How much force would need to be exerted on a merry-go-round with a mass of 178 kg and a radius of 2.4 m to make the speed of a child sitting on the edge 1.5 m/s within 5 seconds having started from rest?
To calculate the force required to accelerate the merry-go-round, we need to use Newton's second law of motion, which states that force (F) is equal to mass (m) times acceleration (a): F = m * a.
In this case, the force is the centripetal force, which is responsible for making an object move in a curved path. The formula for centripetal force is given by the equation:
F = (m * v^2) / r,
where m is the mass of the child, v is the final speed of the child, and r is the radius of the merry-go-round.
In your case, the mass of the child is not provided, but we can use the mass of the merry-go-round (178 kg) as an approximation. Therefore, the force required can be calculated as follows:
F = (m * v^2) / r
F = (178 kg * (1.5 m/s)^2) / 2.4 m
F = (178 kg * 2.25 m^2/s^2) / 2.4 m
F ≈ 167.25 N.
So, the force that would need to be exerted on the merry-go-round to make the child's speed reach 1.5 m/s within 5 seconds would be approximately 167.25 Newtons.