# Solving a Physics Problem: Finding Pole Mass, Forces & Distance

• PhilCam
In summary: Then, use the equations for torque and force in the horizontal and vertical directions to solve for the unknown values. In summary, Peter and Paul are carrying a 6 kg box hung from a 1.4 m long, homogeneous pole of unknown mass. The pole is held horizontally with Peter applying a 67.9 N force at a 60 degree angle and Paul applying an unknown force at a 30 degree angle. To determine the unknown values, a free-body diagram must be drawn and the equations for torque and force in the horizontal and vertical directions must be used to solve for the unknown values.
PhilCam

## Homework Statement

At the end of the semester Peter and Paul are moving out of the dorms. The are holding a 6 kg box hung from a homogeneous pole of unknown mass. The position from which the 6 kg box is hung is also unknown. The length of the pole is 1.4 m. As they carry the box, the pole is horizontal. At the left end of the, Peter applies a force of 67.9 N making an angle of 60 degrees with the horizontal. At the right end, Paul applies an unknown force making a 30 degree angle with the horizontal. The system is in static equilibrium.

A) The x-component of the force applied by Peter is?
B)The magnitude of the force applied by Paul is?
C)The unknown mass of the pole is?
D) The distance to the left end of the pole form the point where the 6 kg mass is hung is?

I have figured out A by 67.9 x Cos 60 = -33.95.

For part B, I assumed that the magnitude of Paul would have to equal the magnitude of Peter's force but I have not been able to come up witht he answer. Thanks.

Start by drawing a free-body diagram of the pole. Remember that in static equilibrium, all forces and all torques must sum to 0.

I would approach this problem by first drawing a free-body diagram of the system and labeling all the known and unknown forces. Then, using the principles of static equilibrium, I would set up equations to solve for the unknowns.

For part A, the x-component of Peter's force can be calculated using the equation Fx = Fcosθ, where θ is the angle between the force and the horizontal. In this case, it would be -33.95 N.

For part B, the magnitude of Paul's force can be found by setting up an equation for the sum of forces in the y-direction, since the system is in static equilibrium. This would be: Fy = Fsinθ + 6kg x g = 0, where g is the acceleration due to gravity. Solving for F, we get F = -29.4 N.

For part C, we can use the equation for torque, τ = r x F, where r is the distance from the point where the force is applied to the point where the mass is hung. Since the system is in static equilibrium, the torque must be equal to zero. Therefore, we can set up the following equation: r x 67.9cos60 - (1.4-r) x 29.4cos30 = 0. Solving for r, we get r = 1.18 m. Then, using the equation for torque again, we can solve for the unknown mass of the pole: 1.18 x 67.9cos60 = (1.4-1.18) x M, where M is the unknown mass. Solving for M, we get M = 7.88 kg.

For part D, the distance to the left end of the pole from the point where the 6 kg mass is hung can be found by subtracting the distance r from the total length of the pole, 1.4 m. Therefore, the distance would be 0.22 m.

In conclusion, by approaching this problem systematically and using the principles of physics, we were able to solve for all the unknown variables and find the answers to the given questions.

## What is pole mass?

Pole mass is a term used in physics to describe the mass of a particle at rest. It is also known as the invariant mass or the rest mass of the particle. It is a fundamental property of a particle and does not depend on its motion or velocity.

## How is pole mass measured?

Pole mass can be measured using a variety of techniques, including particle accelerators, mass spectrometers, and calorimeters. These methods involve measuring the energy and momentum of a particle and using equations such as E=mc^2 to calculate its mass.

## What are the forces involved in solving a physics problem?

The forces involved in solving a physics problem depend on the specific problem at hand. Some common forces include gravity, friction, electromagnetic forces, and nuclear forces. It is important to identify and properly consider all relevant forces in order to accurately solve a physics problem.

## What is the significance of distance in solving a physics problem?

Distance is a crucial factor in many physics problems as it is used to calculate important quantities such as displacement, velocity, and acceleration. It is also essential for understanding the effects of forces and the motion of objects in various situations.

## How can I approach solving a physics problem involving pole mass, forces, and distance?

To solve a physics problem involving pole mass, forces, and distance, it is important to first clearly understand the question and identify any relevant equations or principles. Then, set up a systematic approach to solving the problem, considering all relevant forces and using appropriate units. Finally, double-check the answer and ensure it makes sense in the context of the problem.

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