Final answer:
To find the speed at which the hammer will take off when it is released, we can use the concept of circular motion and centripetal force. The formula F = mv^2/r can be used to calculate the velocity. By plugging in the given values, we find that the hammer will take off with a speed of 31.92 m/s.
Step-by-step explanation:
To determine the speed at which the hammer will take off when it is released, we can use the concept of circular motion and centripetal force. The centripetal force required to keep an object moving in a circle is given by the formula F = mv^2/r, where F is the force, m is the mass, v is the velocity, and r is the radius of the circle.
In this case, the force keeping the hammer moving in a circle is 7430 N, the mass of the hammer is 7.26 kg, and the wire is 1.00 m long. The radius of the circle is equal to the length of the wire. Rearranging the formula, we can solve for v:
v = sqrt(Fr/m)
Plugging in the given values:
v = sqrt((7430 N)(1.00 m)/(7.26 kg)) = sqrt(1020.55 m^2/s^2) = 31.92 m/s
Therefore, the hammer will take off with a speed of 31.92 m/s when it is released.