Solving Rotational Statics: Force Left Support Exerts on Beam

Click For Summary
SUMMARY

The discussion focuses on calculating the force exerted by the left support on a balance beam with a gymnast standing on it. The beam has a mass of 118 kg and a length of 5 m, with the gymnast weighing 46 kg. The equations used include the sum of torques and forces, leading to the equation N1 = (2Lm1g + Lm2g)/2. The user initially calculated N1 incorrectly as 7406.55 N but later corrected their algebraic mistakes to arrive at the correct solution.

PREREQUISITES
  • Understanding of rotational statics principles
  • Knowledge of torque and force equilibrium equations
  • Familiarity with basic physics concepts such as mass, gravity, and acceleration
  • Ability to perform algebraic manipulations and solve equations
NEXT STEPS
  • Study the principles of static equilibrium in physics
  • Learn about torque calculations and their applications in engineering
  • Explore advanced problems in rotational dynamics
  • Practice solving similar problems involving multiple forces and supports
USEFUL FOR

Students in physics or engineering courses, particularly those studying mechanics, as well as educators looking for examples of rotational statics problems.

ryanmk54
Messages
2
Reaction score
0

Homework Statement


A gymnast with mass m1 = 46 kg is on a balance beam that sits on (but is not attached to) two supports. The beam has a mass m2 = 118 kg and length L = 5 m. Each support is 1/3 of the way from each end. Initially the gymnast stands at the left end of the beam.
What is the force the left support exerts on the beam?


Homework Equations


Sum of Torques = 0
Sum of Forces = 0
F = ma
T = rf


The Attempt at a Solution


I set the second beam as the axis of rotation since that is an unknown quantity.
m1 = man
m2 = beam
N1 = first support
N2 = second support

The equations I got are:
m1*g + m2*g - N1 - N2 = 0
-2L*m1*g/3 + LN1/3 - L*m2g/6 = 0

Using the second equation, I solved for N1 = 2Lm1g+Lm2g/2 = 7406.55 which is wrong

What am I doing wrong?
 
Physics news on Phys.org
ryanmk54 said:

Homework Statement


A gymnast with mass m1 = 46 kg is on a balance beam that sits on (but is not attached to) two supports. The beam has a mass m2 = 118 kg and length L = 5 m. Each support is 1/3 of the way from each end. Initially the gymnast stands at the left end of the beam.
What is the force the left support exerts on the beam?


Homework Equations


Sum of Torques = 0
Sum of Forces = 0
F = ma
T = rf


The Attempt at a Solution


I set the second beam as the axis of rotation since that is an unknown quantity.
m1 = man
m2 = beam
N1 = first support
N2 = second support

The equations I got are:
m1*g + m2*g - N1 - N2 = 0
-2L*m1*g/3 + LN1/3 - L*m2g/6 = 0

Using the second equation, I solved for N1 = 2Lm1g+Lm2g/2 = 7406.55 which is wrong

What am I doing wrong?

Check your algebra for solving this equation:

-2L*m1*g/3 + LN1/3 - L*m2g/6 = 0
 
Thank you. I was able to solve it correctly. I'll have to watch out for algebra mistakes.
 

Similar threads

Please help with PHYS-1 Problem Forces/Static/Equilibrium
  • · Replies 5 ·
Replies
5
Views
4K
Rotational Statics Of A Balance Beam
  • · Replies 1 ·
Replies
1
Views
10K
Statically Indeterminate Truck - Finding reaction forces at supports
  • · Replies 8 ·
Replies
8
Views
3K
Static equilibrium: mass on beam
  • · Replies 2 ·
Replies
2
Views
2K
How Do You Calculate Forces and Balance a Hanging Cafe Sign?
  • · Replies 18 ·
Replies
18
Views
3K
Torque Rigid Beam: Find Force Applied by Support 2
  • · Replies 4 ·
Replies
4
Views
2K
Pin and cable supported by a beam
  • · Replies 1 ·
Replies
1
Views
3K
Torque seesaw problem- rotational equilibrium
  • · Replies 7 ·
Replies
7
Views
19K
Frictional Forces: Stacked boxes, pulley with weight.
  • · Replies 1 ·
Replies
1
Views
7K
Chain Sliding on a Pulley: Acceleration and Force Analysis
  • · Replies 6 ·
Replies
6
Views
3K