Did I calculate the acceleration and Tension correctly?

[Bart Allen]

Homework Statement

A frictionless surface is inclined at an angle of 30.0° to the horizontal. A 270-g block on the ramp is attached to a 75.0-g block using a pulley, as shown in Figure 4-62. (a) Draw two free-body diagrams, one for the 270-g block and the other for the 75.0-g block. (b) Find the tension in the string and the acceleration of the 270-g block. (c) The 270-g block is released from rest. How long does it take for it to slide a distance of 1.00 m along the surface? Will it slide up the incline, or down the incline?
Given: θ = 30°
m₁ = 270g (0.270kg)
m₂ = 75g (0.075kg)
g = 9.81m/s²

Homework Equations

F_net = m_totala
a = F_net / m_total
a = F₁ / m₁ = m₁*g*sinθ / m₁

The Attempt at a Solution

So the question asks to solve for both Tension and acceleration of the 270g block which I converted to kilograms 0.270kg, 0.075kg
So I first calculated the acceleration of the specified mass by the doing the following
a_x = F₁ / m₁ = m₁*g*sinθ / m₁ then plug in and solve for acceleration.
0.270*9.81m/s²*sin30° / 0.270
=4.90m/s²
if someone could check to see if I did everything correctly because then it would be easier to calculate the tension and time I'm sure

 

[TSny]

Welcome to PF!

So I first calculated the acceleration of the specified mass by the doing the following
a_x = F₁ / m₁ = m₁*g*sinθ / m₁ then plug in and solve for acceleration.

It's more complicated than this. Gravity is not the only force acting on m₁ that has a component along the slope.

Things will become clearer if you carefully draw a free body diagram for each mass.

 

[Bart Allen]

Welcome to PF!

It's more complicated than this. Gravity is not the only force acting on m₁ that has a component along the slope.

Things will become clearer if you carefully draw a free body diagram for each mass.

I did draw the free body diagram and I know that net force is a factor right? Also normal force

 

[TSny]

I did draw the free body diagram and I know that net force is a factor right? Also normal force

Net force is the sum of the actual forces that act on an object. Can you list all of the forces that act on m₁?

 

[Bart Allen]

Net force is the sum of the actual forces that act on an object. Can you list all of the forces that act on m₁?

Yes so you have gravity pulling down, Netforce, normal force which is perpendicular to the ground, you have the opposing force to the left that pulling it since its heavier then mass2 and the tension of the string that it is pulling

 

[TSny]

gravity pulling down

Yes.

Netforce

Net force is not a separate force acting on the object. Netforce is the vector sum of the actual forces acting on the object. The Netforce is not included on a free body diagram. Only draw the actual physical forces on the diagram.

normal force which is perpendicular to the ground

For a mass on an incline, the direction of the normal force acting on the mass is not perpendicular to the ground.

you have the opposing force to the left that pulling it since its heavier then mass2

If I'm understanding the setup correctly, there is no such force. For any force that you draw on a free body diagram for an object, you should be able to state what other object is responsible for the force. For example, the gravitational force on m₁ is produced by the earth, the normal force is produced by the surface of the incline, the tension force is produced by the string. If you go through this mental exercise for each force, you can avoid putting extra forces on the diagram that don't belong. So, if you claim there is "the opposing force to the left", what object produces this force?

and the tension of the string that it is pulling

Yes.

It would be helpful if you could post a diagram of the setup of the problem and post your free body diagrams for m₁ and m₂.

 

[Bart Allen]

Yes. Net force is not a separate force acting on the object. Netforce is the vector sum of the actual forces acting on the object. The Netforce is not included on a free body diagram. Only draw the actual physical forces on the diagram. For a mass on an incline, the direction of the normal force acting on the mass is not perpendicular to the ground. If I'm understanding the setup correctly, there is no such force. For any force that you draw on a free body diagram for an object, you should be able to state what other object is responsible for the force. For example, the gravitational force on m₁ is produced by the earth, the normal force is produced by the surface of the incline, the tension force is produced by the string. If you go through this mental exercise for each force, you can avoid putting extra forces on the diagram that don't belong. So, if you claim there is "the opposing force to the left", what object produces this force? Yes.

It would be helpful if you could post a diagram of the setup of the problem and post your free body diagrams for m₁ and m₂.

First I really appreciate your help this is really making me think and I'm starting to understand it better!
Secondly I was trying to do that but I have no way of posting it in tried posting it from my Google drive but that didn't work

 

[TSny]

I think this is the setup

Consider m₁. What individual forces act on m₁? For each of these forces, what is the x-component of the force? For m₁, let's take the positive x direction to be parallel to the incline as shown above.

 

[Bart Allen]

I think this is the setup
View attachment 212361

Consider m₁. What individual forces act on m₁? For each of these forces, what is the x-component of the force? For m₁, let's take the positive x direction to be parallel to the incline as shown above.

X component consisting of the Tension? acceleration, and net force?

 

[haruspex]

X component consisting of the Tension? acceleration, and net force?

Yes, tension is an appied force in the X direction, but acceleration is not a force, and the net force is not an applied force - it is the sum of the applied forces.
What other applied force has a component parallel to the plane?