The brachialis muscle exerts a force of 300 N on the radius bone while the muscle is oriented 40° with respect to the proximal surface of the radius. What is the amount of force which is oriented perpendicular to the radius?
Question
The brachialis muscle exerts a force of 300 N on the radius bone while the muscle is oriented 40° with respect to the proximal surface of the radius. What is the amount of force which is oriented perpendicular to the radius?
Solution
To find the force oriented perpendicular to the radius, we need to calculate the vertical component of the force exerted by the brachialis muscle. This can be done using the formula for the component of a vector in a given direction, which is:
F_perpendicular = F * sin(θ)
where: F is the magnitude of the force (300 N in this case), θ is the angle between the force and the direction of interest (40° in this case).
First, convert the angle from degrees to radians because the trigonometric functions in most calculators and programming languages use radians. There are π (approximately 3.14159) radians in 180 degrees, so the conversion factor is π/180.
θ_rad = 40 * π/180 = 0.6981 radians
Then, calculate the vertical component of the force:
F_perpendicular = 300 N * sin(0.6981 rad) = 300 N * 0.6428 = 192.84 N
So, the amount of force which is oriented perpendicular to the radius is approximately 192.84 N.
Similar Questions
How much force must be produced by the fibers of a pennate muscle aligned at 75° to a central tendon to create a tensile force of 400 N in the tendon?
If the biceps brachii, attaching to the radius 2.5 cm from the elbow joint produces 250 N of tension perpendicular to the bone, and the triceps brachii attaching 3 cm away from the elbow joint exerts 200 N of tension perpendicular to the bone how much net torque is present at the joint?Question 23Select one:a.0.25 Nm flexionb.0.25 Nm extensionc.No movement at the jointd.2.5 Nm flexione.2.5 Nm extension
The deltoids exert a force of 100 N at an angle of 45 degrees to the humerus.The tendon inserts 7.5 cm from the shoulder joint axis of rotation.The arm is abducted 45 degrees from the vertical or anatomical position.The combined weight of the upper arm, forearm, and hand is 75 N acts at the center of gravity of the upper extremity which is 15 cm from the shoulder joint axis.What is the torque about the shoulder developed by the deltoids in Nm?
The hamstrings pull on the tibia with a force of 510 N at 30° to the bone; that is the angle between the force vector and tibia is 30°. The distance along the tibia from the knee joint center to the tendon insertion is 3.5 cm. What is the magnitude of the force component that is parallel to the tibia?
If the radius were increased to 40 x its length, what would be the new force? ___________________ x original force.
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.