Download Physics Exam Solutions: Problems Involving Forces, Gravity, and Motion and more Study notes Physics in PDF only on Docsity!
Massachusetts Institute of Technology Physics Department
Physics Exam Fall
SOLUTIONS
Problem p oints
pts a max extension mg sin s mg cos k xmax
xmax mgk^ sin s cos
N=mg cos θ
mg
F =kx
sp
F = μ smg cos
fr
pts b
pts c net force along slop e once the blo ck starts moving k x ; mg sin ; k mg cos ma
max sp eed when a
x mgk^ sin k cos
pts d gravity mg sin xmax x
spring ^ k^ xmax^ ^ x
fricion k mg cos xmax x
pts e Substitute in the results of d for x Add up the total work done by the three
forces If this is zero or larger than zero the spring will b ecome as short as l Thus (^) k x (^) mg x max max^ sin^ ^ ^ k^ cos^ ^
Problem p oints
pts a As the ob ject go es up the comp onent of the resistive force in the vertical y direction
is in the same direction as the gravitational force mg see gure
res,y
F
mg mg
F
res,y
When the ob ject is on the way down the y comp onent of the resistive force is in the
opp osite direction Thus the comp onent of th e force i n th e y direction is smaller on the
way d own than on the way u p Thus it will take longer than sec to come down
pts b For zero acceleration T
q
l (^) For an acceleration a downwards T 0
q
g g ;a If a were msec ^ wed have free fall and the p endulum would b e weightless no
oscillations T! 1 Since a msec ^ T 0 T
p
pts c The viscous term will dominate when v^ C^1 term �^ vcrit where^ vcrit (^) C 2 r ^ When^ the^ viscous term dominates v^ mg term (^) C 1 r ^ The^ mass^ of^ the^ oil^ drop^ is^ given^ by^ m^
(^) r (^) Thus r 3 g (^) � C (^1) C 1 r C 2 r
C 3
r
g C
pts d T ^ ^ f (^) T ^ Hz
pts e The sp eed is maximum when x ie when sint ^
This happ ens when t ^ n where n � � �
t n
and^ the^ max^ sp^ eed^ is^ when^ cos^ t^ Alternatively v ; cos t � This leads to the same times
l
