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paul_harris77
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I am attempting to solve the dynamics question below:
"A car of mass 600kg is driven in a circle of constant radius (100m). It is known that the car becomes unstable under a side force of 6800N. Determine the minimum time allowable for the car to accelerate uniformly from 80 to 100km/h."
m= 600kg, r =100m and F=6800N.
I am assuming that the overall aim is to obtain the tangential acceleration (aθ) i.e. the acceleration in the car's direction of travel, and from that work out the time using the change in velocity of 20km/h.
I have worked out the "resultant" acceleration on the side of the car, using a=F/m = 6800/600 = 11.33ms^-2.
The trouble I am having is splitting this overall "resultant" acceleration into tangential (aθ)
and radial (ar) components.
I know the equation for resultant acceleration is derived from simple pythagoras:
a = sqrt((aθ^2)+(ar^2))
I also have the following equations:
ar = wr^2 (where w is omega and ar is radial acceleration)
aθ = r*alpha (where alpha is angular acceleration)
vθ=wr
Since, w and vθ are changing, I have started by trying to work out the acceleration components in terms of changes in vθ and w over time.
The answer should be 4.9 seconds, but I am stuck with how to get this answer.
Any help would be greatly appreciated.
Many thanks
Paul
"A car of mass 600kg is driven in a circle of constant radius (100m). It is known that the car becomes unstable under a side force of 6800N. Determine the minimum time allowable for the car to accelerate uniformly from 80 to 100km/h."
m= 600kg, r =100m and F=6800N.
I am assuming that the overall aim is to obtain the tangential acceleration (aθ) i.e. the acceleration in the car's direction of travel, and from that work out the time using the change in velocity of 20km/h.
I have worked out the "resultant" acceleration on the side of the car, using a=F/m = 6800/600 = 11.33ms^-2.
The trouble I am having is splitting this overall "resultant" acceleration into tangential (aθ)
and radial (ar) components.
I know the equation for resultant acceleration is derived from simple pythagoras:
a = sqrt((aθ^2)+(ar^2))
I also have the following equations:
ar = wr^2 (where w is omega and ar is radial acceleration)
aθ = r*alpha (where alpha is angular acceleration)
vθ=wr
Since, w and vθ are changing, I have started by trying to work out the acceleration components in terms of changes in vθ and w over time.
The answer should be 4.9 seconds, but I am stuck with how to get this answer.
Any help would be greatly appreciated.
Many thanks
Paul