Speed before impact of an object falling down a slope.

[DAN393]

Homework Statement

A 4.7 kg block is placed on an incline with a 14° angle.
Ignoring friction, what is the acceleration of the block?
If the coefficient of kinetic friction is 0.25 (and has overcome static friction) what is the acceleration of the block?
If the incline is 4.6m long, what is the velocity of the block at the bottom (considering friction)?

Homework Equations

Ff=μFn
Fn=FgCosθ
Fg=4.7kg*9.81m/s^2
F=ma
Force on block due to gravity = 11.15N

The Attempt at a Solution

To find the first part, I used Fnet=ma, rearranged to find a and found the acceleration without friction to be:
FgSinθ/m = 46sin14°N/4.7kg = 2.36m/s^2

Then I calculated Ff to be 11.18N, which means there is no movement, and that is where I'm stumped because the last question would lead one to think that it moved somewhat.

 

[Redbelly98]

If the net force is zero, that means the acceleration is zero. It can still be moving (has velocity not zero).

 

[kerimek]

I would like to point out that the question is incomplete as it does not specify the initial velocity of the block. Without this information, we cannot accurately calculate the final velocity of the block at the bottom of the incline.

However, assuming the initial velocity is 0, we can use the equation vf^2 = vi^2 + 2ad to find the final velocity. Using the acceleration calculated in the first part (2.36m/s^2) and the distance of the incline (4.6m), we can find the final velocity to be approximately 4.15m/s. This takes into account the friction force of 11.18N, which would decrease the final velocity.

Additionally, I would like to mention that the coefficient of kinetic friction does not affect the acceleration of the block down the incline. It only affects the net force acting on the block, which in turn affects the final velocity. Therefore, the acceleration of the block will remain the same regardless of the coefficient of kinetic friction.