Question

On a school playground, a child of mass m sits in a swing and is swinging back and forth. The seat of the swing is supported by two chains, each of length R. When the child is at the lowest point in the swinging motion, the tension in each chain is T. (Use any variable or symbol stated above along with the following as necessary: g.)a)What is the child's speed at the lowest point?v=b)What is the force exerted by the seat on the child at the lowest point? (Enter the magnitude. Neglect the mass of the seat.)n=

Answer 1

Answer:

Part a)

$v = \sqrt{\frac{(mg + 2T)R}{m}}$

Part b)

$F_n = 2(mg + T)$

Explanation:

Part a)

When child is at lowest position of the swing

then we will have

$mg + 2T = F_{net}$

here we know that net force on the child is given as

$F_{net} = \frac{mv^2}{R}$

so we have

$mg + 2T = \frac{mv^2}{R}$

$v = \sqrt{\frac{(mg + 2T)R}{m}}$

Part b)

Force exerted by the seat on the child is the normal force and its equation is given as

$F_n - mg = \frac{mv^2}{R}$

$F_n - mg = mg + 2T$

$F_n = 2(mg + T)$