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a) State Hooke’s law - Leaving Cert Physics - Question 12 - 2011
Question 12
a) State Hooke’s law. A body of mass 250 g vibrates on a horizontal surface and its motion is described by the equation $ a = -16 s $, where $ s $ is the displaceme... show full transcript
Worked Solution & Example Answer:a) State Hooke’s law - Leaving Cert Physics - Question 12 - 2011
Step 1
Step 2
Why does the body vibrate with simple harmonic motion?
Answer
The body vibrates with simple harmonic motion because the acceleration is directly proportional to the negative displacement from the equilibrium position. This relationship can be observed in the given equation: This implies that the force acting on the body is always directed towards the equilibrium position, thus fulfilling the criteria for simple harmonic motion (SHM).
Step 3
Calculate the frequency of vibration of the body?
Answer
To calculate the frequency, we start from the equation of motion: rac{d^2s}{dt^2} = - rac{16s}{1} This indicates that rac{d^2s}{dt^2} = - rac{ ext{ω}^2 s}{1}, where . Therefore, we find:
$$ and to find the frequency $ f $: $$ f = rac{ ext{ω}}{2 ext{π}} = rac{4}{2 ext{π}} \ ≈ 0.64 ext{ Hz} $.Step 4
What is the magnitude of (i) the maximum force, (ii) the minimum force, which causes the body’s motion?
Answer
(i) To find the maximum force, we use:
F_{max} = m imes a_{max} = (0.250 ext{ kg}) imes (0.80) = 0.20 ext{ N} $$ (ii) The minimum force occurs when the body is at the equilibrium position, thus: $$ F_{min} = 0 ext{ N} $$.