Calculate The Magnitude Of The Gravitational Force Exerted On A 4.20 Kg Baby By A 100 Kg Father 0.200 (2023)

Answer:

(a i - 2a j) / 2

Explanation:

a1 = a i

a2 = a j

a3 = - (i + j) (2a) = - 2a i - 2a j

a4 = (i - j) (3a) = 3a i - 3a j

Let the mass of each particle is m.

Use the formula of acceleration of centre of mass

a cm = (m1 a1 + m2 a2 + m3 a3 + m4 a4) / (m1 + m2 + m3 + m4)

a cm = (a i + aj - 2a i - 2a j + 3a i - 3a j) / 4

a cm = ( 2a i - 4a j) / 4

a cm = (a i - 2a j) / 2

Answer:

a)

b) Acceleration = 0.75 m/s²

Explanation:

a) We have force , F = mass x acceleration.

We have force value is same

b) We have

Combined mass

Force

Answer: 4

Explanation:

In order to solve this problem, the Stefan-Boltzmann law will be useful. This law establishes that a black body (an ideal body that absorbs or emits all the radiation that incides on it) "emits thermal radiation with a total hemispheric emissive power proportional to the fourth power of its temperature":

(1)

Where:

is the energy radiated by a blackbody radiator per second, per unit area (in Watts).

is the Stefan-Boltzmann's constant.

is the Surface of the body

is the effective temperature of the body (its surface absolute temperature) in Kelvin.

However, there is no ideal black body (although the radiation of stars like our Sun is quite close). Therefore, we will use the Stefan-Boltzmann law for real radiator bodies:

(2)

Where is the star's emissivity

Knowing this, let's start with the answer:

We have two stars where the emissivity of both is the same:

Star A with a radius and a surface temperature .

Star B with a radius and a surface temperature .

And we are asked to find the ratio of the rate of energy radiated by both stars:

(3)

Where is the rate of energy radiated by Star A and is the rate of energy radiated by Star B.

On the other hand, with the radius of each star we can calculate their surface area, using the formula for tha area of a sphere (assuming both stars have spherical shape):

(4)

(5)

Writting the Stefan-Boltzmann law for each star, taking into consideration their areas:

(6)

(7)

Substituting (6) and (7) in (3):

(8)

(9)

(10)

Finally:

Answer:

(a) 9.36 kHz

(b) 3.12 kHz

Explanation:

(a)

V = speed of sound

= speed of airplane = (0.5) V

f = actual frequency of sound emitted by airplane = 4.68 kHz = 4680 Hz

f' = Frequency heard by the stationary listener

Using Doppler's effect

f' = 9360 Hz

f' = 9.36 kHz

(b)

V = speed of sound

= speed of airplane = (0.5) V

f = actual frequency of sound emitted by airplane = 4.68 kHz = 4680 Hz

f' = Frequency heard by the stationary listener

Using Doppler's effect

f' = 3120 Hz

f' = 3.12 kHz

Answer:

The surface charge density on the plate,

Explanation:

It is given that,

Area of parallel plate capacitor,

Separation between the plates,

Electric field between the plates,

We need to find the surface charge density on the plates. The formula for electric field is given by :

Where

= surface charge density

Hence, this is the required solution.

Answer:

Yes we are right as the force on wire is approx 12500 Lb

Explanation:

Magnetic force on a current carrying bar is given by the equation

here we know that

L = 1.3 m

B = 12 T

i = 4.1 kA

now from above formula we have

So this is equivalent to 12500 Lb force

Explanation:

It is given that,

Radius of earth, r = 6371 km

An earth satellite moves in a circular orbit above the Earth's surface, d = 561 km

So, radius of satellite, R = 6371 km + 561 km = 6932 × 10³ m

Time taken, t = 95.68 min = 5740.8 sec

(a) Speed of the satellite is given by :

d = distance covered

For circular path, d = 2πR

v = 7586.92 m/s

(b) Centripetal acceleration is given by :

Hence, this is the required solution.

The force exerted on the vehicle by the track of mass 2000kg and with a speed of 18m/s is 46600 N.

What is force?

Force is an external agent which is capable of changing an object's state of rest or motion. Force is a push or a pull on an object with some mass that causes it to change its velocity. Force is a vector quantity. This is because it has both magnitude and direction.

