Question

Gear A A=0.05m Gear B Is=0.075m ra=0.1m ay=0.1m/s2 o Cart M is attached to the inner pully of gear B(small radius). It starts from rest. The car accelerates at a constant acceleration of am 0.1 m/s2 1) Indicate the x,y coordinate frame on your paper. 2)Find the angular acceleration of gear A a 3)For 1 rotation of gear A, how much will car M move? 4) If the mass of the cart is 2 kg, Calculate the tension in the string (hint: assume no friction with the ground since the cart is rolling on wheels)

Answer 1

AM = 0.1 m/s Gear B Soln Gear A OR MA= 0.05 m ror Oilm M = 0.075 m am = - Ol î m/s Let of A and do be angular acceleration gear A and gear B At - a B am = LB X rs 3 0.1 = ARX 0.075 os xp = 1.333 rad/s² (cow) Gear meet each other. At R both so - da = 1.333 X 0.1 0.05 ou da = 2.667 rad/s (cw)

Date: Let 't be the time taken by to complete I rotation. gear A O = wot that > 27 = Coxt) + 1 x 2.667xt 2 oot = 2.17 see Hence the acceleration of cart is Constant t=21st HEB FO . O o s = ut t tamt S = Oxt + 1 x 0.1 x(2:17) bis = 0.235 m. COM Hpplying Newton's and law ena- direction

Date: Т- Мам -) 1 = 2x 0. Loe T = 0.2N LA = 2.667 rad/s² (cw) on LA = -2.667 ĥ rad/s² s = 0.235 m or s = -0.235 (E) im 9 T = 0.2N (*)