A train slows down as it rounds a sharp horizontal turn, going from 86.0 km/h to 44.0 km/h in the 13.0 s that it takes to round the bend. The radius of the curve is 140 m. Compute the acceleration at the moment the train speed reaches 44.0 km/h. Assume the train continues to slow down at this time at the same rate.
When i do this question i get accleration as 1.32 m/s^2. It tells me I am within 10% of the right answer but I m not sure how I'm wrong. (btw it is online homework)
Thanks.
86 km/h = 23.9m/s
44 km/h = 12.2 m/s
tangential acceleration = -(23.9-12.2)/13
=-0.9 m/s^2
radial acceleration = v^2/R=12.2^2/140
= 1.06 m/s^2
|a| = sqrt(.9^1+1.06^2)
= 1.94 m/s^2
To find the acceleration of the train at the moment it reaches 44.0 km/h, you can use the formula:
acceleration = (final velocity - initial velocity) / time
First, convert the initial and final velocities from km/h to m/s:
Initial velocity = 86.0 km/h = 86.0 * (1000 m / 1 km) / (3600 s / 1 h)
Initial velocity = 23.9 m/s
Final velocity = 44.0 km/h = 44.0 * (1000 m / 1 km) / (3600 s / 1 h)
Final velocity = 12.2 m/s
Given that the time taken to round the bend is 13.0 s, we can use these values in the acceleration formula:
acceleration = (12.2 m/s - 23.9 m/s) / 13.0 s
acceleration = -11.7 m/s / 13.0 s
acceleration = -0.90 m/s² (rounded to two decimal places)
So, the acceleration at the moment the train speed reaches 44.0 km/h is approximately -0.90 m/s².
Your answer of 1.32 m/s² seems to be the correct magnitude but in the wrong direction. The negative sign indicates that the acceleration is in the opposite direction of the train's velocity. Please check your calculations to ensure that you correctly subtracted the final velocity from the initial velocity and divided by the time.
To solve this problem, you can use the formula for centripetal acceleration:
a = v^2 / r
Where:
a = acceleration
v = velocity
r = radius
First, convert the velocities from km/h to m/s:
Initial velocity, v1 = 86.0 km/h * (1000 m / 1 km) * (1 h / 3600 s) = 23.9 m/s
Final velocity, v2 = 44.0 km/h * (1000 m / 1 km) * (1 h / 3600 s) = 12.2 m/s
Next, plug these values into the formula along with the given radius:
a = (v2^2 - v1^2) / r
a = (12.2^2 - 23.9^2) / 140
a = (148.84 - 571.21) / 140
a = -422.37 / 140
a = -3.02 m/s^2
It seems that your answer of 1.32 m/s^2 is incorrect. The correct answer is -3.02 m/s^2. Make sure to double-check your calculations and units.