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frosja888 [35]
2 years ago
10

A 35.0-kg child swings in a swing supported by two chains, each 3.02 m long. The tension in each chain at the lowest point is 41

4 N.
(a) Find the child's speed at the lowest point.
(b) Find the force exerted by the seat on the child at the lowest point. (Ignore the mass of the seat.)
Physics
1 answer:
n200080 [17]2 years ago
3 0

Answer:

Explanation:

Total tension must support the weight of the child and provide the necessary centripetal force.

    2T = m(g + v²/R)

2(414) = 35.0(9.81 + v²/3.02)

  828 = 35.0(9.81 + v²/3.02)

23.65 = 9.81 + v²/3.02

13.847 = v²/3.02

 41.81 = v²

      v = 6.47 m/s

F = 2(414) = 828 N    (ignoring the weight of the chains and seat)

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A 0.311 kg tennis racket moving 30.3 m/s east makes an elastic collision with a 0.0570 kg ball moving 19.2 m/s west. Find the ve
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<u>Answer</u>:

The velocity of the tennis racket after the collision 14.966 m/s.

<u>Step-by-step explanation:</u>

let the following:

m₁ = mass of tennis racket = 0.311 kg

m₂ = mass of the ball = 0.057 kg

u₁ = velocity of tennis racket before collision = 30.3 m/s

u₂ = velocity of the ball before collision = -19.2 m/s

v₁ = velocity of tennis racket after collision

v₂ = velocity of the ball after collision

Right (+) , Left (-)

An elastic collision is an encounter between two bodies in which the total kinetic energy of the two bodies remains the same.

So, the total kinetic energy before collision = the total kinetic energy after collision.

So, 0.5 m₁ u₁² + 0.5 m₂ u₂² = 0.5 m₁ v₁² + 0.5 m₂ v₂²  ⇒ (1)

Also, the total momentum before collision = the total momentum after collision.

So, m₁ u₁ + m₂ u₂ = m₁ v₁ + m₂ v₂  ⇒ (2)

Solving (1) and (2):

∴ v₁ = [ u₁ * (m₁ - m₂) + u₂ * 2m₂ ]/ (m₁ + m₂)

      = ( 30.3 * (0.311 - 0.057) - 19.2 * 2 * 0.057 ) / ( 0.311 + 0.057)

      = 14.966 m/s.

So, the velocity of the tennis racket after the collision 14.966 m/s.

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