rotational motion

[faoltaem]

would someone be able to tell me if this is right or what i've done wrong? thankyou
1. The problem statement, all variables and given/known data

a) What torque does the bicep muscle have to apply to hold the forearm of mass 1.10 kg and length 30 cm horizontally? Assume the arm is a rod of uniform mass density.
b) What torque does the bicep need to apply if the forearm is to hold a 20 kg weight in one hand at an angle of 20\circ below horizontal?

2. Relevant equations

\tau = Fx = mgx
\tau = Fsin\theta
\Sigma\tau = 0

3. The attempt at a solution

a) m = 1.1kg x = 15cm = 0.15m
\tau = Fx = mgx = 1.1 x 9.81 x 0.15
= 1.61865
= 2Nm

b) m_{o} = 20kg \theta = 20\circ
\Sigma\tau = 0
\tau_{1} + \tau_{2} = 0
\tau_{a} + \tau_{o} = 0 a=arm o=object
\tau_{o} = -\tau_{a}
Fsin\thetar = -mgx
F x sin20 x 0.3 = -(1.1 x –9.81 x 0.15)
0.1026F = 1.61865

F = \frac{1.61865}{0.1026}
= 15.775
= 16Nm

[Astronuc]

Part a is correct. One uses the CM of the arm to determine the moment about the elbow joint.

The logic on part b is not correct. The moment of the object and the moment of the arm work together against the bicep. The torque provided by the bicep must equal the sum of torques of the arm and object.

[faoltaem]

sorry i forgot about the 3rd force
\Sigma\tau = 0
\tau1 + \tau2 + \tau3 = 0
\tau1 + \tau2 = -\tau3

but i'm a little unsure about the force of \tau2 (which i have as the object)

is it: -\tau3 = \tau1 + \tau2
= m1gx1 + m2gx2
= 1.1 x 9.81 x 0.15 + 20 x 9.81 0.3
= 60.47865N
\tau3 = -60.47865N
= -6 x 10^{2}N

[Astronuc]

Be careful with units, torque is N-m, as opposed to force which uses N.

Don't forget the angle 20°, which influences the force normal to the moment arm.

[faoltaem]

ok so
\tau1 = Fsin\theta
= mgsin\theta
= 1.1 x -9.81 x sin 20 x 0.15
= -0.5536Nm

\tau2 = Fsin\theta
= mgsin\theta
= 20 x -9.81 x sin 20 x 0.3
= -20.131Nm

-\tau3 = \tau1 + \tau2
= -0.5536 + -20.131
= -20.685Nm

therefore \tau3 = 20.685Nm
or 20.685Nm in an anticlockwise direction

[Astronuc]

I believe one wants the cosine of the angle (between the weight and the normal to the moment arm) in this case or the sine of the angle between the force and the moment arm (which would be 90° + 20°).

[faoltaem]

so if i change sin 20 to cos 20 (or sin 110) i get:

\tau1 = Fsin
= mgsin
= 1.1 x -9.81 x cos 20 x 0.15
= -1.521Nm

\tau2 = Fsin
= mgsin
= 20 x -9.81 x cos 20 x 0.3
= -55.310Nm

-3 = 1 + 2
= -1.521 + -55.310
= -56.831Nm

therefore 3 = 56.831Nm
or 56.831Nm in an anticlockwise direction

is this the correct answer?
(thankyou for all your help)

[Astronuc]

Looks correct.

Make sure when writing formulae, to provide all the terms.

\tau = \vec{r} \times \vec{F}, where r is the moment arm and F is the force.

http://hyperphysics.phy-astr.gsu.edu/hbase/vctorq.html#vvc6

http://hyperphysics.phy-astr.gsu.edu/hbase/torq2.html

http://hyperphysics.phy-astr.gsu.edu/hbase/torcon.html