100 g mass is attached to a string 75 cm long. swings in a horizontal circle. The mass goes around its path once every 0.8. seconds.
What is centripetal acceleration of the object?
What is the tension in the string?
To find the centripetal acceleration of the object, we can use the formula:
a = (v^2) / r
where:
a is the centripetal acceleration,
v is the velocity of the object, and
r is the radius of the circular path.
First, let's find the velocity (v) of the object. The velocity can be calculated by dividing the circumference of the circular path by the time taken to complete one revolution:
v = (2πr) / T
where:
v is the velocity,
r is the radius of the circular path, and
T is the time taken to complete one revolution.
Given that the radius (r) is 75 cm (or 0.75 m) and the time taken (T) is 0.8 seconds, we can substitute these values into the formula to find the velocity:
v = (2π * 0.75) / 0.8
v ≈ 5.89 m/s (rounded to two decimal places)
Now that we have the velocity, we can substitute it into the centripetal acceleration formula:
a = (5.89^2) / 0.75
a ≈ 45.95 m/s^2 (rounded to two decimal places)
So, the centripetal acceleration of the object is approximately 45.95 m/s^2.
To find the tension in the string, we can use the centripetal force formula:
F = m * a
where:
F is the centripetal force,
m is the mass of the object, and
a is the centripetal acceleration.
Given that the mass (m) is 100 g (or 0.1 kg) and the centripetal acceleration (a) is approximately 45.95 m/s^2, we can substitute these values into the formula to find the centripetal force:
F = 0.1 * 45.95
F ≈ 4.59 N
So, the tension in the string is approximately 4.59 N.