One end of a cord is fixed and a small 0.470-kg object is attached to the other end, where it swings in a section of a vertical circle of radius 2.50 m as shown in the figure below. When θ = 21.0°, the speed of the object is 4.70 m/s. At this instant, find each of the following.
(a) the tension in the string
(b) the tangential and radial components of acceleration
(c) the total acceleration
I have the tension and it is 8.48N and I have the radial component of acceleration. I can't figure out how to get the tangential component of acceleration.
Please help and thank you.
Tangential acceleration is due to gravity. So you are looking for the component of gravity in the direction of the tangent.
tangential acceleration= g*sinorcosine 21
I don't know how your angle is measured, but you will need sin21 or cos21. Draw the figure.
Thank you very much. I used sin21 and it was right.
To find the tangential component of acceleration, you can use the equation for centripetal acceleration:
a = v^2 / r
where "a" is the acceleration, "v" is the speed of the object, and "r" is the radius of the circle. In this case, the speed is given as 4.70 m/s and the radius is given as 2.50 m.
Substituting these values into the equation, we get:
a = (4.70 m/s)^2 / 2.50 m
Simplifying the equation, we have:
a = 22.09 m^2/s^2 / 2.50 m
a = 8.84 m/s^2
So, the tangential component of acceleration is 8.84 m/s^2.
Now, let's summarize the information given in the question:
- Tension in the string (found to be 8.48 N)
- Radial component of acceleration
- Tangential component of acceleration (found to be 8.84 m/s^2)
If you need help with the other parts of the question (b) and (c), please let me know.