Calculating Acceleration and Tension in a Two-Block System with Friction

[wolves5]

A block of mass m1 = 2 kg and a block of mass m2 = 3 kg are tied together and are pulled from rest across the floor by a force of Fp = 30 N. The coefficient of friction of the blocks with the floor is µ = 0.23.

a) What is the acceleration of the two blocks?

For this question, I used Newton's Second Law. I used F=ma. I did 30=(5 kg)(a). I got 6 m/s2 for the acceleration, but that's not right. How do I do the acceleration then?

b) What is the tension in the string between the blocks?
I think I can do b if I get the accelration from part a. I think the equation is T=ma.

 

[Yuqing]

For a, you're forgetting friction in the net force sum. Try b after you get a.

 

[wolves5]

Is that Fk=(mew)(mass)(acceleration)? But then what's Fk?

 

[Yuqing]

I think you're misunderstanding what exactly the coefficient of kinetic friction is. It is the ratio of the frictional force to the normal force of the object.

 

[rwisz]

So, T=(5 kg)(6 m/s2) = 30 N.

Hello! Your approach is correct, but there are a few things to consider in order to get the correct answers. Let's go through the steps together.

a) To calculate the acceleration, we need to take into account the friction force acting on the blocks. This force opposes the motion and needs to be subtracted from the applied force Fp. So the equation would be: Fp - µmg = ma. Here, µ is the coefficient of friction, m is the total mass of the blocks (2 kg + 3 kg = 5 kg), and g is the acceleration due to gravity (9.8 m/s^2). Plugging in the values, we get: 30 N - (0.23)(5 kg)(9.8 m/s^2) = (5 kg)(a). Solving for a, we get an acceleration of 4.87 m/s^2.

b) Now that we have the correct acceleration, we can use the equation T=ma to find the tension in the string. So, T = (5 kg)(4.87 m/s^2) = 24.35 N.

It's important to remember that in this system, the tension in the string is the same for both blocks, but the acceleration is different due to the difference in mass. I hope this helps clarify the process for you. Keep up the good work!