hey, i was wondering if someone could explain and help me with this problems.
please and thank you!
A person holds an object of mass m = 4 kg on the palm of the hand with the arm stretched as shown in the attached figure. Use the torque equilibrium equation to determine the magnitude of the force F exerted by the biceps muscle when a = 27 cm, b = (0.15 · a), and the angle θ = 75°. Neglect the weight of the lower arm.
A person bends over as shown in the attached figure, part (a), and lifts an object of mass m = 29.2 kg while keeping the back parallel with the floor. The muscle that attaches 2/3 of the way up the spine maintains the position of the back. This muscle is called the back muscle or latissimus dorsi muscle. The angle between the spine and the force T in this muscle is θ = 10°.
I can't offer any help without a diagram.
Sure! I can help you with these physics problems.
For the first problem, we can use the torque equilibrium equation to determine the magnitude of the force exerted by the biceps muscle. The torque equilibrium equation states that the sum of the torques acting on an object in equilibrium must be zero.
In this case, the torque exerted by the weight of the object is counteracted by the torque exerted by the force F. The torque due to the weight of the object can be calculated as (m*g*d), where m is the mass of the object, g is the acceleration due to gravity (approximately 9.8 m/s^2), and d is the perpendicular distance between the point of rotation (the shoulder joint) and the line of action of the weight.
To find the torque exerted by the force F, we can use the equation Torque = Force * Distance * sin(theta), where theta is the angle between the force and the perpendicular distance. In this case, the distance would be b, and the angle would be theta.
So, in summary, the torque equilibrium equation would be:
(m*g*d) = F * b * sin(theta)
Now, we can substitute the given values into this equation. Assuming the acceleration due to gravity is 9.8 m/s^2, we have:
m = 4 kg
a = 27 cm = 0.27 m
b = 0.15 * a = 0.15 * 0.27 = 0.04 m
theta = 75°
Plugging in these values, the equation becomes:
(4 kg * 9.8 m/s^2 * d) = F * (0.04 m) * sin(75°)
To determine the magnitude of the force F, we need to find the value of d. The given figure does not provide the value of d, so it's not possible to directly solve for F without additional information.
Moving on to the second problem, we are asked to determine the angle between the spine and the force T, which is held by the back muscle or latissimus dorsi muscle.
To find this angle, we can use the concept of equilibrium of forces. If the person is lifting the object while keeping the back parallel with the floor, the net force acting on the person's body should be zero in the vertical direction.
In this case, the weight of the object is counteracted by the vertical component of the force T. The weight of the object can be calculated as (m * g), where m is the mass of the object and g is the acceleration due to gravity (approximately 9.8 m/s^2).
The vertical component of the force T can be calculated as T * cos(theta), where theta is the angle between the force T and the vertical direction (which is 90 degrees, since the person is keeping the back parallel with the floor).
Setting up the equilibrium equation, we have:
(m * g) = T * cos(theta)
Plugging in the given values, we have:
m = 29.2 kg
theta = 10°
The equation becomes:
(29.2 kg * 9.8 m/s^2) = T * cos(10°)
Now, we can solve for the magnitude of the force T by rearranging the equation:
T = (29.2 kg * 9.8 m/s^2) / cos(10°)
Evaluating this expression, we can determine the magnitude of the force T exerted by the back muscle to maintain the position of the back.