Respuesta :
Answer:
(a) τ = 26.58 Nm
(b) τ = 18.79 Nm
Explanation:
(a)
First we find the torque due to the ball in hand:
τ₁ = F₁d₁
where,
τ₁ = Torque due to ball in hand = ?
F₁ = Force due to ball in hand = m₁g = (3 kg)(9.8 m/s²) = 29.4 N
d₁ = perpendicular distance between ball and shoulder = 60 cm = 0.6 m
τ₁ = (29.4 N)(0.6 m)
τ₁ = 17.64 Nm
Now, we calculate the torque due to the his arm:
τ₁ = F₁d₁
where,
τ₂ = Torque due to arm = ?
F₂ = Force due to arm = m₂g = (3.8 kg)(9.8 m/s²) = 37.24 N
d₂ = perpendicular distance between center of mass and shoulder = 40% of 60 cm = (0.4)(60 cm) = 24 cm = 0.24 m
τ₂ = (37.24 N)(0.24 m)
τ₂ = 8.94 Nm
Since, both torques have same direction. Therefore, total torque will be:
τ = τ₁ + τ₂
τ = 17.64 Nm + 8.94 Nm
τ = 26.58 Nm
(b)
Now, the arm is at 45° below horizontal line.
First we find the torque due to the ball in hand:
τ₁ = F₁d₁
where,
τ₁ = Torque due to ball in hand = ?
F₁ = Force due to ball in hand = m₁g = (3 kg)(9.8 m/s²) = 29.4 N
42.42 cm = 0.4242 m
τ₁ = (29.4 N)(0.4242 m)
τ₁ = 12.47 Nm
Now, we calculate the torque due to the his arm:
τ₁ = F₁d₁
where,
τ₂ = Torque due to arm = ?
F₂ = Force due to arm = m₂g = (3.8 kg)(9.8 m/s²) = 37.24 N
d₂ = perpendicular distance between center of mass and shoulder = 40% of (60 cm)(Cos 45°) = (0.4)(42.42 cm) = 16.96 cm = 0.1696 m
τ₂ = (37.24 N)(0.1696 m)
τ₂ = 6.32 Nm
Since, both torques have same direction. Therefore, total torque will be:
τ = τ₁ + τ₂
τ = 12.47 Nm + 6.32 Nm
τ = 18.79 Nm
A)The magnitude of the torque about his shoulder if he holds his arm straight out to his side, parallel to the floor will be 26.58 Nm.
What is torque?
Torque is the force's twisting action about the axis of rotation. Torque is the term used to describe the instant of force. It is the rotational equivalent of force. Torque is a force that acts in a turn or twist.
The amount of torque is equal to force multiplied by the perpendicular distance between the point of application of force and the axis of rotation.
m is the mass of steel ball = 3.0 kg in his hand.
L is the length of the arm is 60 cm long
M is the mass of arm=3.8 kg,
The torque is given as;
The magnitude of the torque about his shoulder if he holds his arm straight out to his side, parallel to the floor is found as;
[tex]\rm \tau_1 = F \times d \\\\ \rm \tau_1 = 29.4 \times 0.63 \\\\ \rm \tau_1 =17.64 \ Nm[/tex]
The torque due to the arm;
[tex]\rm \tau_2= F \times d \\\\ \rm \tau_2 = mg \times d \\\\ \rm \tau_2 =3.8 \times 9.81 \times 0.24 \ Nm \\\\ \rm \tau_2=8.94 \ Nm[/tex]
The net torque for case 1 will be;
[tex]\tau = \tau_1 + \tau_2\\\\ \rm \tau = 17.64 Nm + 8.94 Nm\\\\ \tau = 26.58 Nm[/tex]
Hence the magnitude of the torque about his shoulder if he holds his arm straight out to his side, parallel to the floor will be 26.58 Nm.
B) the magnitude of the torque about his shoulder if he holds his arm straight, but 45∘ below horizontal will be 18.79 Nm.
The torque is due to the weight of the ball;
[tex]\rm \tau_1= F \times d \\\\ \rm \tau_1 = mg \times d \\\\ \rm \tau_1 =3.8 \times 9.81 \times 0.4242 \ Nm \\\\ \rm \tau_1= 12.47 \ Nm[/tex]
The torque due to the arm will be;
[tex]\rm \tau_2= F \times d \\\\ \rm \tau_2 = mg \times d \\\\ \rm \tau_2 =3.8 \times 9.81 \times 0.1696 \ Nm \\\\ \rm \tau_2=6.32 \ Nm[/tex]
The net torque in case 2 will be
[tex]\tau = \tau_1 + \tau_2\\\\ \rm \tau = 12.47 Nm + 6.32 Nm\\\\ \tau = 18.79 Nm[/tex]
Hence the magnitude of the torque about his shoulder if he holds his arm straight, but 45° below horizontal will be 18.79 Nm
To learn more about the torque refer to the link;
brainly.com/question/6855614
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