Solve Torque & Force: 2 Questions Homework

[BATBLady]

Homework Statement

1) In an isometric exercise a person places a hand on a scale and pushes vertically downward, keeping the forearm horizontal. This is possible because the triceps muscle applies an upward force M perpendicular to the arm, as the drawing indicates. The forearm weighs 23.0 N and has a center of gravity as indicated. The scale registers 128 N. Determine the magnitude of M. Distances from the elbow joint (point of rotation) and the muscle: 0.025m ; the cg of the arm: 0.15m ; where the hand rests on the scale: 0.30m
http://www.webassign.net/v4cgiaubel.3@osu/student.pl?l=20090605154839aubel.3@osu1402545781

2)A 1340 N uniform beam is attached to a vertical wall at one end and is supported by a cable at the other end. A W = 2000 N crate hangs from the far end of the beam. The angle from the wall to the beam is 30 degrees, the angle from the cable to the horizontal is 50 degrees. Angle from the box to the bar is 60 degrees.
(a) Calculate the magnitude of the tension in the wire.
(b) Calculate the magnitude of the horizontal and vertical components of the force that the wall exerts on the left end of the beam.
http://www.webassign.net/v4cgiaubel.3@osu/student.pl?l=20090605154839aubel.3@osu1402545781

Homework Equations

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The Attempt at a Solution

1) I was using the $$E\$$ T= (F1*d1) + (F2*d2) +...+ (Fn*dn) = 0

2) $$E$$T= T_cable*d*sin80-W_b*d_b*sin60-W_c*d_c*sin60
and solving for T_cable
then F_x and F_y I was trying to solve with a similar equation to #1.

I haven't been able to figure out either. Any and all help would be greatly appreciated. I tried to insert the pictures, but for some reason they won't insert them.

 

[anathema]

it is important to approach problems like these using a systematic and logical approach. The first step would be to identify all the given information, including the forces involved, distances, and angles. Then, using the appropriate equations and principles of physics, you can solve for the unknowns.

For the first problem, it seems like you are on the right track by using the equation ΣT = 0, which represents the equilibrium of torques. However, it is important to note that the torque is not simply the force multiplied by the distance, but rather the force multiplied by the perpendicular distance from the pivot point (in this case, the elbow joint). So the equation should be written as ΣT = 0 = M*d*cosθ - 23.0N*0.15m*sinθ - 128N*0.30m*sinθ, where θ is the angle between the force M and the horizontal direction.

For the second problem, you can approach it by considering the equilibrium of forces in both the horizontal and vertical directions. In the horizontal direction, the tension in the cable and the horizontal component of the force from the wall must balance the weight of the beam and crate. In the vertical direction, the vertical component of the force from the wall must balance the weight of the beam and crate. Using the given angles and the trigonometric identities, you can write equations for each direction and solve for the unknowns.

In both of these problems, it is important to carefully consider the direction and sign of each force, as well as the definition of torque and the equilibrium conditions. With a systematic approach, you should be able to solve these problems successfully.

 

[nlightner]

1) In this problem, we are dealing with torque and force. Torque is a measure of the rotational force applied to an object, while force is a measure of the push or pull on an object. In order to solve this problem, we can use the equation T = F*d*sin(theta), where T is torque, F is force, d is the distance from the point of rotation, and theta is the angle between the force and the lever arm (distance from the point of rotation). We can also use the equation Fnet = ma, where Fnet is the net force acting on the object, m is the mass of the object, and a is the acceleration.

In this case, we can consider the hand as the point of rotation, and the triceps muscle as the force being applied. The weight of the forearm will also contribute to the net force acting on the arm. Using the given distances, we can calculate the torque applied by the triceps muscle as T = M*d*sin(90°), where M is the unknown force, d is the distance from the elbow joint to the muscle (0.025m), and sin(90°) is equal to 1. The torque due to the weight of the forearm can be calculated as T = 23.0 N*0.15 m*sin(90°). Since the forearm is not rotating, the net torque must be equal to 0, so we can set these two equations equal to each other and solve for M. This will give us the magnitude of the force applied by the triceps muscle.

2) In this problem, we are dealing with a beam attached to a wall and supported by a cable, with a crate hanging from the far end. We need to calculate the magnitude of the tension in the wire and the horizontal and vertical components of the force that the wall exerts on the left end of the beam.

To find the tension in the wire, we can use the equation T = mg, where T is tension, m is the mass of the crate, and g is the acceleration due to gravity. However, we need to take into account the angles involved. The force of gravity is acting vertically downward, so we need to find the vertical component of the tension, which is given by T*sin(50°). This must be equal to the weight of the crate, so we can set these two equations equal to each other and solve for T.

To find