Torque/Vertical Force Problem

  • Thread starter kp87
  • Start date
  • Tags
    Force
In summary, we are trying to find the vertical forces (A and B) on the two supports of a horizontal beam with a piano (275 kg) resting a quarter of the way from one end. Using the equation Tcw=Tccw (sum of clockwise moments equals sum of counterclockwise moments), we can set up a system of equations to solve for A and B. The solution is 1042N for the support closest to the piano and 2391N for the support farthest from the piano.
  • #1
kp87
7
0

Homework Statement


A 75.0 kg horizontal beam is supported at each end. A 275 kg piano rests a quarter of the way from one end. What is the vertical force on the support closest to the piano?
What is the vertical force on the support farthest from the piano?

Homework Equations


Tcw=Tccw



The Attempt at a Solution


I tried using Tcw=Tccw
so Fpiano*r1+Fbeam*r2=Fbeam*r3
so 275*9.81*3/4+75*9.81*1/2=Fb*1
So I got 2391N for the farthest beam
and 275*9.81*1/4+75*9.81*1/2=Fb*1
and got 1042N for the closer one but they seem to be wrong...
can you guys help me on this?

nvm... I got the answer now I did it backwards so the one with 1042N is farthest and 2391N is the closest...
thanks lol
 
Last edited:
Physics news on Phys.org
  • #2
Simplify your notation. Let A be the reaction force at the support closer to the piano (let's say, the left one), and B the other reaction force. Then set the sum of moments around support B (the one further from the piano) equal to zero. Let the length of the beam be L.

Edit: don't forget to count the weight of the beam (whose resultant is acting at the center of the beam) in your calculation.
 
  • #3


I would like to confirm that your solution is correct. It is important to note that in this problem, we are dealing with torque, which is a measure of the turning force on an object. The equation Tcw=Tccw, also known as the principle of moments, states that the sum of clockwise torques must equal the sum of counterclockwise torques for an object to be in rotational equilibrium.

In this case, we have two counterclockwise torques (from the piano and the beam) and one clockwise torque (from the support closest to the piano). By setting these torques equal to each other, we can solve for the unknown vertical force on the support closest to the piano.

Similarly, for the support farthest from the piano, we have two counterclockwise torques (from the piano and the beam) and one clockwise torque (from the support farthest from the piano). By setting these torques equal to each other, we can solve for the unknown vertical force on the support farthest from the piano.

Overall, your solution demonstrates a good understanding of the principles of torque and rotational equilibrium. Keep up the good work!
 

What is torque?

Torque is a measure of the force that can cause an object to rotate around an axis. It is calculated by multiplying the force applied to an object by the distance from the axis of rotation to the point where the force is applied.

What is vertical force?

Vertical force, also known as weight or gravitational force, is the force exerted by a mass due to gravity. It acts in a downward direction and is equal to the mass of an object multiplied by the acceleration due to gravity (9.8 m/s² on Earth).

How are torque and vertical force related?

Torque and vertical force are related because torque is dependent on the force applied to an object and the distance from the axis of rotation, while vertical force is a type of force that can contribute to the overall torque on an object.

What is the equation for calculating torque?

The equation for calculating torque is torque = force x distance from axis of rotation. It is typically measured in units of newton-meters (Nm) or foot-pounds (ft-lb).

How can you increase torque in a vertical force problem?

To increase torque in a vertical force problem, you can either increase the force applied to the object or increase the distance from the axis of rotation at which the force is applied. This will result in a greater torque and can be achieved by using a longer lever arm or applying more force to the object.

Similar threads

  • Introductory Physics Homework Help
Replies
4
Views
1K
Replies
6
Views
634
  • Introductory Physics Homework Help
Replies
14
Views
1K
  • Introductory Physics Homework Help
Replies
15
Views
1K
  • Introductory Physics Homework Help
Replies
11
Views
1K
  • Introductory Physics Homework Help
Replies
1
Views
4K
  • Mechanics
Replies
2
Views
826
  • Introductory Physics Homework Help
Replies
1
Views
2K
  • Introductory Physics Homework Help
Replies
4
Views
4K
  • Introductory Physics Homework Help
Replies
7
Views
1K
Back
Top