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Can you please answer all parts and show work. Thank you. See figure of a fricti

ID: 1838201 • Letter: C

Question

Can you please answer all parts and show work. Thank you.

See figure of a frictionless track that marbles can be rolled down. The circular loop near the middle has radius R = 0.45 m. The right end of the track rises to height y = 0.35 m. A marble, mass m = 0.17 kg, is put on the track and released from rest at height H = 1.3 m at the left of the figure. When it reaches the right end of the track, it's velocity v is unknown. a. Compute the potential energy of the marble at its starting point on the left of the track. b. Compute the kinetic energy & the velocity v_1 of the marble when it has reached the bottom part of the track just before it starts onto the loop. c. Compute the potential energy, the kinetic energy, & the velocity v_3 of the marble when it has reached the right end of the track. d. Compute the potential energy, the kinetic energy, & the velocity o v_2 f the marble when it has reached the top of the loop. e. What Physical Principle did you use to solve parts b, c, & d?

Explanation / Answer

a) potential energy at starting point = mgh = .17x9.8x1.3= 2.1658

b) the kinetic energy at the starting point is zero. As the track is frictionless no energy is lost.

By conservation of energy,

U0 + K0 = U1+ K1

Mg (1.3) = Mg(0)+ (mv12)/2

Solving V1 = 5.047m/s

Kinetic energy at bottom =(mv12)/2 = 2.1658

D) at the top mg =( mv22)/r

Solving v2 = 2.1m/s

Potential energy = mgh = mg(2R) = 1.4994

Kinetic energy = (mv22)/2 = .3749

C, potential energy at the end of the track = mgh = .17x9.8x.35= .5831

(Mv12)/2=(Mv32)/2 +mgh

(Mv32)/2 = 2.1658-.5831

V3 = 4.315m/s

Kinetic energy at the end of track is 1.5827

E) conservation of energy