- #1
Lee333
- 4
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A particle of mass 0.014 kg is traveling on a radius 0.9m at a rotational velocity of 36+5*t rad.s-1.
How many revolutions does the particle go thorugh in 4.8 seconds? [revs]
What is the radial force on the particle at 4.8 seconds? [N] (Hint: consider directions)
(question I'm stuck on)
What is the absolute magnitude of force on the particle at 4.8 seconds? [N]
We know that the radial acceleration = v^2/r
To find the amount of revolutions I simply integrated the rotational velocity with respect to time, and found that the particle rotated 230.4 radians or 36.69 revs.
The second question is the question that I seem to be getting wrong. The way I tried to solve it was by firstly finding the rotational velocity after 4.8 seconds:
w = 36+5*4.8
= 60 rad/s
thus we know that the translational velocity is:
v= rw
= 60*0.9
= 54 m/s
we know that the radial acceleration, ra, can be defined by:
ra = v^2/r
= 54^2/0.9
= 3240
thus the radial force, Fr, is:
Fr = m*ra
=0.014*3240
=45.36 N
the above question i am getting wrong for some reason. any help would be appreciated
For the final question we know that the angular acceleration is 5 rad/s^2
this means the linear acceleration of the particle is 4.5 m/s.
we know the translational force will be Ft=m*a
Ft = 0.014*4.5
= 0.063
So we can work out the total magnitude of the force like so:
F_tot = sqrt(0.063^2+45.36^2)
= 45.36
How many revolutions does the particle go thorugh in 4.8 seconds? [revs]
What is the radial force on the particle at 4.8 seconds? [N] (Hint: consider directions)
(question I'm stuck on)
What is the absolute magnitude of force on the particle at 4.8 seconds? [N]
We know that the radial acceleration = v^2/r
To find the amount of revolutions I simply integrated the rotational velocity with respect to time, and found that the particle rotated 230.4 radians or 36.69 revs.
The second question is the question that I seem to be getting wrong. The way I tried to solve it was by firstly finding the rotational velocity after 4.8 seconds:
w = 36+5*4.8
= 60 rad/s
thus we know that the translational velocity is:
v= rw
= 60*0.9
= 54 m/s
we know that the radial acceleration, ra, can be defined by:
ra = v^2/r
= 54^2/0.9
= 3240
thus the radial force, Fr, is:
Fr = m*ra
=0.014*3240
=45.36 N
the above question i am getting wrong for some reason. any help would be appreciated
For the final question we know that the angular acceleration is 5 rad/s^2
this means the linear acceleration of the particle is 4.5 m/s.
we know the translational force will be Ft=m*a
Ft = 0.014*4.5
= 0.063
So we can work out the total magnitude of the force like so:
F_tot = sqrt(0.063^2+45.36^2)
= 45.36