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ziro4ka [17]
3 years ago
12

(a) What is the angular speed ω about the polar axis of a point on Earth's surface at a latitude of 55° N? (Earth rotates about

that axis.) (b) What is the linear speed v of the point? What are (c) ω and (d) v for a point at the equator? (Note: Earth radius equals 6370 km and let one day be 24 hours)
Physics
1 answer:
Vaselesa [24]3 years ago
6 0

Answer

given,

radius of earth = 6370 km

earths latitude = 55° N

time  = 24 hour = 86400 s

angular speed = ω

a) \omega = \dfrac{2\pi}{T}

\omega = \dfrac{2\pi}{86400}

\omega = 7.27 \times 10^{-5}rad/s

b) v = r\omega cos\theta

v = 6370\times 7.27 \times 10^{-5}\times cos 55^0

v = 266 m/s

c) ω at equator

\omega = \dfrac{2\pi}{T}

\omega = \dfrac{2\pi}{86400}

\omega = 7.27 \times 10^{-5}rad/s

d) v = r\omega cos\theta

v = 6370\times 7.27 \times 10^{-5}\times cos 0^0

v = 463 m/s

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The lemon trees will always be the same so they are the constants. The independent variable is the water amount because it is changing. The dependent variable is the amount of lemons because it is the variable being tested. (If we change the amount of water how many lemons will be produced?)

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2 years ago
A hamster in it's ball starts at rest and accelerates to 3ms1 in 6 seconds.
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Explanation:

Ball starts from rest . Time taken = 6 seconds. Distance travelled by ball. ∴Distance travelled = 9 m

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7 0
2 years ago
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
A force has both______ and _______. Question 1 options: Speed and impact Magnitude and direction Motion and speed Direction and
Travka [436]

Answer:

magnitude

and direction

Explanation:

5 0
2 years ago
A frame hanging on a wall is held by two cables. The tension in each cable is 30 N, and the cables make an angle of 45° with the
Vesna [10]

Answer:

(D) 42.4N

Explanation:

Since the frame is at rest, the net force acting on it must be 0. There are three forces acting on it: the gravity and the opposing forces of the two cables.

Since the gravity is a vertical force, we are only interested in the vertical components of the remaining forces. The net force equation is

F_net = 0 = F_g -2 * F_y

The vertical force of one cable (using the information in the drawing) is:

F_y = 30N * sin 45 deg = 21.21N

Now the weight can be determined:

0 = F_g - 2 * F_y

F_g= 2 * F_y = 2 * 21.21N = 42.4N

The weight of the frame is about 42.4N.


6 0
3 years ago
Read 2 more answers
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