When you lift an object by moving only your forearm, the main lifting muscle in your arm is the biceps. suppose the mass of a forearm is 1.40 kg . if the biceps is connected to the forearm a distance dbiceps = 2.50 cm from the elbow, how much force fbiceps must the biceps exert to hold a 1000 g ball at the end of the forearm at distance dball = 33.0 cm from the elbow, with the forearm parallel to the floor? how much force felbow must the elbow exert? draw the vectors starting from the point of application of each force. the location and orientation of the vectors will be graded. the length of the vectors will not be graded?

Respuesta :

[tex]\tau = \sum \overrightarrow r \times \overrightarrow F = 0 \\ \\ \tau = -(2.5 cm)F + (16.5cm) * (1.4kg)(9.81 \frac{m}{s^2} ) + (33cm)*(1kg)(9.81 \frac{m}{s^2} ) \\ \\ F = 220 N[/tex]
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Newton's second law for rotational motion we can find the answer for the force exerted by the bicep is:

              F = 219.9 N

Parameters given

  • Forearm mass m = 1.4 kg
  • Distance to elbow x = 2.50 cm = 0.0250 m
  • Ball mass M = 1 kg
  • Distance to elbow L = 33.0 cm = 0.330 m

To find

  • Bicep Force.

Newton's second law for rotational motion establishes the relationship between torque, moment of inertia and angular acceleration, in the special case that angular acceleration is zero, it is called rotational equilibrium condition.

           Σ τ  = 0

           τ = F r sin θ

Where τ is torque, F the force and (r sin θ) the distance perpendicular to the turning point.

The reference system is a coordinate system with respect to which measurements are made, in the attached we can see a diagram of the forces where the reference system is taken at the elbow and the counterclockwise turns are positive.

Let's write Newton's second law.

Suppose the forearm is homogeneous, so its center of mass is in the middle of the length.

               [tex]- F x + W_{bicep} \frac{L}{2} + W_{ball} L = 0\\F = \frac{(\frac{m}{2} +M) g L }{x}[/tex]

             

Let's calculate.

               F = [tex]\frac{(\frac{1.40}{2} + 1.0 ) 9.8 \ 0.33 }{0.025 }[/tex]  

               F = 219.9 N

In conclusion using Newton's second law for rotational motion we can find the answer for the force exerted by the bicep is:

              F = 219.9 N

Learn more here:  brainly.com/question/6855614

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