Basic Physics Problem: Acceleration and Tension of Connected Blocks"

[kikisf20c]

Hi guys,i'm happy to join you.
I have the problem shown below for homework and i don't know how to solve it. This is becouse i have missed a lot of lessons during this month becouse of an illness.
I will apreciate it if anyone can help me with the problem. Thanks.

Problem:
Two blocks, one 0.8 kg and the other 2.0 kg are connected by a massless string over a frictionless pulley. The coefficient of kinetic friction is 0.14, and the downward ramp angle is 60 degrees.

a) Determine the acceleration of the blocks.

b) Calculate the tension of the string.

 

[tiny-tim]

Welcome to PF!

Hi kikisf20c! Welcome to PF!

(which mass is hanging vertically? and is that 60º from the horizontal?)

The tension in the string will be the same at both ends (because the pulley is frictionless).

And the acceleration of both blocks will be the same (beacuse the length of the string is constant).

And the friction force is µ times the normal force.

So apply good ol' Newton's second law to each block (separately) …

what do you get?

 

[nlightner]

Hello! I'm sorry to hear about your illness and I hope you're feeling better. Let's work through this problem together.

First, we need to understand the basic principles of physics that apply to this problem. Acceleration is a measure of how quickly an object's velocity changes over time. In this case, the blocks are connected by a string and will move together, so we can treat them as one system.

The tension of the string is the force that is pulling the blocks together and keeping them connected. It is important to note that the tension is the same throughout the entire string.

Now, let's move on to solving the problem. We can use Newton's Second Law, which states that the net force on an object is equal to its mass times its acceleration (F=ma). In this case, the net force is the sum of all the forces acting on the blocks.

a) To determine the acceleration, we need to first calculate the net force. The blocks are connected by a string, so the tension in the string is pulling them together. However, there is also a force of friction acting against the motion of the blocks. We can calculate the net force using the formula Fnet = T - μkmg, where T is the tension, μk is the coefficient of kinetic friction, m is the mass of the block, and g is the acceleration due to gravity (9.8 m/s^2).

Plugging in the values for the 0.8 kg block, we get Fnet = T - (0.14)(0.8 kg)(9.8 m/s^2) = T - 1.09 N. For the 2.0 kg block, Fnet = T - (0.14)(2.0 kg)(9.8 m/s^2) = T - 2.71 N. Since the blocks are connected by the same string, the tension is the same for both blocks. Therefore, we can set these two equations equal to each other: T - 1.09 N = T - 2.71 N. Solving for T, we get T = 1.62 N.

Now that we know the net force, we can use Newton's Second Law to calculate the acceleration: Fnet = ma. Plugging in the values, we get 1.62 N = (0.8 kg + 2.0 kg)a. Solving for a, we