An athlete whirls a 7.50-kg hammer tied to the end of a 1.1-m chain in a horizontal circle. The hammer moves at the rate of 1.3 rev/s.(a) What is the centripetal acceleration of the hammer?(b) What is the tension in the chain?

Could it be that I've been doing it wrong for the past 40+ years too, unless of course there is a not-so-minute chance that the textbook answer is wrong?

no its just that this is in revolutions per second (goes around the whole circle) when it should be redious per second. most questions just give it in seconds so it would be correct the other way (unless of course it is given in revolutions per second like in this problem).

To find the centripetal acceleration of the hammer, we can use the formula:

a = (v^2) / r

where:
a = centripetal acceleration
v = velocity
r = radius

In this case, we are given that the hammer moves at a rate of 1.3 rev/s. To find the velocity, we need to convert this to m/s by multiplying it by the circumference of the circular path.

First, let's find the circumference of the circular path. The circumference (C) can be calculated using the formula:

C = 2πr

Given that the radius (r) is 1.1 m, we can calculate the circumference:

C = 2 * π * 1.1 = 6.9 m (approximately)

Now, let's calculate the velocity (v) using the formula:

v = C * rev/s

v = 6.9 m * 1.3 rev/s = 8.97 m/s (approximately)

Now we can substitute the values of v and r into the centripetal acceleration formula to find the centripetal acceleration (a):

a = (v^2) / r
a = (8.97 m/s)^2 / 1.1 m
a = 80.46 m^2/s

Therefore, the centripetal acceleration of the hammer is approximately 80.46 m^2/s.

Now let's move on to finding the tension in the chain. The tension in the chain is equal to the centripetal force acting on the hammer, which is given by the formula:

F = m * a

where:
F = centripetal force
m = mass of the hammer
a = centripetal acceleration

In this case, the mass of the hammer is given as 7.50 kg, and we found the centripetal acceleration to be 80.46 m^2/s. Substituting these values into the formula, we can find the tension in the chain:

F = 7.50 kg * 80.46 m^2/s
F ≈ 603.45 N

Therefore, the tension in the chain is approximately 603.45 N.

acceleration= w^2 r= (1.3*2PI rad/sec)^2 1.1m

tension= masshammer*acceleration

Acctually i just found the answer for the acceleration, its similar to what you said except that you don't square it.The tension is (mass)(acceleration).

well, it is nice to know I have been doing it wrong, apparently, for 50 years.

I see here in Canada they are doing it my way also. Well, they are Canadians.

http://theory.uwinnipeg.ca/physics/circ/node6.html