Question: A 39.0-kg child swings in a swing supported by two chains, each 2.94 m

Question

Question:

A 39.0-kg child swings in a swing supported by two chains, each 2.94 m long. The tension in each chain at the lowest point is 352 N.

(a) Find the child's speed at the lowest point.
( )m/s

(b) Find the force exerted by the seat on the child at the lowest point. (Ignore the mass of the seat.)
( )N (upward)

Question:

A coin placed 30.4 cm from the center of a rotating, horizontal turntable slips when its speed is 49.8 cm/s.

(a) What force causes the centripetal acceleration when the coin is stationary relative to the turntable?

( static friction - inertia - kinetic friction - centrifugal force ) whisch one of those ?

(b) What is the coefficient of static friction between coin and turntable?

( )

Explanation / Answer

(A)
F(n) = 2*T - m*g = m*a

where
T is the tension (since there is two chains, we multiply it by two),
m is the mass,
g = 9.81 m/s^2,
a is acceleration in the normal direction

a = v^2 / r

where
v is the speed
r is the radius. So substituting this equation into our original equation we have:

2*T - m*g = m*(v^2 / r)

Solving for v, we get:

2*(352) - (39)*(9.8) = (39)*(v^2/2.94)
v = 4.93 m/s
Child's speed at the lowest point, v = 4.93 m/s

Part B)
Since the tension in the chain at the lowest point is 352 N, we know that since there are two chains, the force exerted by the seat is simply:

F = 2*(350)
F = 704 N
Force exerted by the seat on the child at the lowest point, F = 704 N

Please post seperate question in seperate post.

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