Hanging Block Inclined plane

[polishdude20]

Homework Statement

An 18kg cart is connected to a 12kg hanging block at the bottom of the incline (ignore friction)

What is the magnitude of acceleration of the cart?

Homework Equations

F=ma
Fx=Fgsinx
Fy=FgCosx

The Attempt at a Solution

well without the hanging weight i calculatoed the force parallel to the plane to be 101.2 N
and the force perpendicular to the plane is 144.5 N
I tried adding the X force (101.2N) to the downward force of the weight on the pulley (176.4 ) and then dividing by the total masses. But I can never get the right answer its supposed to be 7.3 m/s*2 but I don't know how its obtained.

 

[polishdude20]

can anyone help?

 

[jhae2.718]

Try drawing a free body diagram of each block. What forces act on each?

Then use the fact that $$\Sigma \vec{F} = m\vec{a}$$ to find the net acceleration.

 

[polishdude20]

yes i tried that and i don't know do i add the fg of the hanging block to the Fx of the block on the plane?

 

[rwisz]

I would approach this problem by first analyzing the forces acting on the system. We have the force of gravity acting on both the cart and the hanging block, which can be calculated using the equation F=mg. We also have the normal force from the incline, which is equal in magnitude to the force of gravity perpendicular to the incline. Since there is no friction, we can ignore that force.

Next, we can use Newton's second law, F=ma, to determine the acceleration of the system. We know that the net force acting on the system is the sum of the forces parallel to the incline, which is equal to the force of gravity on the cart (F=mg) minus the force of gravity on the hanging block (F=mg). This gives us a net force of 18g-12g=6g.

Using the equation F=ma, we can plug in the net force of 6g and the total mass of the system (18kg+12kg=30kg) to solve for acceleration. This gives us an acceleration of 6g/30kg = 0.2g = 1.96 m/s^2. This is the acceleration of the system as a whole, which includes both the cart and the hanging block.

To find the acceleration of the cart alone, we can use the same equation, F=ma, but this time the net force acting on the cart is only the force parallel to the incline (101.2 N). Plugging in this value and the mass of the cart (18kg), we get an acceleration of 101.2N/18kg = 5.62 m/s^2. This is the acceleration of the cart as it moves up the incline.

In conclusion, the magnitude of acceleration of the cart is 5.62 m/s^2, while the magnitude of acceleration of the entire system is 1.96 m/s^2. It is important to note that the hanging block does not have any acceleration since it is being supported by the pulley.