a child sitting 1.10 m from the center of a merry go round moves with a speed of 1.25 m/s. calculate the centripetal acceleration of the child and the net horizontal force exerted on the child (mass = 25 kg).
so i did a = 1.25^/1.1 = 1.42 m/s^2
then F =ma = 25(1.42) = 35.5N is that right?
The centripetal acceleration is
a = V^2/R and the force is
F = m a = m V^2/R.
m = 25 kg
V = 1.25 m/s
R = 1.10 m
Do the numbers.
Oh, why did the child sit so far from the center of the merry go round? It's like they're chasing the magic candy or something! Well, let's calculate the centripetal acceleration and the net horizontal force for our daring little rider.
To find the centripetal acceleration, we can use the formula:
a = v^2 / r
Where:
a is the centripetal acceleration
v is the speed of the child (1.25 m/s)
r is the distance from the center (1.10 m)
Plugging in the values, we get:
a = (1.25 m/s)^2 / 1.10 m
And after some number crunching, we find that the centripetal acceleration of the child is approximately 1.42 m/s^2.
Now, for the net horizontal force, we can use Newton's second law, which states:
Fnet = m * a
Where:
Fnet is the net force
m is the mass of the child (25 kg)
a is the centripetal acceleration we just calculated (1.42 m/s^2)
Substituting the values, we have:
Fnet = 25 kg * 1.42 m/s^2
Which gives us a net horizontal force of approximately 35.5 N. That's a pretty strong force holding our little adventurer in place!
To calculate the centripetal acceleration of the child, we can use the formula:
Centripetal acceleration (a) = (velocity (v))^2 / radius (r)
where velocity (v) is the speed of the child and radius (r) is the distance between the child and the center of the merry go round.
Given:
Speed of the child (v) = 1.25 m/s
Distance of the child from the center (r) = 1.10 m
Substituting these values into the formula, we have:
a = (1.25 m/s)^2 / 1.10 m
Calculating this:
a = 1.5625 m^2/s^2 / 1.10 m
a ≈ 1.4205 m/s^2
Therefore, the centripetal acceleration of the child is approximately 1.4205 m/s^2.
To calculate the net horizontal force exerted on the child, we can use Newton's second law of motion:
Force (F) = mass (m) × acceleration (a)
Given:
Mass of the child (m) = 25 kg
Centripetal acceleration (a) = 1.4205 m/s^2 (as calculated above)
Substituting these values into the formula, we have:
F = 25 kg × 1.4205 m/s^2
Calculating this:
F = 35.5125 N
Therefore, the net horizontal force exerted on the child is approximately 35.5125 N.