Question

A2.0Kg ball is suspended by a thread of length 1m. It is pulled aside until the thred makes an angle of 30°with the vertical. How much work is done against gravity?the ball is now released.Find its velocity at the lowest point. Ignore air resistance and tale g equal to 10ms-2.

Answer 1

you just need to find the height through which the ball is raised...now after displacement the ball made 30deg. with the vertical...now we need to find the vertical displacement of the ball ... to do that....

u just need to compute 1* cos 30 ... this will give u the new length of the string in the vertical direction which obviously will be less than the original 1 m ...

if u are failing to catch up with this u canvisualize it in another way ...just drop down a perpendicular from the new position of the ball to the vertical....the point where it cuts the initial length of the string is what we have just found out... i mean sort of.... we've actually found the length of the pendulum from that point to the point of hanging...so the new length of the pendulum in the vertical direction is 1 * cos 30
and to find out the displacement , u just need to subtract it from the initial length i.e. 1 m...so displacement = 1 - 1*cos30 = D work = force *displacement = mass of the ball * g * displacement
now u can place the values and find the answer...for me it comes out to be 0.267 joules one might ask why did we compute the vertical displacement when the ball is making horizontal displacement as well... and the answer is that only vertical displacement is along the line of action of gravitational force and not the horizontal displacement ....

this is so because
W= f * displacement *cos theta ....
and in the case of horizontal displacement ,
the angle theta = 90 and cos of 90 = 0 .... hence the horizontal displacement isnt considered..