Block On Incline Projected Up With Initial Speed

[Becca93]

Homework Statement

A block with mass m = 7.4 kg slides down an inclined plane of slope angle 43.8 ° with a constant velocity. It is then projected up the same plane with an initial speed 3.10 m/s. How far up the incline will the block move before coming to rest?


The attempt at a solution

You need to find the force parallel of the block on the incline, so

Fpara = mgsinθ
Fpara = (7.4)(9.8)sin(43.8)
Fpara = 50.194 N

Acceleration down is
a = F/m
a = 50.194/7.4
a = 6.783

If the block begins moving up at Vi = 3.10 m/s, and Vf = 0, then
Vf^2 = Vi^2 + 2ad
0 = 3.1^2 + (2)(-6.783)d
d = -(3.1)^2 / -13.566
d = 0.708

This is not correct. Obviously, I'm doing this wrong, but I'm not sure of any other way to do it. I feel like having such a large acceleration down can't possibly be correct, and if that is indeed the case, how do I find acceleration of the block as it goes up the incline?

 

[Liquidxlax]

You stated that the block slides at a constant velocity down, and since gravity is acceleration that means there must be a frictional force acting on the block which you must find. If the block is moving at a constant velocity downwards this means that F_tot has to equal zero, so this will allow you to calculate the force of frictiona and the coefficient of kinetic friction.

F_// = Fpara = mgsinθ = F_f = μ_kF_N

so you need to solve for the F_N force normal to find μ_k and the normal force is perpendicular to the plane.

[You do not really need to find μ_k just the force of friction.] Knowing the force of friction and the force of gravity acting against the block as it moves up you will be able to solve for the acceleration of the block and then be able to find the distance at which it stops at.



EDIT*** what you need to do is now the force of friction and force of gravity are acting in the same direction and initially when the block is sliding down they are equal and opposite but when the block is sliding up then they are equal and the same. So you need to sum them up and then solve for the acceleration

 

[Becca93]

You stated that the block slides at a constant velocity down, and since gravity is acceleration that means there must be a frictional force acting on the block which you must find. If the block is moving at a constant velocity downwards this means that F_tot has to equal zero, so this will allow you to calculate the force of frictiona and the coefficient of kinetic friction.

F_// = Fpara = mgsinθ = F_f = μ_kF_N

so you need to solve for the F_N force normal to find μ_k and the normal force is perpendicular to the plane.

[You do not really need to find μ_k just the force of friction.] Knowing the force of friction and the force of gravity acting against the block as it moves up you will be able to solve for the acceleration of the block and then be able to find the distance at which it stops at.



EDIT*** what you need to do is now the force of friction and force of gravity are acting in the same direction and initially when the block is sliding down they are equal and opposite but when the block is sliding up then they are equal and the same. So you need to sum them up and then solve for the acceleration

As it doesn't mention friction in the problem, aren't we supposed to assume that the incline is frictionless?

Either way, I'm working it out like you said now.

 

[Liquidxlax]

As it doesn't mention friction in the problem, aren't we supposed to assume that the incline is frictionless?

Either way, I'm working it out like you said now.

if it was frictionless then the block would be accelerating down the plane and not moving at a constant velocity.

 

[Becca93]

if it was frictionless then the block would be accelerating down the plane and not moving at a constant velocity.

Good point.

Since on the way down,
Fpara = Ff
50.194 = 50.194

and both of them are acting in the same direction going the opposite way, Ff becomes 100.388, the acceleration back is ridiculously high. It ends up as 13.56 m/s^2. Which is almost 50 km/h. Which doesn't seem in the realm of possibility.

What am I doing wrong?

 

[Liquidxlax]

looks right to me. I wouldn't worry about it seeming real considering it's just a made up question not a real life problem

 

[Becca93]

looks right to me. I wouldn't worry about it seeming real considering it's just a made up question not a real life problem

When you plug that acceleration into the equation Vf^2 = Vi^2 + 2ad, you get 0.345 which is incorrect.

Is there something to this that I'm missing?

 

[Rome_Leader]

Draw a free body diagram for the block on the incline. Note that while gravity acts straight down from the block, the normal force has components. As such, if we sum the forces acting in the y direction, you will get an expression for FN (the normal force) in terms of gravity (I leave it to you to figure out which trigonometric ratio to use).

Also, you may or may not be aware that if an object slides with constant velocity down a slope, its coefficient of friction is equal to tanθ. With this knowledge, and the normal force, we can find the frictional force.

Using Newton's Second Law, if we return to the x direction, and sum those forces as we did for the y direction, we should be able to find the acceleration of the block, at which point you can use a basic kinematics equation that involves known variables of acceleration, final and initial speed and the required unknown distance to solve for the distance. (I believe you have already made reference to this equation.)

Hope this helps! :)

 

[I like Serena]

Hi Becca93!

Good point.

Since on the way down,
Fpara = Ff
50.194 = 50.194

and both of them are acting in the same direction going the opposite way, Ff becomes 100.388, the acceleration back is ridiculously high. It ends up as 13.56 m/s^2. Which is almost 50 km/h. Which doesn't seem in the realm of possibility.

What am I doing wrong?

How did you get Fpara?
I get a different value (52.34 N).
Edit: sorry, your value is right.

Btw, your acceleration is not ridiculously high.
In particular you can not convert it to a speed of 50 km/h, since it is not a speed, it's an acceleration (that's just a little over the standard acceleration of gravity).

 

[Becca93]

Hi Becca93!



How did you get Fpara?
I get a different value (52.34 N).

Btw, your acceleration is not ridiculously high.
In particular you can not convert it to a speed of 50 km/h, since it is not a speed, it's an acceleration (that's just a little over the standard acceleration of gravity).

Hey! Thanks for pointing that out. I used mgcosθ to get Fn, and mgsinθ to get Fpara.

I did get the answer to the question though! It ended up being 0.354 m, not 0.345 m like I got earlier.

Thanks to everyone for the help! It was seriously appreciated!