a 45 kg boy sits on a horse on a carousel 5.0 m from the center of the circle. he makes a revolution every 8.0 s.
calculate his speed.
what is centripetal force acting on the boy?
a = v^2/r = 5(2π/8)^2
F = ma
To calculate the speed of the boy, you can use the formula for calculating the circumference of a circle. The circumference of a circle is given by the formula:
Circumference = 2 * π * radius
In this case, the radius is given as 5.0 m. So, substituting the radius into the formula, we have:
Circumference = 2 * π * 5.0 m
Next, we need to find the time taken for one revolution, which is given as 8.0 s. The speed is calculated by dividing the circumference by the time:
Speed = Circumference / Time
Substituting the values we have calculated, we get:
Speed = (2 * π * 5.0 m) / 8.0 s
Now we can solve for the speed:
Speed = (2 * 3.14 * 5.0 m) / 8.0 s
= (31.4 m) / 8.0 s
= 3.925 m/s
Therefore, the speed of the boy is approximately 3.925 m/s.
To calculate the centripetal force acting on the boy, you can use the formula for centripetal force:
Centripetal Force = Mass * Velocity² / Radius
The mass of the boy is given as 45 kg. We have already calculated the velocity to be 3.925 m/s, and the radius is still 5.0 m. Substituting these values into the formula, we have:
Centripetal Force = 45 kg * (3.925 m/s)² / 5.0 m
Simplifying further:
Centripetal Force = 45 kg * (15.405625 m²/s²) / 5.0 m
= 136.46484375 N
Therefore, the centripetal force acting on the boy is approximately 136.46 N.