Posted by sandhu on Wednesday, November 24, 2010 at 4:29am.
The firetruck goes around a 180°, 162 m radius circular curve. It enters the curve with a speed of 12.6 m/s and leaves the curve with a speed of 38.8 m/s. Assuming the speed changes at a constant rate, what is the magnitude of the total acceleration of the firetruck just after it has entered the curve?
physics - MathMate, Wednesday, November 24, 2010 at 8:16am
From the length of the curve (L=ðr), calculate the average tangential acceleration, At
= (38.8-12.6)/L
Find the radial acceleration due to curvature at entry to curve (v=12.6m/s)
Ar=v²/r
=12.6²/r
Since the two accelerations are perpendicular to each other, add Ar and At vectorially.
physics - sandhu, Wednesday, November 24, 2010 at 7:50pm
I don't understand how you get At = (38.8 - 12.6)/L.Please explain
Thanks.
I differ somewhat
I believe that At = change in tangential speed / time. I think he meant t not L
get the time from average speed (38.8+12.6)/2 = 25.7 m/s
now it went pi R = pi(162) = 509 meters
so the time in the turn was
t = 509/25.7 = 19.8 seconds
so I get At = (38.8 -12.6)/19.8
= 1.32 m/s^2
Distance is pi(R) but displacement is only 2R ,the diameter of the semi-circle
It is the scalar, not the vector, distance we are interested in for the magnitude of the acceleration.
Thank you for clarifying
To find the average tangential acceleration (At), you need to know the change in velocity (Δv) and the distance traveled along the curve (L). The formula for average tangential acceleration is:
At = Δv / L
In this case, the initial velocity (v1) is 12.6 m/s, and the final velocity (v2) is 38.8 m/s. The change in velocity is:
Δv = v2 - v1 = 38.8 - 12.6 = 26.2 m/s
The length of the curve (L) can be calculated using the formula L = πr, where r is the radius of the curve. In this case, the radius is given as 162 m, so we have:
L = π * 162 = 321.6π m
Now we can substitute the values into the formula for average tangential acceleration:
At = Δv / L = 26.2 / (321.6π) ≈ 0.0258 m/s²
Therefore, the magnitude of the total acceleration of the firetruck just after it has entered the curve is approximately 0.0258 m/s².