# Ball moving up an incline and coming down.

• bolas
In summary, the ball is rolled up an incline at an angle x with the horizontal and has an acceleration of 0.25g directed down the incline. Using the equation of motion, the distance it moves up the incline before reversing its direction can be determined by Vi^2 = 4.9 m/s^2 *x. The minimum initial velocity can then be calculated using the given speed v. The angle of the incline can be calculated by equating the acceleration to g sin(theta), giving an approximate value of 14.47 degrees.
bolas
"a ball is rolled up an incline (at an angle x with the horizontal). For the angle x and the ball involved, the acceleration of the ball is 0.25g and directed down the incline. If the ball is released with speed v, determine the distance it moved up the incline before reversing its direction as a term of all other variables. What is the minimum initial velocity?"

Anyone can give me a hint on how to approach this problem? :(

Last edited:
Well, try to present us some of your work, there must be some thoughts on how to solve the problem.

This is what I have so far..

Using equation of motion..

Vf^2 = Vi^2 + 2*a*x

a = 0.25g = 0.25*(-9.8 m/s^2) = -2.45 m/s^2

Vf = 0 m/s
Vi = ?
x = s = ?

0 = Vi^2 + 2(-2.45 m/s^2)x
0 = Vi^2 - 4.9 m/s^2 * x

-Vi^2 = -4.9 m/s^2 * x

Vi^2 = 4.9 m/s^2 *x

x = vi^2/4.9 m/s^2

Gave up? :(

bolas said:
Gave up? :(

No need to give up, since the answer seems correct.

For this problem based on the given information that th acceleration is 0.25g down the incline plane, can I assume then that the angle is...

0.25g = gsin(theta)
theta = 14.47 deg ?

bolas said:
For this problem based on the given information that th acceleration is 0.25g down the incline plane, can I assume then that the angle is...

0.25g = gsin(theta)
theta = 14.47 deg ?

You have nothing to assume, since the accelearion is 0.25g, which must equal g sin(theta), so theta ≈ 14.47 deg.

## 1. How does the angle of the incline affect the motion of the ball?

The steeper the incline, the faster the ball will accelerate downwards. This is because the force of gravity acts more directly on the ball, causing it to move faster.

## 2. What role does friction play in the movement of the ball up and down the incline?

Friction acts in the opposite direction of the ball's motion, slowing it down as it moves up the incline and speeding it up as it moves down. In the absence of friction, the ball would continue to roll at a constant speed.

## 3. Can the ball reach the same height when it comes back down the incline?

If there is no friction, the ball will reach the same height as it started from when it comes back down the incline. However, in the presence of friction, some of the ball's energy will be converted to heat, causing it to reach a slightly lower height.

## 4. How does the mass of the ball affect its motion on the incline?

The mass of the ball does not affect its motion on the incline as long as the force of gravity and the force of friction remain constant. However, a heavier ball may experience more resistance from friction, causing it to slow down more than a lighter ball.

## 5. Is the motion of the ball on the incline affected by the surface of the incline?

Yes, the surface of the incline can affect the motion of the ball. A smoother surface with less friction will allow the ball to roll more easily, while a rougher surface with more friction will slow the ball down.

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