An athlete whirls a 6.6 kg hammer tied to
the end of a 1.2 m chain in a horizontal circle.
The hammer moves at the rate of 0.432 rev/s.
What is the centripetal acceleration of the
hammer? Assume his arm length is included
in the length given for the chain.
Answer in units of m/s
2
What is the tension in the chain?
Answer in units of N
centripetal acceleration is v^2/r
The tension in the chain is m*v^2/r
where v is the speed = 2*PI*r*f
where f is the frequency; r is the radius; m is the mass
v = 2*PI*1.2*0.432
solve for the acceleration and tension using the above equations
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
Given:
mass of the hammer (m) = 6.6 kg
velocity (v) = 0.432 rev/s
radius (r) = 1.2 m
First, let's convert the velocity from rev/s to m/s.
To do this, we can multiply the velocity by 2π since one revolution is equal to 2π radians:
v = (0.432 rev/s) * (2π rad/rev) ≈ 2.714 m/s
Now we can plug in the values into the centripetal acceleration formula:
a = (2.714^2 m/s^2) / 1.2 m ≈ 6.125 m/s^2
Therefore, the centripetal acceleration of the hammer is approximately 6.125 m/s^2.
To find the tension in the chain, we can use Newton's second law of motion:
F = m * a
where:
F = force (tension in the chain)
m = mass of the hammer
a = centripetal acceleration
Plugging in the values:
F = (6.6 kg) * (6.125 m/s^2) ≈ 40.275 N
Therefore, the tension in the chain is approximately 40.275 N.
To find the centripetal acceleration of the hammer, we can use the formula:
centripetal acceleration (a) = (angular velocity (ω))^2 * radius (r)
Given:
mass of the hammer (m) = 6.6 kg
angular velocity (ω) = 0.432 rev/s
radius (r) = 1.2 m
First, let's convert the angular velocity from rev/s to rad/s. Since there are 2π radians in one revolution, we can multiply the angular velocity by 2π to get it in rad/s.
ω = 0.432 rev/s * 2π rad/rev = 0.861 π rad/s
Now, we can substitute the values into the formula to find the centripetal acceleration:
a = (0.861 π rad/s)^2 * 1.2 m
Calculating this using a calculator:
a ≈ 3.462 m/s^2
Therefore, the centripetal acceleration of the hammer is approximately 3.462 m/s^2.
To find the tension in the chain, we can use Newton's second law of motion. In this case, the tension in the chain provides the centripetal force needed to keep the hammer moving in a circle.
The formula is:
tension (T) = mass (m) * centripetal acceleration (a)
Given:
mass of the hammer (m) = 6.6 kg
centripetal acceleration (a) ≈ 3.462 m/s^2
Substituting the values into the formula:
T = 6.6 kg * 3.462 m/s^2
Calculating this using a calculator:
T ≈ 22.8192 N
Therefore, the tension in the chain is approximately 22.8192 N.