due to gravity (g) = 9.81 m/s².
Step 2: Check what we are asked to find out.
Work done = Change in Potential energy
The stuff required to solve this question is potential energy. Using the formula: P = mgh. Where P is Potential energy, m is mass, g is acceleration due to gravity and h is height.
Step 3: Substitute the known values in the above formula.
→ P = 70 × 2.5 × 9.81
→ P = 1716.75 J
Hence, the work done against the force of gravity is 1716.75 J.
any help here please ???
Answer:
16 reflection,incidence
The SI unit for weight is ________.
A. mass
B. kilogram
C. newton
D. acceleration of gravity
E. weight
Answer:
Newton
Explanation:
The SI unit for weight is newton.
A person with a mass of 80 kg is at rest. What is their momentum? Write the
number only. *
Your answer
Answer:
0
Explanation:
because no distance covered by body
The gauge pressure in a balloon in measured by means of an open-tube manometer that uses water (density=1.00×103 kg/m3) . What gauge pressure is indicated by a difference of 0.0171 m in the heights of the water columns?
The gauge pressure in the balloon as indicated by a difference of 0.0171 m in the heights of the water columns is 167.58 Pa.
Gauge pressure of the balloon
The gauge pressure in the balloon is the pressure inside the balloon due to the water columns relative to the atmospheric pressure.
The gauge pressure in the balloon as indicated by a difference of 0.0171 m in the heights of the water columns is calculated as follows;
P = ρgΔh
P = (1,000)(9.8)(0.0171)
P = 167.58 Pa
Thus, the gauge pressure in the balloon as indicated by a difference of 0.0171 m in the heights of the water columns is 167.58 Pa.
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Explain why is dressing table mirror may become dirsty if wiped with a cloth on a warm day.
When you rub a dry cloth across glass, it creates charged static electricity, which attracts little non-charged dust particles.
Two identical twins, Sallie and Serena, are playing one December on a large merry-go-round (a disk mounted parallel to the ground on a vertical axle through its center) in their school playground in northern Minnesota. Each twin has a mass of 30.9 kg. The icy coating on the merry-go-round surface makes it frictionless. The merry-go-round revolves at a constant rate as the twins ride on it. Sallie, sitting a distance 1.85 m from the center of the merry-go-round, must hold on to one of the metal posts attached to the merry-go-round with a horizontal force of 59.0 N to keep from sliding off. Serena is sitting at the edge, a distance of 3.64 m m from the center; Serena must also hold on to a metal post on the merry-go-round to keep from sliding off.
Required:
What is the ratio of Serena?s speed to Sallie's speed (both speeds are measured by a stationary observer watching the spinnning merry-go-round)?
For a twin mass of 30.9 kg, sitting at a distance of 1.85 m, with a horizontal force of 59.0 N the ratio of Serena's speed to Sallie's speed is mathematically given as
V= 2.06:1
Generally, the equation for the velocity is mathematically given as
v = w r
Therefore
[tex]\frac{v serena}{vsallie} = \frac{r serena}{r sallie}[/tex]
V= 3.63/1.76
V= 2.06
In conclusion, the ratio is
V= 2.06:1
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When resting, a person generates about 412005 joules of heat from the body. The person is submerged neck-deep into a tub containing 2124 kg of water at 20.9 °C. If the heat from the person goes only into the water, find the water temperature.
If a person generates about 412005 joules of heat from the body, the water temperature is mathematically given as
t=21.6296C
What is the water temperature.?Question Parameter(s):
The person is submerged neck-deep into a tub containing 2124 kg of water at 20.9 °C
Generally, the equation for the Heat is mathematically given as
Heat gained =Heat loess
Thereofore
mw*cw*(t-2160)=1.5*10^5
[tex]t=21.60+\frac{1.5*10^5}{mw*Cw}\\\\t=21.60+\frac{1.5*10^5}{1.2*10^3*4186}[/tex]
t=21.6296C
In conclusion, the tempreature
t=21.6296C
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define what is physics
In my own words, I would say that physics is an area of science that seeks to explain and understand the fundamental nature of the dynamics of objects, essentially defining how objects can interact, in space and in time.