Question

I. [Ipt) A professor of mass m = 76 kg is seated on a light harness connected tn a rope and pulley system as shown. The professor's feet touch a uniform plank of mass m suspended from the right end of the plank. The professor is a distance = 2.30 m from the hinge; the plank has length L4.10 m 10 kg which is supported by a hinge a the wall. A mass Min a light hucket is Answer true ur false lo the staletienls below; eg, if the (irst one is true and the rest are false, enler TTFTE i. If the plank remains horizontal. the force of the profcssor on the plank is cqual to the tension in the ropc i. If M>0, the plank can remain horizontal for some valucs of M. i.If M 0 and the plank remains horizontal, the tension in the rope does not depend on the ratio of to L iv. The weight of the plank leads to a counter-clockwisc torque on the plank, taken about the hinge. v. If the right end of the plank accelerates slowly downward, the tension in the rope T> mg-

Answer 1

FBD Professor FBD Professor FBD Plank 21 IND FN = mg-T -- i mpg or T = mg-FN Yng [mp = mpfont] EF= R+T-mpg - Mg - Fw=0 =) R+T-mpg -Mg-mg+T=0 → 25+R-(mp+ M+m)g=0 ---® Moment about hinge EM = LT-LMg - Fr - Ļ mpg = 0 l= 2.30m 2=4.10m => b= 4(23) = 0.5614 =) T-mg -0.561 FN -0.5 mpg =0 = T - Mg - 0.561 mg +0.561T - 0.5 mpg = 0 → T- (M +10.561m + 0.5mp)g te wees T= (17.5M + 2 832). > R = (2512M + 82102)N & Fn = -(17.5M +87.2). (Not possible in this i False (since FN #T) I ) True (iii) False (10) False (V) True. Cave)