Why is the halo of a galaxy the most important part of a galaxy?

i)  The average resistive force acting on the car is approximately 2.4 × 10³ N. ii)  The kinetic energy of the car is 3,888 J. b) The average braking force exerted on the car is coming to rest is approximately 259.2 N. ii)  The average braking force exerted on the car is coming to rest is approximately 259.2 N. 2) c) The change in temperature of each rear brake is approximately 0.907 Kelvin.

i) Given information:

Mass of the car (m) = 960 kg

Speed of the car (v) = 9.0 m/s

The angle of the slope (θ) = 15°

Resistive force (Fr) = m × g × sin(θ)

Fr = 960 × 9.8 × sin(15°)

Fr = 2.4 × 10³ N

Therefore, the average resistive force acting on the car is approximately 2.4 × 10³ N.

(ii) To calculate the kinetic energy of the car, we can use the formula:

Kinetic energy (KE) = (1/2) × m × v²

KE = (1/2) × 960 × (9.0)²

KE = 3,888 J

Therefore, the kinetic energy of the car is 3,888 J.

(b) The average braking force exerted on the car is:

Average braking force = Change in kinetic energy/braking distance

Average braking force = KE / braking distance

Average braking force = 3,888 / 15

Average braking force = 259.2 N

Therefore, the average braking force exerted on the car in coming to rest is approximately 259.2 N.

(ii) The work done by a force can be calculated using the formula:

Work = Force × Distance × cos(θ)

3,888 = Force × 15 × cos(0°)

Since cos(0°) = 1, the equation simplifies to:

3,888 = Force × 15

Force = 3,888 ÷ 15

Force = 259.2 N

Therefore, the average braking force exerted on the car in coming to rest is approximately 259.2 N.

2) (c) To calculate the change in temperature of each rear brake, we can use the formula:

Change in heat energy = mass × specific heat capacity × change in temperature

Change in heat energy = Work

The work done by the braking force is equal to the product of the force and the braking distance (15 m),

Therefore, the change in heat energy for each brake is:

Change in heat energy = Work = Force × braking distance

Change in heat energy = 259.2 × 15 = 3,888 J

Now, we can use the formula to find the change in temperature:

Change in heat energy = mass × specific heat capacity × change in temperature

3,888  = 5.2 × 900 × change in temperature

change in temperature ≈ 0.907 K

Therefore, the change in temperature of each rear brake is approximately 0.907 Kelvin.

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Answer: The weight of the cannonball on Earth is 200 N

Explanation:

Weight is defined as the force exerted by the body on any surface. It is also defined as the product of mass of the body multiplied by the acceleration due to gravity.

Mathematically,

[tex]W=mg[/tex]

where,

W = weight of the cannonball

m = mass of the cannonball = 20 kg

g = acceleration due to gravity on Earth = [tex]10m/s^2[/tex]

Putting values in above equation, we get:

[tex]W=20kg\times 10m/s^2=200N[/tex]

Hence, the weight of the cannonball on Earth is 200 N

The angular momentum of the projectile about the origin when the particle is at the following locations is zero

A projectile of mass m is launched with an initial velocity making an angle θ with the horizontal as shown below (attached). The projectile moves in the gravitational field of the Earth. The angular momentum of the projectile about the origin when the particle is at the following locations. (Use the following as necessary: vi, θ, m, and g for the acceleration due to gravity.)

[tex]L=r x p[/tex]

Angular momentum is zero because there is no r.  Since the angular momentum depends on then cross product of the position vector and momentum vector which is in the same direction as velocity, therefore the formula for the angular momentum can be written as [tex]mvr_{perpendicular}[/tex], where the cross product component of r vector along/parallel to velocity/momentum is 0.

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The amplitude is 2.30mm, frequency is 118 Hz, wavelength is 0.899 m, wave speed is 106 m/s, the wave is moving in the direction of decreasing x, tension in the rope is 28 N and the average power transmitted by the wave is approximately 0.38W.

The wave function of a travelling wave on a thin rope is given by y(x,t) = 2.30mm * cos[(6.98rad/m) * x + (742 rad/s) * t]. From this equation, we can derive the following information:

Amplitude - This is the maximum displacement of a point on the wave and is determined by the coefficient before the cosine in the equation. Therefore, the amplitude is 2.30mm.

Frequency - This can be obtained by dividing the wave speed by the wavelength. The coefficient in front of the 't' in the equation is equivalent to 2π times the frequency (since there are 2π rad in one wave cycle). Therefore, the frequency f = (742 rad/s)/(2π) = 118 Hz.

Wavelength - This is represented by the reciprocal of the coefficient in front of 'x' in the equation. Therefore, the wavelength λ = 2π/(6.98 rad/m) = 0.899 m.

Wave Speed - This can be found by multiplying frequency and wavelength together. Hence, wave speed v = f * λ = 118 Hz * 0.899 m = 106 m/s.

Direction the wave is travelling - The symbol '+' in front of 't' in the equation tells us that the wave is moving in the direction of decreasing x.

Tension in the rope - This can be found using the wave speed that we have already calculated and the rope's mass per unit length µ (mass/length = 0.00338 kg / 1.35 m = 0.00250 kg/m). The tension T can be calculated using the formula v = sqrt(T/µ), which gives T = µ * v² = 0.00250 kg/m * (106 m/s)² = 28 N.

Average power transmitted by the wave - The power P carried by wave is given by the formula P = 0.5 * µ * v * A² * ω², where A is the amplitude, ω is the angular frequency (which is the coefficient in front of 't' in the equation). Substituting the values we find: P = 0.5 * 0.00250 kg/m * 106 m/s * (2.30 mm)² * (742 rad/s)² ≈ 0.38 W.

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