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nata0808 [166]
3 years ago
10

A pendulum of length l=5.0m attached to the ceiling carries a ball of mass 10.0 kg. The ball (a massive bob) is moved from its s

tationary equilibrium position to some distance such that the pendulum’s rope makes an angle of 60∘∘ with the vertical and then is released and allowed to swing. What is the total energy of the system at the moment of release in joules? Assume the lowest point on the trajectory to be y=0. (Do not include unit in answer)
Physics
1 answer:
never [62]3 years ago
3 0

Answer:

    Em₀ = 245 J

Explanation:

We can solve this problem with the concepts of energy conservation, we assume that there is no friction with the air.

Initial energy the highest point

        Em₀ = U

        Em₀ = m g h

The height can be found with trigonometry

The length of the pendulum is L and the length for the angle of 60 ° is L ’, therefore the height from the lowest point is

         h = L - L’

         cos θ = L ’/ L

         L ’= L cos θ

          h = L (1 - cos θ)

We replace

         Em₀ = m g L (1- cos θ)

Let's calculate

         Em₀ = 10 9.8 5.0 (1 - cos 60)

         Em₀ = 245 J

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What can you infer about a wave with a short wavelength?
raketka [301]

Answer:

- It can be infer that it has a lower frequency.

<em>In the case of electromagnetic waves.</em>

- A short wavelength means a lower energy,

Explanation:

The wavelength is the distance between two consecutive crests or valleys while the frequency is the number of crests that pass for a specific point in an interval of time.

For example, a person makes laundry once a weak.

In this example, the event is represented by the laundry and the interval of time is once a weak

The velocity of a wave is defined as:

v = \nu \cdot \lambda  (1)

Where nu is the frequency and \lambda is the wavelenth

\lambda =  \frac{v}{\nu}  (2)

Notice from equation 2 that the wavelength is inversely proportional to the frequency (when the wavelength increases the frequency decreases).

In the case of electromagnetic waves, a short wavelength means a lower energy, as it can be seen in equation 4 (inversely proportional).

E = h\nu  (3)

E = \frac{hc}{\lambda} (4)

8 0
3 years ago
Read 2 more answers
A roller coaster car may be approximated by a block of mass m. Thecar, which starts from rest, is released at a height h above t
elena55 [62]

Answer:

The first part can be solved via conservation of energy.

mgh = mg2R + K\\K = mg(h-2R)

For the second part,

the free body diagram of the car should be as follows:

- weight in the downwards direction

- normal force of the track to the car in the downwards direction

The total force should be equal to the centripetal force by Newton's Second Law.

F = ma = \frac{mv^2}{R}\\mg + N = \frac{mv^2}{R}

where N = 0 because we are looking for the case where the car loses contact.

mg = \frac{mv^2}{R}\\v^2 = gR\\v = \sqrt{gR}

Now we know the minimum velocity that the car should have. Using the energy conservation found in the first part, we can calculate the minimum height.

mgh = mg2R + \frac{1}{2}mv^2\\mgh = mg2R + \frac{1}{2}m(gR)\\gh = g2R + \frac{1}{2}gR\\h = 2R + \frac{R}{2}\\h = \frac{5R}{2}

Explanation:

The point that might confuse you in this question is the direction of the normal force at the top of the loop.

We usually use the normal force opposite to the weight. However, normal force is the force that the road exerts on us. Imagine that the car goes through the loop very very fast. Its tires will feel a great amount of normal force, if its velocity is quite high. By the same logic, if its velocity is too low, it might not feel a normal force at all, which means losing contact with the track.

7 0
3 years ago
An electron moves with velocity v⃗ =(5.8i−6.7j)×104m/s in a magnetic field B⃗ =(−0.81i+0.60j)T.
Minchanka [31]

Answer:

Fₓ = 0,  F_{y} = 0  and  F_{z}<em> = - 3.115 10⁻¹⁵   N</em>

Explanation:

The magnetic force given by the expression

       F = q v xB

the bold are vectors,  the easiest analytical way to determine this force in solving the determinant

   F = q \left[\begin{array}{ccc}i&j&k\\5.8&-6.7&0\\-0.81&0.6&0\end{array}\right]  10^{4}

   F = 1.6 10⁻¹⁵ [ i( 0-0) + j (0-0) + k^( 5.8 0.60 - 0.81 67) ]

   F =i^0 + j^0   - k^  3.115 10⁻¹⁵   N

   

Fₓ = 0

F_{y} = 0

F_{z}<em> = - 3.115 10⁻¹⁵   N</em>

6 0
3 years ago
What is the difference between kinetic and potential energy and how do they work?
Iteru [2.4K]

To explain, I will use the equations for kinetic and potential energy:

PE = mgh\\KE = \frac{1}{2}mv^{2}

<h3>Potential energy </h3>

Potential energy is the potential an object has to move due to gravity.  An object can only have potential energy if 1) <u>gravity is present</u> and 2) <u>it is above the ground at height h</u>.  If gravity = 0 or height = 0, there is no potential energy.  Example:

An object of 5 kg is sitting on a table 5 meters above the ground on earth (g = 9.8 m/s^2).  What is the object's gravitational potential energy?  <u>(answer: 5*5*9.8 = 245 J</u>)

(gravitational potential energy is potential energy)

<h3>Kinetic energy</h3>

Kinetic energy is the energy of an object has while in motion.  An object can only have kinetic energy if the object has a non-zero velocity (it is moving and not stationary).  An example:

An object of 5 kg is moving at 5 m/s.  What is the object's kinetic energy?  (<u>answer: 5*5 = 25 J</u>)

<h3>Kinetic and Potential Energy</h3>

Sometimes, an object can have both kinetic and potential energy.  If an object is moving (kinetic energy) and is above the ground (potential), it will have both.  To find the total (mechanical) energy, you can add the kinetic and potential energies together.  An example:

An object of 5 kg is moving on a 5 meter table at 10 m/s.  What is the objects mechanical (total) energy?  (<u>answer: KE = .5(5)(10^2) = 250 J; PE = (5)(9.8)(5) = 245 J; total: 245 + 250 = 495 J</u>)

7 0
3 years ago
A 10 kg box is 1.3 m above the ground. How much potential energy does it have? (g on Earth of 9.8 m/s?
Volgvan
Potential energy = mgh
Potential energy = 10 x 9.8 x 1.3
Potential energy = 127.4 J
8 0
3 years ago
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