The vehicle experiences two forces which are acting on it. The forces include its weight which is pulling it down that is away from the center of the track and the normal force of the track which is pushing up towards the center of the track.

Therefore, the sum of the forces towards the center of the track will be:

∑F = ma

N − mg = m v² / r

where, N = normal force,

m = mass of the object,

g = acceleration due to gravity,

v = velocity of the object,

r = radius of the track

N = mg + m v² / r

N = m (g + v² / r)

Given that, m = 2000 kg, v = 18 m/s, and r = 24 m:

Therefore, N = 2000 (9.8 + (18)² / 24)

N = 46600 N

Therefore, the force exerted on the vehicle by the track is 46600N.

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Answer:

46600 N

Explanation:

The vehicle has two forces acting on it: weight pulling down (away from the center of the track) and normal force of the track pushing up (towards the center of the track).

Sum of the forces towards the center of the track:

∑F = ma

N − mg = m v² / r

N = mg + m v² / r

N = m (g + v² / r)

Given m = 2000 kg, v = 18 m/s, and r = 24 m:

N = 2000 (9.8 + 18² / 24)

N = 46600 N

The track pushes on the vehicle with a force of 46600 Newtons.

Answer:

8.83 rad/s²

Explanation:

w₀ = initial angular speed of the disk = 0 rad/s

w = final angular speed of the disk = 30.3 rad/s

t = time period of rotation of the disk = 3.43 sec

= Angular acceleration of the disk

Angular acceleration of the disk is given as

inserting the values

= (30.3 - 0)/3.43

= 8.83 rad/s²

Answer:

q = 1.815 \times 10^{-8} C

Charge on one plate is positive in nature and on the other plate it is negative in nature.

Explanation:

E = 8.20 x 10^5 V/m, A = 25 cm^2, d = 22.45 mm

According to the Gauss's theorem in electrostatics

The electric field between the two plates

Charge, q = surface charge density x area

q = 1.815 \times 10^{-8} C

Answer:

4 m/s

Explanation:

M = mass of the hammer = 8.91 kg

m = mass of the metal piece = 0.411 kg

h = height gained by the metal piece = 3.88 m

Potential energy gained by the metal piece is given as

PE = mgh

PE = (0.411) (9.8) (3.88)

PE = 15.6 J

KE = Kinetic energy of the hammer

Given that :

Potential energy of metal piece = (0.219) Kinetic energy of the hammer

PE = (0.219) KE

15.6 = (0.219) KE

KE = 71.2 J

v = speed of hammer

Kinetic energy of hammer is given as

KE = (0.5) M v²

71.2 = (0.5) (8.91) v²

v = 4 m/s

Answer:

Explanation:

For gravitational force we know that

F = mg

now we have

Now electrostatic force

here we have

Now magnetic force on it is given by

Answer:

(A) 667.5 N/m

(B)

Explanation:

(A) Let the spring constant be k.

Using the formula F = kx

k = 251 / 0.376

K = 667.5 N/m

(B)

Work done

W = 0.5 × kx^2

W = 0.5 × 667.5 × 0.376 × 0.376

W = 47.2 J

(a) The velocity of the object will be zero at the maximum height

(b) The velocity of the object changes direction.

(c) The acceleration due to gravity will not have the same sign on the way up as on the way down.

(A) The velocity of the object decreases as the object ascends upwards and eventually becomes zero at the maximum height. As the object descends downwards, the velocity increases and becomes maximum before the object hits the ground.

(B) The velocity of the object is always directed in the direction of the motion of the object. As the object moves upward, the direction of the object is upward and as the object moves downwards the direction of the object is downwards. Thus, the velocity of the object changes direction.

(c) The upward motion of the object is opposite direction to acceleration due to gravity and the sign of acceleration due to gravity becomes negative.

As the object moves downwards, it will be moving in the same direction as the acceleration due to gravity. The sign of acceleration due to gravity is positive.

Thus, the acceleration due to gravity will not have the same sign on the way up as on the way down.

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Answer:

a) The velocity is zero when the object is at the highest vertical point (peak). b) Yes, at the peak, the velocity for an instant gets to zero and then the direction of motion and the velocity will be downwards.

C) No, the direction of ‘g’ will be opposite in direction when the object is on the way down when compared to what it was during the upward motion.

