Force Problem Help: Acceleration and Tension of Connected Objects | Figure P4.62

[parwana]

Three objects are connected by light strings as shown in Figure P4.62. The string connecting the m1 = 4.00 kg mass and the m2 = 4.00 kg mass passes over a light frictionless pulley.


Figure P4.62

(a) Determine the acceleration of each mass. m/s2 (magnitude)

(b) Determine the tension in the two strings.
string between m1 and m2 N
string between m2 and the 3.00 kg mass N


I try and try but still don't get it right. Please help

 

[OlderDan]

Three objects are connected by light strings as shown in Figure P4.62. The string connecting the m1 = 4.00 kg mass and the m2 = 4.00 kg mass passes over a light frictionless pulley.


Figure P4.62

(a) Determine the acceleration of each mass. m/s2 (magnitude)

(b) Determine the tension in the two strings.
string between m1 and m2 N
string between m2 and the 3.00 kg mass N


I try and try but still don't get it right. Please help

Draw a free body diagram for each object that moves in the problem. You will have three different tensions to deal with. Come back when you have three equations from applying Newtons second law to each object. If you can, solve them yourself.

 

[kyle8921]

I understand that this type of problem involves analyzing the forces acting on each object and using Newton's laws of motion to determine the acceleration and tension. I will provide a step-by-step approach to solving this problem and hopefully help you understand the concept better.

Step 1: Draw a free-body diagram for each object. This will help us visualize the forces acting on each object.

Object m1: The forces acting on m1 are its weight (mg) downwards and the tension force (T1) upwards.

Object m2: The forces acting on m2 are its weight (mg) downwards, the tension force (T1) downwards (since it is connected to m1), and the tension force (T2) upwards (since it is connected to the 3.00 kg mass).

Object 3.00 kg: The forces acting on the 3.00 kg mass are its weight (mg) downwards and the tension force (T2) downwards (since it is connected to m2).

Step 2: Apply Newton's second law of motion (F=ma) to each object.

Object m1: The net force acting on m1 is T1 - mg. Since the acceleration is unknown, we can set up the equation as T1 - mg = ma. We also know that m1 = 4.00 kg, so we can substitute that into the equation. T1 - 4.00 kg * 9.8 m/s^2 = 4.00 kg * a. Solving for a, we get a = (T1 - 39.2 N)/4.00 kg.

Object m2: The net force acting on m2 is T2 - T1 - mg. We can set up the equation as T2 - T1 - mg = ma. We also know that m2 = 4.00 kg, so we can substitute that into the equation. T2 - T1 - 4.00 kg * 9.8 m/s^2 = 4.00 kg * a. Solving for a, we get a = (T2 - T1 - 39.2 N)/4.00 kg.

Object 3.00 kg: The net force acting on the 3.00 kg mass is T2 - mg. We can set up the equation as T2 - mg = ma. We also know that m = 3.