Ball rolling off an inclined plane

In summary, the ball is rolling off an inclined plane and travels 10cm in 1 second. To find the distance it will travel in 3 seconds, the equation x = x0 + v0t + at2/2 should be used to calculate the acceleration. The correct answer is 0.9m.
  • #1
Avathacis
43
0

Homework Statement



A ball is rolling off an inclined plane. After 1 second the ball has traveled 10cm. How far will it travel in 3 seconds?

Homework Equations



v = l/t
v = v0t + at
x = x0 + v0t + at2/2

The Attempt at a Solution



v = l/t1

v = v0t + at (there's no starting velocity, so)

l/t1 = at1

l = at21

a = l/t21

l3 = x0 + v0t + at2/2

l3 = at2/2

l3 = (l/t21 + t2) 1/2

l3 = 0.45m

The answer should be 0.9m, so i guess I'm supposed to lose the 1/2 somewhere.
 
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  • #2
Avathacis said:
v = l/t
This only applies if the speed is constant, which is not the case here.

x = x0 + v0t + at2/2
Use this to figure out the acceleration.
 
  • #3
Doc Al said:
This only applies if the speed is constant, which is not the case here.


Use this to figure out the acceleration.

Thanks! Done!
 

1. What is the physics behind a ball rolling off an inclined plane?

When a ball is placed on an inclined plane, it experiences a force due to gravity pulling it downwards. This force is broken down into two components: the weight of the ball acting downwards and the normal force acting perpendicular to the plane. As the ball rolls down the incline, its gravitational potential energy is converted into kinetic energy, causing it to speed up.

2. How does the angle of the inclined plane affect the ball's motion?

The steeper the incline, the greater the angle of the plane, and the faster the ball will roll down. This is because a steeper incline means a larger component of the ball's weight is acting parallel to the plane, causing a greater acceleration. However, if the angle of the incline becomes too steep, the ball may roll too quickly and lose contact with the plane.

3. What factors affect the speed of the ball rolling down an inclined plane?

The speed of the ball depends on the angle of the inclined plane, the mass of the ball, and the force of gravity. The steeper the angle, the greater the acceleration and the faster the ball will roll. A heavier ball will also roll faster due to the increased force of gravity acting on it.

4. What is the relationship between the height the ball is released from and the distance it will roll on the inclined plane?

The height the ball is released from does not affect the distance it will roll on the inclined plane. This is because, according to the law of conservation of energy, the potential energy at the top of the incline is equal to the kinetic energy at the bottom. Therefore, the ball will roll the same distance regardless of the height it is released from.

5. How does friction affect the motion of the ball on an inclined plane?

Friction between the ball and the inclined plane will act to slow down the ball's motion, reducing its speed and distance rolled. Additionally, if the friction force is strong enough, it may prevent the ball from rolling at all. This is why smooth, frictionless surfaces are often used in experiments involving inclined planes to minimize its effects on the motion of the ball.

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