What is the angular acceleration if the weight is 24.0 cm from the elbow joint, her forearm has a moment of inertia of 0.240 kg⋅m2, and the net force she exerts is 759 N at an effective perpendicular lever arm of 2.00 cm?

The complete question is;

To develop muscle tone, a woman lifts a 2.00-kg weight held in her hand. She uses her biceps muscle to flex the lower arm through an angle of 60.0º . What is the angular acceleration if the weight is 24.0 cm from the elbow joint, her forearm has a moment of inertia of 0.240 kg.m², and the net force she exerts is 759 N at an effective perpendicular lever arm of 2.00 cm?

α = 42.76 rad/s²

Explanation:

We are given;

Mass; m = 2 kg

Distance; r = 24cm = 0.24m

Moment of inertia of the forearm; I = 0.24 kg.m²

Muscle Force; F = 759N

Perpendicular distance to lever arm; r' = 2cm = 0.02m

Angle at which she flexes arm; θ=60°

Let's assume that the arm starts extended vertically downwards. and we take the elbow joint as the point about which we calculate the torque.

Thus, we know that torque is given by the formula ;

τ = Force x Perpendicular distance

Thus, the toque exerted by force in the muscle is;

τ_muscle = 759 x 0.02 = 15.18 N.m

Also, torque exerted by the lifted weight is given as 0 because perpendicular distance is zero.

Thus, the net torque on the lower arm is;

τ_net = τ_muscle - τ_weight

τ_net = 15.18 - 0 = 15.18 N.m

Now, let's calculate moment of inertia of lifted weight.

The moment of inertia is given by;

I = mr²

Thus, moment of Inertia of lifted weight is; I_weight = 2 x 0.24² = 0.115 kg.m²

Thus,total moment of inertia is;

I_total = I_arm + I_weight

Thus, I_total = 0.24 + 0.115 = 0.355 kg.m²

Now, we can calculate the angular acceleration.

It's gotten from the equation;

τ_net = I_total•α

Where α is angular acceleration.

Thus making α the subject, we have ; α = τ_net/I_total

α = 15.18/0.355 = 42.76 rad/s²

a solenoid is created by wrapping a l = 90 m long wire around a hollow tube of diameter d = 4.5 cm.   the wire diameter is d = 0.9 mm.   the solenoid wire is then connected to a power supply so that a current of i = 9 a flows through the wire.

randomized variablesl = 90 m

d = 4.5 cm

d = 0.9 mm

i = 9 a                                          

write an expression for the number of turns, n, in the solenoid. you do not need to take into account the diameter of the wire in this calculation.

calculate the number of turns, n, in the solenoid.

write an expression for the length of the solenoid (l2) in terms of the diameter of the hollow tube d.

calculate the length of the solenoid (l2)   in meters.

calculate the magnitude of the magnetic field at the center of the solenoid in teslas.

explanation:

talk back to him about the sport and show him your expertise or leave the room