Tom and Jerry push on the 3 m diameter merry-go-round

[BrownBoi7]

Tom and Jerry both push on the 3 m diameter merry-go-round shown in the figure attached.

(a) If Tom pushes with a force of 40 N and Jerry pushes with a force of 35.2 N, what is the net torque on the merry-go-round?

(b) What is the net torque if Jerry reverses the direction by 180 degrees without changing the magnitude of his force?

My attempt:
FT = Force exerted by Tom = 40 N
FJ = Force exerted by Jerry = 35.2 N

T = Torque = RF sinΘ

TT = 1.5 m * 40 N * sin 60 = 1.5 m * 40 N * -0.304 = -18.28 Nm
TJ = 1.5 m * 35.2 N * sin 80 = 1.5 m * 35.2 N * -0.993= --52.43 Nm

(a) Net T= -18.28 Nm + (- 52.43 Nm) = -70.71 Nm

(b) When Jerry reverses,
Net T = -18.28 Nm - (-52.43 Nm) = 34.15 Nm


My answers didn't match my professor's answers. I believe I went about it the right way. Could somebody please point out where I messed up?

Thanks!

 

[jackarms]

I think it's just a problem with your signs. For your torques, you solved both of them to be negative, but that can't be since they push the merry-go-round in different directions. Check that, and you should be good.

 

[BrownBoi7]

Are my values for sin 60 and sin 80 right?

Aren't they both going clockwise? Figure never told me which guy is going which direction.

 

[collinsmark]

Either change your calculator mode to "Deg" instead of "Rad" or convert your 60^o and 80^o to radians before taking the sine.

 

[PhanthomJay]

Are my values for sin 60 and sin 80 right?

Aren't they both going clockwise? Figure never told me which guy is going which direction.

After you change your sine and sign, it should be obvious from inspection based on the given direction and location of the forces as to which force tends to rotate the object clockwise and which force tends to rotate it counterclockwise. The net torque is how much cw or ccw?

 

[BrownBoi7]

TT = 1.5 m * 40 N * sin 60 = 1.5 m * 40 N * 0.866 = 51.96 Nm
TJ = 1.5 m * 35.2 N * sin 80 = 1.5 m * 35.2 N * 0.985= 52.008 Nm

So, Tom's going clockwise and Jerry anticlockwise?

(a) 51.96 Nm - 52.008 Nm = -0.048 Nm
(b) 51.96 Nm + 52.008 Nm = 103.968 Nm

Are the right now?

 

[PhanthomJay]

TT = 1.5 m * 40 N * sin 60 = 1.5 m * 40 N * 0.866 = 51.96 Nm

51.9970 N-m cw or ccw (minus or plus)?

TJ = 1.5 m * 35.2 N * sin 80 = 1.5 m * 35.2 N * 0.985= 52.008 Nm

51.9615 N-m cw or ccw(minus or plus)?

So, Tom's going clockwise and Jerry anticlockwise?

The merry-go-round is free to totate about the black dot at its center. So when tom pushes it on its left hand side as shown, will the thing tend to spin in the direction of a clock's hands cw as viwed from your screen or the other way ccw?

(a) 51.96 Nm - 52.008 Nm = -0.048 Nm

make math correction and round off to 2 decimal places...what direction (cw or ccw) does the minus sign indicate?

(b) 51.96 Nm + 52.008 Nm = 103.968 Nm

ok, round it off, but what direction does the plus sign indicate?