What is the acceleration and tension?

Question

A 3kg block is hanging at the side of a table and is attached to a 5kg block on a table which is frictionless, with a string. Determine the acceleration of the blocks and the tension in the string. Draw free body diagrams for each block and show forces and direction of acceleration. Use sum of all forces = mass *acceleration.

Answer 1

This is a modified Atwood machine problem (can google this to see what an Atwood machine is).

Step 1: Draw a picture (see video).

Step 2: Draw a free-body diagram for each mass.

Step 3: Use Newton's second law (∑F = ma) and the free-body diagrams to set up the relationships (equations) for each mass. The only force acting on the 5 kg block is tension from the string: ∑F₂ = T = m₂a. The forces acting on the 3 kg block are the force due to gravity (mg) and the tension from the string: ∑F₁ = F_g - T ⇒ m₁g - T = m₁a , The tension in the string is the same for both masses, so you can substitute in for T: ∑F₁ = m₁g - m₂a = m₁a .

Step 4: Done with the physics part! Now you have a system of equations for which you can find the acceleration (and thereby the Tension also). m₁ , m₂ , are given and g= 9.8 m/s² . Substitute and solve for a. Then use T = m₂a to find the tension.