During the disc event, Ashton swings a discus of mass 2.0 kg in uniform circular motion - Leaving Cert Physics - Question 6 - 2018
Question 6
During the disc event, Ashton swings a discus of mass 2.0 kg in uniform circular motion. The radius of orbit of the discus is 1.2 m and the discus has a velocity of ... show full transcript
Worked Solution & Example Answer:During the disc event, Ashton swings a discus of mass 2.0 kg in uniform circular motion - Leaving Cert Physics - Question 6 - 2018
Step 1
(i) Derive an expression to show the relationship between the radius, velocity and angular velocity of an object moving in uniform circular motion.
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Answer
For an object moving in uniform circular motion, the relationship between angular velocity (ω), linear velocity (v), and radius (r) is given by:
ω=rv
Where:
ω is the angular velocity in radians per second.
v is the linear velocity.
r is the radius of the circular path.
Step 2
(ii) Calculate the angular velocity of the discus immediately prior to its release.
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Answer
Using the relationship derived earlier:
ω=rv=1.220.4
Calculating this gives:
ω=17rad s−1
Step 3
(iii) Calculate the centripetal force acting on the discus just before Ashton releases it. In what direction does this force apply?
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The formula for centripetal force (F) is:
F=rmv2
Substituting the values:
F=1.2(2)(20.42)=693.6N
The direction of the centripetal force is towards the center of the circular path.
Step 4
(f) his velocity in the horizontal direction,
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The horizontal velocity (vh) is found using the cosine of the angle:
vh=vcosθ=10.9cos(43°)
Calculating:
vh=7.97m s−1
Step 5
(ii) the length of the jump.
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Using the formula for distance traveled:
s=vh⋅t=7.97⋅1.03
Calculating:
s=8.21m
Step 6
(i) State the principle of conservation of energy.
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The principle of conservation of energy states that energy cannot be created or destroyed; it can only be transformed from one form to another.
Step 7
(ii) What is meant by the centre of gravity of a body?
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The centre of gravity of a body is the point at which its weight appears to act, effectively where the mass of the body is concentrated for the purpose of calculating weight and balance.
Step 8
(iii) what is the maximum height above the ground to which he can raise his centre of gravity?
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Answer
Using the conservation of energy:
h=2gv2+hinitial=2×9.89.22+0.98
Calculating:
h=4.26+0.98=5.24m
Step 9
(iv) Draw a diagram to show any forces acting on Ashton when he is at his highest point, as shown in the photograph.
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At the highest point, the forces acting on Ashton include:
Gravitational force (weight) acting downwards.
Any upward forces that might be acting momentarily (e.g., air resistance), but primarily the gravitational force dominates.
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