Two Objects, Acceleration is Given, Find Tension of rope on frictionless pulley

[spacewrangler]

Picture has two objects, one on top of the other - the bottom object has a mass of 8 kg. The top object has a mass of 4 kg. The coefficient of friction between bottom object and floor is 0.3. The coefficient of friction between the two objects is 0.2. Acceleration is 4 m/s2. A rope is on a pulley starting from bottom box, thru top box. What is Tension?

I have been working on this problem for about two hours. I've found normal force and frictional force for both objects... every problem I've found similar on the internet solves for acceleration... but acceleration is given in this case. Please help find T1.

Must turn in by 4:45. Any help would be greatly appreciated. I'm extremely frustrated.

-KL

 

[tiny-tim]

Welcome to PF!

Hi spacewrangler ! Welcome to PF!

(4:45 which time-zone?)

Sorry, I don't understand what the rope and pulley are doing …

where is the pulley, which direction is the rope going either side of the pulley, and how does the rope avoid obstructing the top box?

 

[kerimek]

Hello KL,

I understand your frustration with this problem. Let's work through it together to find the tension in the rope.

First, let's draw a free body diagram for each object. The bottom object has a weight of 8 kg and is in contact with the floor, so it experiences a normal force and a frictional force due to the coefficient of friction between the object and the floor. The top object has a weight of 4 kg and is in contact with the bottom object, so it experiences a normal force and a frictional force due to the coefficient of friction between the two objects. In addition, both objects are connected by a rope that goes over a frictionless pulley.

Next, let's write out the equations of motion for each object. For the bottom object, we know that the net force in the vertical direction is equal to the weight minus the normal force, which is equal to the mass times the acceleration (Fnet = m*a). We also know that the frictional force is equal to the coefficient of friction times the normal force (Ffr = μ*Fn). We can use these equations to solve for the normal force and the frictional force for the bottom object.

For the top object, we know that the net force in the vertical direction is equal to the weight minus the normal force, which is also equal to the mass times the acceleration. We can use this equation to solve for the normal force for the top object.

Now, let's consider the horizontal direction. Since the pulley is frictionless, the tension in the rope will be the same on both sides of the pulley. This means that the tension in the rope on the bottom object (T1) is equal to the tension in the rope on the top object (T2). We can use this information to set up an equation for the horizontal forces on each object.

Finally, we can use these equations to solve for the tension in the rope (T1). We can substitute in the values we know (masses, acceleration, coefficients of friction) and solve for T1. It may also be helpful to use a system of equations to solve for T1 and T2 simultaneously.

I hope this helps guide you in finding the tension in the rope. Remember to always draw a clear diagram and write out all the relevant equations before plugging in values. Good luck!