# Block sliding down incline shaped as circle

In summary: In this case, Sqrt(2(8)/4) = Sqrt(4) = 2 seconds.In summary, the block has an acceleration of 4m/s^2 while sliding along the horizontal plane. It takes 2 seconds for the block to slide horizontally and come to rest. The radius of the curved incline is unknown.

## Homework Statement

A 2-kilogram block is released from rest at the top of a curved incline in the shape of a quarter circle of radius R. The block then slides onto a horizontal plane where it finally comes to rest 8 meters from the beginning of the plane. The curved incline is frictionless, but there is an 8 Newton force of friction on the block while it slides horizontally. Assume g=10N/kg
A) Determine the magnitude of the acceleration of the block while it slides along the horizontal plane.
B) what time elapses while the block is sliding horizontally
C)Calculate the radius of the incline in meters

## Homework Equations

F/m=a
t= 2(delta)x/a (squared)

## The Attempt at a Solution

a- 8N/2kg=4m/s^2
b- T=2(8m)/4m/s^2 (squared)= 2 sec
c-?

a) OK

b) I don't know what equation you are using there, but it's wrong and doesn't give the answer of 2 seconds. 2 seconds is the right answer (as per my equation below), but your equation gives an answer of 1 second or 16 seconds depending on how you did it (see example below).

t = 2(8)/42 = 16/16 = 1
or you squared everything
t = (2(8)/4)2 = (16/4)2 = 16
Both of these are wrong. It appears you have rearranged the below equation incorrectly.

You want to use the SUVAT equations of motion. In this case: s=vt+0.5at2, where s = distance traveled (8m), v = final speed (0m/s) and a = acceleration (from part a).

Substitute in the values and you end up with s=0.5at2. Rearrange and that will give you the travel time.

Based on my SUVAT equation above, yours should be: Sqrt(2s/a) = t.

## 1. What is the force that causes the block to slide down the incline?

The force that causes the block to slide down the incline is gravity. As the block moves down the incline, it experiences a component of its weight that is directed down the incline, causing it to accelerate.

## 2. How does the mass of the block affect its sliding motion?

The mass of the block affects its sliding motion by determining the magnitude of the force of gravity acting on it. A heavier block will experience a greater force of gravity and therefore accelerate more quickly down the incline.

## 3. Is the shape of the incline important in determining the block's sliding motion?

Yes, the shape of the incline is important in determining the block's sliding motion. The circular shape of the incline creates a curved path for the block to follow, which affects its acceleration and velocity.

## 4. What other factors affect the block's sliding motion down the inclined circle?

Other factors that affect the block's sliding motion down the inclined circle include the coefficient of friction between the block and the incline, as well as any external forces acting on the block, such as air resistance.

## 5. How do you calculate the acceleration of the block down the inclined circle?

The acceleration of the block down the inclined circle can be calculated using the formula a = gsinθ, where a is the acceleration, g is the acceleration due to gravity (9.8 m/s^2), and θ is the angle of the incline. This formula assumes no friction or external forces acting on the block.

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