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DanielleElmas [232]

3 years ago

15

(10%) Problem 10: A 7.25-kg bowling ball moving at 9.85 m/s collides with a 0.875-kg bowling pin, which is scattered at an angle

of θ = 21.5° from the initial direction of the bowling ball, with a speed of 10.5 m/s.

1 answer:

siniylev [52]3 years ago

5 0

Answer

given,

mass of bowling ball = 7.25 Kg

moving speed of the bowling ball = 9.85 m/s

mass of bowling in = 0.875 Kg

scattered at an angle = θ = 21.5°

speed after the collision = 10.5 m/s

angle of the bowling ball

$tan \theta_1 = \dfrac{-[m_2v_2Sin \theta_2]}{m_1v_1 - (m_2v_2cos \theta_2)}$

$tan \theta_1 = \dfrac{-[0.875\times 10.5 \times Sin 21.5^0]}{7.25\times 9.85 - (0.875\times 10.5 \times cos 21.5^0)}$

$tan \theta_1 = \dfrac{-[3.3672]}{62.86}$

$tan \theta_1 = 0.0536$

$\theta_1 =-3.066^0$

b) magnitude of final velocity

$v = \dfrac{-m_2v_2sin\theta_2}{m_1 sin\theta_1}$

$v = \dfrac{-0.875 \times 10.5 sin21.5^0}{7.25 sin(-3.066^0)}$

v = 8.68 m/s

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Answer: Option C

<u>Explanation: </u>

According to Newton’s second law of motion, any external force applied on an object is directly proportional to the mass and acceleration of the object. In order to state this law in terms of acceleration, it is stated that acceleration exhibited by any object is directly proportional to the net force applied on the object and inversely proportional to the mass of the object as shown below:

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So if two objects A and B are identical which means they have same mass, then the acceleration attained by the object will be directly proportionate to the net forces exerted on the objects only.

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Utilizamos la fórmula:

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1) Mechanical energy is conserved in all the situations listed

2) True

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4) The potential energy of the block is 490 J

5) The potential energy of the elevator is 750,000 J

Explanation:

1)

The mechanical energy of an object is the sum of its kinetic energy (KE) and its potential energy (PE):

$E=KE+PE$

Where

KE is the energy due to the motion of the object

PE is the energy due to the position of the object (it can be either gravitational potential energy or elastic potential energy)

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Child on a swing --> there is a continuous conversion between gravitational potential energy and kinetic energy

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Bow and Arrow --> there is a conversion between elastic potential energy of the bow and kinetic energy of the arrow

Roller Coaster --> there is a continuous conversion between gravitational potential energy and kinetic energy

2)

The potential energy of an object is given by

$PE=mgh$

where

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While the kinetic energy is given by

$KE=\frac{1}{2}mv^2$

where

v is the speed of the object

As an object falls to the ground, its height h decreases, therefore the potential energy PE decreases as well. However, the speed of the object, v, increases during the fall, and therefore the kinetic energy KE increases. This means that potential energy is converted into kinetic energy.

3)

Potential energy is the energy possessed by an object due to its position. It can be of two types:

Gravitational potential energy: it is the potential energy due to the position of an object in a gravitational field. It is calculated as $mgh$ , as shown in part 2)
Elastic potential energy: it is the potential energy stored in an elastic object when it is stretched or compressed. It is calculated as $\frac{1}{2}kx^2$ , where k is the spring constant of the elastic object and x is the stretching/compression of the object relative to its equilibrium position.

4)

The potential energy stored in an object held above the ground is given by

$PE=mgh$

where

m is the mass of the object

g is the acceleration of gravity

h is the height of the object relative to the ground

For the object in this problem, we have

m = 10 kg

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h = 5 m

Substituting, we find

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5)

As before, the potential energy of the elevator is given by

$PE=mgh$

where m is its mass and h is its height above the ground.

Here we don't have the mass of the elevator. However, we know its weight:

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But we also know that the weight of an object is equal to the product between its mass and the acceleration of gravity:

$W=mg$

So we can rewrite the potential energy as

$PE=Wh$

and the height of the elevator is

h = 500 m

Therefore, its potential energy is

$PE=(1500)(500)=750,000 J$

Learn more about potential energy:

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3 years ago