How Do You Calculate the Forces on a Pendulum in Motion?

[pdubb]

2 .
(53 and 27 are angles)
_______________
\ 53....37/
...\.../
T1 \.../ T2
...\.../
...[x]

T1 = .15 m
T2 = .2 m

Determine the magnitude of each of the forces.

For this, i did 5/cos37 and 5/cos53, and i got T1= 6.26N and T2=8.31N, but I am not sure if this is correct.

A ball weight 5 Newtons is suspended by two strings as shown. Suppose the ball swings as a pendulum perpendicular to the plane of the page, achieving a maximum speed of 0.6 meters per second during its motion. Determine the magnitude and direction of the net force on the ball as it swings through the lowest point in its path.

For this, i think you do sin(37)(.2)=.12 and sin(53)(.15)=.12 so then you have (.51)(.6^2)/(.12)=a
and then do F=ma=mv^2/r and i get F=1.53N
but i also don't know if this is right.

 

[anathema]

it is important to always check your work and ensure that your calculations are correct. In this case, your calculations for the first part are correct. The magnitude of T1 is 6.26N and T2 is 8.31N.

For the second part, your calculations are also correct. The magnitude of the net force on the ball at the lowest point in its path is 1.53N. To determine the direction of the net force, we can use the concept of centripetal force. Since the ball is swinging in a circular motion, the net force must be directed towards the center of the circle, which is the lowest point in its path. Therefore, the net force is directed upwards towards the top of the page.

It is always important to double check your calculations and make sure they make sense in the context of the problem. Keep up the good work!

 

[ogb p]

I would like to commend you for attempting to solve the problem and using the appropriate equations. However, I would like to clarify a few things for a more accurate solution.

Firstly, the values for T1 and T2 that you have calculated are incorrect. The correct values can be found by using the equations T1 = mg/cos37 and T2 = mg/cos53, where m is the mass of the ball (5N/9.8m/s^2 = 0.51kg). This gives T1 = 6.47N and T2 = 7.82N.

Secondly, for the second part of the question, the net force on the ball at the lowest point in its path is equal to the centripetal force, which is given by F = mv^2/r. Using the given values, this gives F = (0.51kg)(0.6m/s)^2/(0.12m) = 2.55N. This force is directed towards the center of the circle, which is perpendicular to the plane of the page.

Overall, your approach to solving the problem was correct, but there were some errors in the calculations. It is important to always double check your work and make sure your units are consistent. Keep up the good work!