As the hammer spins, it's acceleration is produced by its changing direction, even if the velocity remains constant. This is centripetal acceleration and force. To calculate these values, we need to know a little bit about circular motion.
To calculate the speed, you need to know the distance traveled in a period of time. We know the time required is 0.5 seconds, and the distance can be calculated by using the circumference of a circle. The circumference is 2*pi*r or 2*(3.14)*(.6). Therefore the circumference is 3.77 meters, and the velocity is 7.54 meters/second.
To find the acceleration, use the formula for centripetal acceleration, which is v^2/r. (7.54^2)/(0.6) = 95.75 meters per second squared.
Finally, to find the force, you multiply mass times acceleration - 95.75*7 kg, equaling 670.25 Newtons.
In the situation described in this problem, the hammer can be modeled as an object undergoing uniform circular motion. In this kind of motion, the speed of the object is constant, but since the direction of motion is constantly changing (as the object moves around in circle), there is acceleration directed towards the center of the circle, known as centripetal acceleration.
The speed of the hammer can be calculated as v = C/T, where C is the circumference of the circle and T is the time it takes to complete one revolution, 0.50 s. The circumference formula is C = 2*pi*r, where r is the radius of the circle.
Then, v = (2*pi*r)/T = (2*pi*0.60)/(0.50) = 7.5 m/s (rounded to the two significant digits, as are the rest of the given values).
The acceleration of the hammer can be found from the formula for centripetal acceleration:
a_c = v^2/r = (7.5)^2/0.60 = 95 m/s^2.
The centripetal force—that is, the force responsible for the centripetal acceleration—is produced by the tension in the chain attached to the hammer. It equals the product of the hammer's mass and the centripetal acceleration:
F = ma_c = 7*95 N = 670 N (again, rounded to the two significant digits).
Note that this value is much (ten times) greater than the hammer's weight, which is mg = 7*9.8 N = 67 N.
Centripetal force is the force required to keep an object moving in a circle. Objects in motion tend to stay in motion, so, to prevent spinning objects from flying off in the straight line that their momentum would normally carry them, another force, perpendicular to their straight momentum, must accelerate them towards the center of their rotation. When talking about planetary orbits, this force is gravity; when talking about race cars, this force is the friction of tires on asphalt; when talking about the hammer toss, this force is the tension of the string.
To calculate the hammer's centripetal force and acceleration, we need the circular velocity of the hammer. Since we have the rotation time, we can calculate the hammer's speed based on the the circumference of its circuit. This is equal to 2πr = (2)(3.14)(0.6) = ~3.77 meters. The hammer travels that time in half a second, so its velocity is ~7.54 m/s
The Centripetal Acceleration Formula is simple: a = v^2 / r. Plugging in our the velocity from part a and the radius from the prompt, we get (7.54)^2 / 0.6 = ~95.75. The tension on the hammer string is equivalent to an acceleration of 95.75 meters per second squared.
Finally, the force affecting the hammer is simply that acceleration times the mass or 7 * 95.75 = 670.25 Newtons of force.
http://hyperphysics.phy-astr.gsu.edu/hbase/cf.html
http://www.softschools.com/formulas/physics/centripetal_acceleration_formula/71/
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