Force of a pin holding up a beam
A 2.5 m uniform 15 kg beam is attached at an angle of 30 degrees above the horizontal to a wall by a pin. The other end of the beam is supported by a massless cable attached from the end of the beam to the wall. The support cable makes an angle of 60 degrees with respect to the wall. A weight of 350 N is suspended 30 cm from the end of the beam. What is the magnitude and direction of the force of the wall acting on the beam?
Shouldn't the force be in the direction of the beam? So I just use the torques to find the tension force, set the walk force in the x direction equal to the tension's x direction, and the use the angle to find the full force?
Answer
In general you never want to assume you know the direction of the force of a wall. It is best to write it in terms of its components Fx and Fy. You can treat these components as if they were two separate forces pointing in the x and y directions respectively, and at the end you can recombine them into the total force of the wall to find the direction and magnitude.
Draw a picture, then draw all the forces acting on the beam. Thinking it through we have:
- Force of gravity on the beam, pointing down
- Fx and Fy from the wall
- Suspended weight, pointing down
- Tension from cable, pointing along cable
You know the net force and net torque must be zero, so set the x and y components of the net force to zero and set the sum of the torques to zero.
Customer support service by UserEcho
In general you never want to assume you know the direction of the force of a wall. It is best to write it in terms of its components Fx and Fy. You can treat these components as if they were two separate forces pointing in the x and y directions respectively, and at the end you can recombine them into the total force of the wall to find the direction and magnitude.
Draw a picture, then draw all the forces acting on the beam. Thinking it through we have:
- Force of gravity on the beam, pointing down
- Fx and Fy from the wall
- Suspended weight, pointing down
- Tension from cable, pointing along cable
You know the net force and net torque must be zero, so set the x and y components of the net force to zero and set the sum of the torques to zero.