Translational Equilibrium Practice problem

Thread starter hraghav
Start date Feb 18, 2024
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Equilibrium Translational

Feb 18, 2024

hraghav

Homework Statement: So I am basically stuck at one of the practice problems. The questions states that: A box of mass 𝑀=52.9kg is on a rough surface. It is being pulled by a force of magnitude 𝑇 at an angle of 𝜃=18.4 degrees with the horizontal. The box has a coefficient of static friction 𝜇=0.393 with the surface. What is the angle the force of friction makes with the positive x-axis and positive z-axis? What is the angle the normal force makes with the positive x-axis and positive z-axis?

Relevant Equations: So for frictional force angles I tried to do 180 - 18.4 = 161.6 degrees for x axis as frictional force is in the opposite direction of the force applied and z axis is 18.4. For normal force x axis I did 18.4 and z axis I did 90-18.4. But I got all of them wrong not sure what I am doing wrong. Could someone please help me with this. I have also attached a picture for the problem for reference. Thank you!

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Feb 18, 2024

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Feb 19, 2024

hraghav

Thank you I did find my mistake, I was considering the force of rope vector for my calculations. which was not the right way. The correct answer for the frictional forces was 180 degree in x axis and 90 in the z axis and for normal force was 90 x axis and 0 in the z axis!

FAQ: Translational Equilibrium Practice problem

What is translational equilibrium?

Translational equilibrium occurs when the sum of all forces acting on an object is zero, resulting in the object either being at rest or moving with a constant velocity. This means there is no net force causing a change in the object's motion.

How do you determine if an object is in translational equilibrium?

To determine if an object is in translational equilibrium, you need to calculate the vector sum of all the forces acting on the object. If the resultant force is zero, then the object is in translational equilibrium. This involves breaking down the forces into their components and ensuring that the sum of the forces in each direction (usually x and y) is zero.

What are some common examples of translational equilibrium in everyday life?

Common examples of translational equilibrium include a book resting on a table (where the gravitational force is balanced by the normal force from the table), a car moving at a constant speed on a straight road (where the driving force is balanced by friction and air resistance), and a suspended chandelier (where the tension in the chain balances the weight of the chandelier).

How do you solve a translational equilibrium practice problem?

To solve a translational equilibrium practice problem, follow these steps: (1) Draw a free-body diagram of the object, showing all the forces acting on it. (2) Break down each force into its components along the x and y axes. (3) Write equations for the sum of the forces in each direction. (4) Set these sums equal to zero (since the net force must be zero). (5) Solve the resulting system of equations to find the unknown forces or other quantities.

What are the key formulas used in translational equilibrium problems?

The key formulas used in translational equilibrium problems are the equations for the sum of the forces in each direction. For the x-direction: ΣF_x = 0, and for the y-direction: ΣF_y = 0. These equations ensure that the net force in each direction is zero, indicating translational equilibrium.