# Speed before impact of an object falling down a slope.

• DAN393
In summary, the conversation discusses finding the acceleration of a 4.7 kg block placed on an incline at a 14° angle, ignoring friction. The first part of the problem involves using Fnet=ma to find the acceleration without friction, resulting in a value of 2.36m/s^2. The conversation then introduces the coefficient of kinetic friction and asks for the acceleration considering friction. Using the equation Ff=μFn and the given values, the calculated force of friction is 11.18N, indicating that there is no movement. However, it is important to note that even with a net force of zero, the block may still have a non-zero velocity.
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.

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

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.

## 1. What is the relationship between the speed and slope of an object falling down?

The speed of an object falling down a slope is directly proportional to the slope of the surface it is falling on. This means that the steeper the slope, the faster the object will fall.

## 2. How does the initial velocity affect the speed before impact of an object falling down a slope?

The initial velocity of an object, or the speed at which it is already moving when it begins to fall down the slope, will also affect the final speed before impact. The higher the initial velocity, the faster the object will be moving when it reaches the bottom of the slope.

## 3. Is the speed before impact of an object falling down a slope affected by the mass of the object?

Yes, the mass of an object will also affect its speed before impact. Objects with larger mass will have a greater gravitational force acting on them, causing them to fall faster than objects with smaller mass.

## 4. Does air resistance play a role in the speed before impact of an object falling down a slope?

Yes, air resistance can affect the speed of an object falling down a slope. The amount of air resistance will depend on the shape and surface area of the object, and it may slow down the object's descent. However, this will not have as significant of an impact as the other factors mentioned.

## 5. How can we calculate the speed before impact of an object falling down a slope?

The speed before impact can be calculated using the equation v = √(2gh), where v is the final speed before impact, g is the acceleration due to gravity (9.8 m/s²), and h is the height of the slope. This equation assumes no air resistance and a negligible initial velocity.

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