A bowling ball of mass m=5 kg hangs from a massless string of length L=10.0 m fr

ID: 2129594 • Letter: A

Question

A bowling ball of mass m=5 kg hangs from a massless string of

length L=10.0 m from the ceiling of a large lecture hall. With the ball

starting from rest and hanging straight down, the professor pushes

horizontally on the ball with a varying force F, to move the bowling

ball a distance d=3.50 m to the side.

(a) What is the magnitude of the horizontal force supplied by the

professor on the bowling ball at the end of the displacement where

the ball is again motionless?

(b) During the time that the ball is being displaced, what is the total

work done on the bowling ball?

done by the gravitational force?

(d) During the time that the ball is being displaced, what is the work done on the ball by the tension

in the rope?

(e) Knowing that the ball is motionless before and after its displacement, use the answers to (b), (c),

and (d) to find the work the professor

X = horizontal dispalcement = 3.5 m

Q = angle subtand by the string with vertical = sin^-1( 3.5/10) =20.4 degree

T = tension in string

balancing the force on the ball :: T*cos(Q) = mg .........(1)

T*sin(Q) = F................(2)

hence from (1) and (2) F = mg*tan(Q)

=5*9.8*2.67

= 18.22 N

b) change in kinetic energy =

0 = work done by all forces

hence work done by all forces =0

c) y = vertical displacement = 10 -10cos(20.4) =0.627 m

work done by gravitaional force = -mg*y = -30.73 N

d) work done by tension =0 , because tension is always perpendicular to dispalcement

e) work done by F + work done by mg +work done by tensnsion = 0

work done by F = - work done by mg = 30.73 N

f) becuause F is not constant force , F is variable force

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