A group of students observes that a wooden block (m = 0.40 kg) on the end of a string with a radius of 0.7 meters makes 12 rotations in 20.7 seconds when twirled.
Calculate the centripetal acceleration of the wooden block:
Calculate the tension in the string acting on the wooden block:
To calculate the centripetal acceleration of the wooden block, use the formula:
ac = (4π²r)/T²
where:
ac = centripetal acceleration
r = radius of the string
T = time for one rotation (period of motion)
Given:
r = 0.7 meters
T = 20.7 seconds / 12 rotations = 1.725 seconds/rotation
Substituting the values into the formula:
ac = (4π² * 0.7) / (1.725²)
Calculating:
ac ≈ 9.6 m/s²
Therefore, the centripetal acceleration of the wooden block is approximately 9.6 m/s².
To calculate the tension in the string acting on the wooden block, use the formula:
T = mac
where:
T = tension in the string
m = mass of the wooden block
ac = centripetal acceleration
Given:
m = 0.40 kg
ac = 9.6 m/s²
Substituting the values into the formula:
T = (0.40 kg) * (9.6 m/s²)
Calculating:
T = 3.84 N
Therefore, the tension in the string acting on the wooden block is 3.84 N.
To calculate the centripetal acceleration of the wooden block, we can use the formula:
a = (4π²r) / T²
Where:
- a is the centripetal acceleration
- π is a mathematical constant, approximately equal to 3.14159
- r is the radius of the circular motion
- T is the time period of one complete rotation
Given:
- r = 0.7 meters
- T = 20.7 seconds (time for 12 rotations)
Let's start by calculating the time period for one complete rotation (t):
t = T / 12
Now, we can plug in the values into the formula to find the centripetal acceleration:
a = (4π² * r) / t²
Next, let's calculate the tension in the string acting on the wooden block. The tension in the string can be found using the formula:
T = m * a
Where:
- T is the tension in the string
- m is the mass of the wooden block
- a is the centripetal acceleration
Given:
- m = 0.40 kg (mass of the wooden block)
- a (centripetal acceleration) can be calculated from the previous step
We can now substitute the values into the formula to calculate the tension in the string (T).
Now, let's perform the calculations to find the answers.
11.9
a=v^2/r=(2PIr/perioid)^2/r
= 4PI^2 r/(12/20.7)
tension= mass*acceleration