Explanation:

a) Since gravity is acting on the object and trying to pull it down to earth, the ball will slow down to a velocity of zero when the ball starts its free fall downward.

b) When the direction of the object changes, its velocity will also change direction.

c) When the ball has a positive velocity, gravity is pulling it in the opposite direction, so it has a negative acceleration trying to slow it down. When the ball's velocity is negative (downward free fall), the acceleration will be positive at the instant when the ball hits the ground. The only way to stop the ball from falling is a positive force upward, which results in a positive acceleration when the ball hits the ground.

Hope this helps :)

Answer:

0.032 m

Explanation:

Consider the forces acting on the block

m = mass of the block = 1.50 kg

= Static frictional force

= Normal force on the block from the wall

= Spring force due to compression of spring

= Force of gravity on the block = mg = 1.50 x 9.8 = 14.7 N

k = spring constant = 860 N/m

μ = Coefficient of static friction between the block and wall = 0.54

x = compression of the spring

Spring force is given as

= kx

From the force diagram of the block, Using equilibrium of force along the horizontal direction, we get the force equation as

=

= kx eq-1

Static frictional force is given as

= μ

Using eq-1

= μ k x eq-2

From the force diagram of the block, Using equilibrium of force along the vertical direction, we get the force equation as

=

Using eq-2

μ k x = 14.7

(0.54) (860) x = 14.7

x = 0.032 m

Answer:

Final temperature = 52.44 °C

Explanation:

We have equation for thermal expansion

ΔL = LαΔT

We have change in length = Circumference of 2.35 cm radius - Circumference of 2.34 cm radius = 2π x 2.35 - 2π x 2.34 = 0.062 cm

Length of eyeglass frame = 2π x 2.34 = 14.70 cm

Coefficient of linear expansion, α = 1.30 x 10⁻⁴ °C⁻¹

Substituting

0.062 = 14.70 x 1.30 x 10⁻⁴ x ΔT

ΔT = 32.44°C

Final temperature = 32.44 + 20 = 52.44 °C

Answer:

- 0.23

0.56

Explanation:

= initial velocity of the particle = =

= final velocity of the particle = =

t = time interval = 4.00 sec

= average acceleration = ?

Using the kinematics equation

= + t

= + (4)

= 4

=

hence

Average acceleration along x-direction = - 0.23

Average acceleration along y-direction = 0.56

Explanation:

The resistance of a wire is given by :

Where

is the resistivity of the wire

l = initial length of the wire

A = initial area of cross section

If length and the area of cross section of the wire is doubled then new length is l' and A', l' = 2 l and A' = 2 A

So, new resistance of the wire is given by :

R' = R

So, the resistance of the wire remains the same on doubling the length and the area of wire.

Answer:

a) 17 N

b) 21 N

Explanation:

At the 3 o'clock position, the sum of the forces towards the center is:

∑F = ma

T = m v² / r

19 = m v² / r

At the 12 o'clock position, the sum of the forces towards the center is:

∑F = ma

T + mg = m v² / r

T + (0.18)(9.8) = 19

T = 17.2 N

At the 6 o'clock position, the sum of the forces towards the center is:

∑F = ma

T − mg = m v² / r

T − (0.18)(9.8) = 19

T = 20.8 N

Rounding to two significant figures, the tensions are 17 N and 21 N.

Answer:

6.6 x 10^5 Nm^2/C

Explanation:

E = 125000 N/C

Area, A = length x width = 2.5 x 5 = 12.5 m^2

θ = 65 degree

electric flux, φ = E A Cosθ

φ = 125000 x 12.5 x Cos 65

φ = 6.6 x 10^5 Nm^2/C

Here, we are required to evaluate the electric flux through the rectangle.

The electric flux through the rectangle is;

φ = 6.6 × 10^5 Nm²/C

The electric flux through a body is given as;

electric flux, φ = E A Cosθ

where;.

• φ = electric flux
• E = Electric field magnitude
• A = Area
• θ = angle between the electric field vector and the vector normal

The Area of the rectangle, A = 2.5 × 5

Therefore, A = 12.5m².

Therefore, the electric flux, φ = E A Cosθ

φ = 125000 × 12.5 × Cos65

φ = 660,341 Nm²/C.

φ = 6.6 × 10^5 Nm²/C

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