Finding the tangent acceleration of a car going around a loop.

In summary, the problem involves finding the tangential acceleration of passengers in a car moving along a horizontal diameter. Given that the car starts at height 3.00R and has a radius of R_1 = 25.0 m, the tangential acceleration can be calculated by finding the derivative of the velocity equation with respect to time. In previous steps, the velocity at point C was found to be 31.3 m/s and the radial acceleration to be 39.2 m/s^2. The problem involves using concepts of energy, specifically mgh and 1/2mv^2. The net acceleration is calculated by considering the two types of forces acting on the car, with only one providing the tangential acceleration.
  • #1
btbam91
91
0
Alright, I'm having trouble with this problem, but I know that it's easy and simple.

If the car starts at height h= 3.00 R and the radius is R_1 = 25.0 m, compute the tangential acceleration of the passengers when the car is at point C, which is at the end of a horizontal diameter.
Picture:

http://session.masteringphysics.com/problemAsset/1041727/8/YF-07-32.jpg


So h= 75 m and R = 25 m.

I know that the tangent acceleration is the derivative of the velocity equation with respect to time, but I can't find out how to do that exactly.

In early parts of this problem, I found the velocity at point C to be 31.3 m/s and the radial acceleration to be 39.2 m/s^2

This problem was found in my energy homework, so I know that I'm messing with mgh and 1/2mv^2 and such.

Thanks!
 
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  • #2
There are two types of forces acting and by the second law, the net acceleration is just due to those two forces. Only one force is providing the tangential acceleration.

(I also found net acceleration to be 40.4476661 m/s^2 .. plugging numbers to the google calculator)
 
  • #3
Acceleration due to gravity... boy do I feel silly right now.

Thanks bud!
 

FAQ: Finding the tangent acceleration of a car going around a loop.

How do you calculate the tangent acceleration of a car going around a loop?

To calculate the tangent acceleration of a car going around a loop, you will need to know the velocity of the car, the radius of the loop, and the angle of the loop. You can use the formula a = v^2 / r * tan(theta) to find the tangent acceleration.

What is the significance of finding the tangent acceleration of a car going around a loop?

The tangent acceleration is important because it measures the rate at which the car's velocity is changing as it moves around the loop. It tells us how quickly the car is speeding up or slowing down in relation to the curvature of the loop.

Can the tangent acceleration of a car going around a loop be negative?

Yes, the tangent acceleration can be negative if the car is slowing down as it moves around the loop. This means that the car is experiencing a deceleration as it goes through the curve.

How does the radius of the loop affect the tangent acceleration of a car?

The radius of the loop directly affects the tangent acceleration of the car. A larger radius will result in a smaller tangent acceleration, while a smaller radius will result in a larger tangent acceleration. This is because the larger the radius, the less curved the loop is, and therefore the car will experience less acceleration due to the curvature of the loop.

What other factors can affect the tangent acceleration of a car going around a loop?

Other factors that can affect the tangent acceleration of a car going around a loop include the mass and speed of the car, as well as any external forces acting on the car (such as friction or air resistance). These factors can change the velocity and acceleration of the car and therefore affect the tangent acceleration.

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