Tarzan, whose mass is 90.0 kg swings from a vine that is 3.0 meters long. His speed at the bottom of the swing is 4.0 m/s. What is his centripetal acceleration? How much centripetal force acted on him to keep him swinging in a circle?
To find Tarzan's centripetal acceleration, we can use the formula:
a = v² / r
where:
a = centripetal acceleration
v = velocity
r = radius
Given that Tarzan's speed at the bottom of the swing is 4.0 m/s and the length of the vine is 3.0 meters, we can substitute these values into the formula:
a = (4.0 m/s)² / 3.0 m
a = 16.0 m²/s² / 3.0 m
a ≈ 5.33 m/s²
Therefore, Tarzan's centripetal acceleration is approximately 5.33 m/s².
To calculate the centripetal force acting on Tarzan, we can use the formula:
F = m * a
where:
F = centripetal force
m = mass
a = centripetal acceleration
Given that Tarzan's mass is 90.0 kg and the centripetal acceleration is approximately 5.33 m/s², we can substitute these values into the formula:
F = 90.0 kg * 5.33 m/s²
F ≈ 479.7 N
Therefore, the centripetal force acting on Tarzan to keep him swinging in a circle is approximately 479.7 N.