A gray physics cart is on a horizontal physics track in the lower-division physi

Question

A gray physics cart is on a horizontal physics track in the lower-division physics lab at Yale. The gray cart happens to weigh 30.4 N and is initially at rest... A gray physics cart is on a horizontal physics track in the lower-division physics lab at Yale. The gray cart happens to weigh 30.4 N and is initially at rest. A string is attached to the cart, pulled horizontally along the physics track, and over a pulley This pulley has a diameter of 17.1 cm, a mass of 627 g, and a rotational form factor of 0.473. When Grace pulls the string down at an angle of 60.2 degrees from the horizontal with a 13.4 N force, the string rotates the pulley without slipping and the gray physics cart moves towards the pulley. (10 Points) Determine the angular acceleration of the pulley. a) 39.9 s b) 83.3 s 2 c) 528 s 2 d) 46.2 s e) 23.1 s 2 f) 147s 2 g) 19.9 s

Explanation / Answer

let the tension in string of cart be T

T = ma

13.4 - T = (i alpha)/R

adding both equations,

13.4 = ma +  (i alpha)/R

13.4 = m*alpha R + fMR^2/R

13.4 = alpha(30.4/9.8*0.171/2 +0.473*0.627*0.171/2)

alpha = 13.4/(30.4/9.8*0.171/2 +0.473*0.627*0.171/2)

= 46.2 s^-2

option d is correct

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