A 0.25 kg stone tied to a 0.5 m string whirls at a speed of 4 m/s. What is the centripetal acceleration acting on the stone?
V^2/R is the acceleration. You don't need to know the mass unless you want the centripetal FORCE.
V = 4 m/s and 0.5 m is the radius, R.
To find the centripetal acceleration acting on the stone, we can use the formula
\[ a_c = \frac{v^2}{r} \]
where:
\( a_c \) is the centripetal acceleration,
\( v \) is the speed of the object in meters per second (m/s),
and \( r \) is the radius of the circular path in meters (m).
In this case, the speed of the stone is given as 4 m/s, and the radius of the circular path, which is the length of the string, is 0.5 m.
Substituting these values into the formula, we have:
\[ a_c = \frac{4^2}{0.5} \]
Simplifying:
\[ a_c = \frac{16}{0.5} = 32 \, \text{m/s}^2 \]
Therefore, the centripetal acceleration acting on the stone is \( 32 \, \text{m/s}^2 \).