suppose the hammer has a mass of 7.26kg, the wire is 1.00m long, and the force keeping the hammer moving in a circle is 7.43 x 10^3N. what will the hammer's speed be when the thrower releases the wire?
Centripetal force= mv^2/r
solve for v.
31.99
To calculate the speed of the hammer when the thrower releases the wire, we can use the concept of centripetal force. Centripetal force is the force required to keep an object moving in a circular path.
The centripetal force can be determined using the formula:
Fc = (m * v^2) / r
Where:
Fc is the centripetal force
m is the mass of the object
v is the velocity of the object
r is the radius of the circular path
In this case, the force keeping the hammer moving in a circle is given as 7.43 x 10^3 N, the mass of the hammer is 7.26 kg, and the length of the wire is 1.00 m.
Rearranging the formula, we can solve for the velocity:
v = √(Fc * r / m)
Plugging in the values:
v = √((7.43 x 10^3 N) * (1.00 m) / (7.26 kg))
Calculating the expression in the square root:
v ≈ √(10152.98 N⋅m / 7.26 kg)
v ≈ √1399.65 m^2/s^2
Taking the square root:
v ≈ 37.42 m/s
Therefore, the hammer's speed when the thrower releases the wire is approximately 37.42 m/s.