If a drummer at a gig hits his a drum that has a diameter of .2m with a stick that has a mass of 0.5kg at .03m from the center. What percentage radial region is impacted with a force twice as great as the initial impact force?
Don't get caught up in the words.
([ii-x^3y^2]-(r^3)(.5d))
Plug in your values, tell me what you get.
82.2%?
Correct! (:
To answer this question, we need to calculate the force exerted by the drummer's initial impact and then find the radial region impacted with a force twice as great.
Step 1: Calculate the initial impact force.
The formula to calculate force is F = m * a, where F is the force, m is the mass, and a is the acceleration.
In this scenario, the drummer hits the drum with a stick, producing an initial impact force. Since the drummer hits the drum at a distance of 0.03m from the center, this will create a torque as well.
To calculate the force, we need to consider both the linear motion and the rotational motion.
Linear motion:
The linear acceleration (a) can be calculated using the formula a = v / t, where v is the linear velocity and t is the time taken to reach the drum surface.
Assuming the drummer hits the drum with a constant velocity and reaches the drum surface almost instantly, we can consider t as very small, approaching zero. In that case, the linear acceleration (a) can be considered infinite (∞).
Rotational motion:
The torque (τ) exerted due to the drum hit can be calculated using the formula τ = I * α, where I is the moment of inertia and α is the angular acceleration.
Moment of inertia (I) for a thin circular disk can be calculated using the formula I = 0.5 * m * r^2, where m is the mass of the drum and r is the radius.
In this case, the radius (r) can be calculated as half of the drum's diameter, which is 0.2m/2 = 0.1m.
So, I = 0.5 * m * (0.1m)^2 = 0.005 * m kg.m^2 (moment of inertia)
The angular acceleration (α) can be calculated using the formula α = a / r, where a is linear acceleration and r is the radius.
Since we assumed a linear acceleration of ∞, the angular acceleration will also be ∞.
Now, considering that we have a torque (τ) and a moment of inertia (I), we can determine the angular acceleration (α) but not the linear force (F).
Unfortunately, without knowing the specific details of the drum hit, the specific values for linear velocity, and the exact time of impact, we cannot determine the linear force (F) exerted by the drummer initially. Therefore, we cannot proceed to calculate the percentage radial region impacted with a force twice as great as the initial impact force.
To find a more accurate answer, we would need additional information such as the velocity of the drummer' or the time taken for the stick to reach the drum surface.