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valkas [14]
2 years ago
11

A rock of mass m is thrown straight up into the air with initial speed |v0 | and initial position y = 0 and it rises up to a max

imum height of y = h. A second rock with mass 2m (twice the mass of the original) is thrown straight up with an initial speed of 2|v0 |. What maximum height does the second rock reach?
Physics
1 answer:
REY [17]2 years ago
7 0

Answer:

Explanation:

Case 1:

mass = m

initial velocity = vo

final velocity = 0

height = y

Use third equation of motion

v² = u² - 2as

0 = vo² - 2 g y

y = vo² / 2g       ... (1)

Case 2:

mass = 2m

initial velocity = 2vo

final velocity = 0

height = y '

Use third equation of motion

v² = u² - 2as

0 = 4vo² - 2 g y'

y ' = 4vo² / 2g

y' = 4 y

Thus, the second rock reaches the 4 times the distance traveled by the first rock.

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3 years ago
A spring with spring constant 15 N/m hangs from the ceiling. A ball is attached to the spring and allowed to come to rest. It is
Lana71 [14]

Answer:

a

   m  = 0.169 \ kg

b

  |v_{max} |=  0.5653 \ m/s

Explanation:

From the question we are told that

    The  spring constant is  k =  14 \ N/m

     The  maximum extension of the spring is  A =  6.0 \ cm  =  0.06 \ m

     The number of oscillation is  n  =  30

      The  time taken is  t  =  20 \ s

Generally the the angular speed of this oscillations is mathematically represented as

           w = \frac{2 \pi}{T}

where T is the period which is mathematically represented as

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substituting values

     T  =  \frac{20}{30 }

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       w =  9.421 \ rad/s

this angular speed can also be represented mathematically as

       w =  \sqrt{\frac{k}{m} }

=>   m  =\frac{k }{w^2}

substituting values

      m  =\frac{ 15 }{(9.421)^2}

      m  = 0.169 \ kg

In SHM (simple harmonic motion )the equation for velocity is  mathematically represented as

        v =  - Awsin (wt)

The  velocity is maximum when  wt = \(90^o) \ or \ 1.5708\ rad

     v_{max} = -  A* w

=>   |v_{max} |=  A* w

=>    |v_{max} |=   0.06 * 9.421

=>   |v_{max} |=  0.5653 \ m/s

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