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 5 rotations in 20.7 seconds when twirled.
1)Calculate the centripetal acceleration of the wooden block:
2)Calculate the tension in the string acting on the wooden block:
To calculate the centripetal acceleration of the wooden block, we can use the formula:
\(a = \frac{{v^2}}{{r}}\)
Where:
- \(a\) is the centripetal acceleration
- \(v\) is the linear velocity of the wooden block
- \(r\) is the radius of the circular path
To calculate the linear velocity, we first need to determine the angular velocity (ω) of the wooden block. We know that the block makes 5 rotations in 20.7 seconds. One rotation is equal to \(2π\) radians, so the angular velocity can be calculated as:
\(ω = \frac{{2π \cdot \text{{rotations}}}}{{\text{{time}}}}\)
Substituting the given values:
\(ω = \frac{{2π \cdot 5}}{{20.7}}\)
Now, using the angular velocity, we can find the linear velocity by multiplying it by the radius:
\(v = ω \cdot r\)
Substituting the given values:
\(v = \left(\frac{{2π \cdot 5}}{{20.7}}\right) \cdot 0.7\)
Once we have the linear velocity, we can calculate the centripetal acceleration:
\(a = \frac{{v^2}}{{r}}\)
Substituting the values into the formula will give us the answer to the first question.