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Katarina [22]
3 years ago
13

Whats the mass of the sun times pi?

Physics
1 answer:
Ivan3 years ago
3 0
6.24894195 × 1030<span> kilograms</span>
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A cart, which has a mass of 2.30 kg is sitting at the top of an inclined plane, which is 4.50 meters long and meets the horizont
expeople1 [14]

Answer:

a) The gravitational potential energy before the cart rolls down the incline is 24.6 J.

b) The magnitude of the force that causes the cart to roll down is 5.47 N.

c) The acceleration of the cart is 2.38 m/s²

d) It takes the cart 1.94 s to reach the bottom of the incline.

e) The velocity of the cart at the bottom of the inclined plane is 4.62 m/s.

f) The kinetic energy of the cart as it reaches the bottom of the incline is 24.6 J.

g) The work done by the gravitational force is 24.6 J.

Explanation:

Hi there!

a) The gravitational potential energy is calculated using the following equation:

EP = m · g · h

Where:

EP = gravitational potential energy.

m = mass of the object.

g = acceleration due to gravity.

h = height at which the object is located.

The height of the inclined plane can be calculated using trigonomoetry:

sin 14.0° = height / lenght

sin 14.0° = height / 4.50 m

4.50 m · sin 14.0° = height

height = 1.09 m

Then, the gravitational potential energy will be:

EP = m · g · h

EP = 2.30 kg · 9.81 m/s² · 1.09 m = 24.6 J

The gravitational potential energy before the cart rolls down the incline is 24.6 J.

b) Please, see the attached figure for a graphical description of the problem and the forces acting on the cart. The force that causes the cart to accelerate down the incline is the horizontal component of the weight (Fwx in the figure). The magnitude of this force can be obtained using trigonometry:

sin 14° = Fwx / Fw

The weight of the cart (Fw) is calculated as follows:

Fw = m · g

Fw = 2.30 kg · 9.81 m/s²

Fw = 22.6 N

Then, the x-component of the weight will be:

FW · sin 14° = Fwx

22.6 N · sin 14° = Fwx

Fwx = 5.47 N

The magnitude of the force that causes the cart to roll down is 5.47 N.

c)Using the equation of Fwx we can calculate the acceleration of the cart:

Fwx = m · a

Where "m" is the mass of the cart and "a" is the acceleration.

Fwx / m = a

5.47 N / 2.30 kg = a

a = 2.38 m/s²

The acceleration of the cart is 2.38 m/s²

d) To calculate the time it takes the cart to reach the bottom of the incline, let´s use the equation of position of the cart:

x = x0 + v0 · t + 1/2 · a · t²

Where:

x = position of the cart at time t.

x0 = initial position.

v0 = initial velocity.

a = acceleration.

t = time.

Considering the initial position as the point at which the cart starts rolling (x0 = 0) and knowing that the cart starts from rest (v0 = 0), let´s find the time it takes the cart to travel the 4.50 m of the inclined plane:

x = 1/2 · a · t²

4.50 m = 1/2 · 2.38 m/s² · t²

2 · 4.50 m / 2.38 m/s² = t²

t = 1.94 s

It takes the cart 1.94 s to reach the bottom of the incline.

e) The velocity of the cart at the bottom of the inclined plane can be obtained using the following equation:

v = v0 + a · t

v = 0 m/s + 2.38 m/s² · 1.94 s

v = 4.62 m/s

The velocity of the cart at the bottom of the inclined plane is 4.62 m/s.

f) The kinetic energy can be calculated using the following equation:

KE = 1/2 · m · v²

Where:

KE =  kinetic energy.

m = mass of the cart.

v = velocity of the cart.

KE = 1/2 · 2.30 kg · (4.62 m/s)²

KE = 24.6 J

The kinetic energy of the cart as it reaches the bottom of the incline is 24.6 J.

The gain of kinetic energy is equal to the loss of gravitational potential energy.

g) The work done by the gravitational force can be calculated using the work-energy theorem: the work done by the gravitational force is equal to the negative change in the gravitational potential energy:

W = -ΔPE

W = -(final potential energy - initial potential energy)

W = -(0 - 24.6 J)

W = 24.6 J

This can also be calculated using the definition of work:

W = Fw · d

Where "d" is the distance traveled in the direction of the force, that is the height of the inclined plane:

W = 22.6 N · 1.09 m = 24.6 J.

The work done by the gravitational force is 24.6 J.

4 0
3 years ago
How many electrons have been removed from a positively charged electroscope if it has a net charge of 1.6× 10−13 C?
Alexxx [7]

Answer:

Tu mujhe banaye ga face dekh aapna mirror me

6 0
2 years ago
Read 2 more answers
You are observing a spacecraft moving in a circular orbit of radius 100,000 km around a distant planet. You happen to be located
Natalija [7]

To solve this problem we will apply the concepts related to centripetal acceleration, which will be the same - by balance - to the force of gravity on the body. To find this acceleration we must first find the orbital velocity through the Doppler formulas for the given periodic signals. In this way:

v_{o} = c (\frac{\lambda_{max}-\bar{\lambda}}{\bar{\lambda}}})

Here,

v_{o} =  Orbital Velocity

\lambda_{max} = Maximal Wavelength

\bar{\lambda}} = Average Wavelength

c = Speed of light

Replacing with our values we have that,

v_{o} = (3*10^5) (\frac{3.00036-3}{3})

<em>Note that the average signal is 3.000000m</em>

v_o = 36 km/s

Now using the definition about centripetal acceleration we have,

a_c = \frac{v^2}{r}

Here,

v = Orbit Velocity

r = Radius of Orbit

Replacing with our values,

a = \frac{(36km/s)^2}{100000km}

a= 0.01296km/s^2

a = 12.96m/s^2

Applying Newton's equation for acceleration due to gravity,

a =\frac{GM}{r^2}

Here,

G = Universal gravitational constant

M = Mass of the planet

r = Orbit

The acceleration due to gravity is the same as the previous centripetal acceleration by equilibrium, then rearranging to find the mass we have,

M = \frac{ar^2}{G}

M = \frac{(12.96)(100000000)^2}{ 6.67*10^{-11}}

M = 1.943028*10^{27}kg

Therefore the mass of the planet is 1.943028*10^{27}kg

7 0
3 years ago
According to ancient greek thought, what is the difference between violent and natural motion
zzz [600]
Natural was thought to be straight up or straight down and violent was thought to be the result of a push or pull
7 0
3 years ago
G=(6.67x10^-11 Nm^2/Kg^2)(6.4x10^23 Kg)<br> /3396km^2
QveST [7]

Answer:

search it up baby girl

Explanation:

..

7 0
3 years ago
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