A child moves with a speed of 5.40 m/s when positioned 14.0 m from the center of a merry-go-round. Calculate the net force (in newtons) exerted on the child, whose mass is 26.0 kg.

To calculate the net force exerted on the child, we can use the centripetal force equation:

F = (m * v^2) / r

where:
F is the net force,
m is the mass of the child,
v is the velocity of the child, and
r is the radius of the merry-go-round.

Given:
m = 26.0 kg (mass of the child)
v = 5.40 m/s (velocity of the child)
r = 14.0 m (radius of the merry-go-round)

Plugging in the values, we have:

F = (26.0 kg * (5.40 m/s)^2) / 14.0 m

Simplifying the equation, we get:

F = (26.0 kg * 29.16 m^2/s^2) / 14.0 m

Now, canceling out the unit of meters, we have:

F = 26.0 kg * 29.16 m/s^2 / 14.0

Calculating this, we get:

F ≈ 54.286 N

Therefore, the net force exerted on the child is approximately 54.286 newtons.