98. On which of these hills does the ball roll down with increasing speed and decreasing acceleration along the path? (Use this example if you wish to explain to someone the difference between speed and acceleration.)
99. If you drop an object, its acceleration toward the ground is 10 m/s2. If you throw it down instead, will its acceleration after leaving your hand be greater than 10 m/s2?
Ignore air resistance. Defend your answer.
100. Can you think of a reason why the acceleration of the object thrown downward through the air in the preceding question would actually be less than 10 m/s2?
99. If you drop an object:
Vo = 0 = Initial velocity.
a = g = 10 m/s^2.
If you throw it down:
Vo > 0
a = g = 10 m/s^2.
So in both cases, the acceleration remains constant at 10 m/s^2.
98. To determine on which hill the ball rolls down with increasing speed and decreasing acceleration along the path, we can consider the physics concept of potential energy and kinetic energy. Assuming there is no friction or other external forces, the ball will experience changes in potential and kinetic energy as it moves along the hill.
One way to compare speed and acceleration is by looking at the relationship between them. Speed is the rate at which an object changes its position over time, while acceleration is the rate at which an object changes its velocity over time.
In this scenario, if the ball is rolling down a hill, it will start with some initial potential energy at the top of the hill, and as it rolls downward, this potential energy is converted into kinetic energy. At the same time, the ball experiences acceleration due to the force of gravity acting on it.
Now, when the ball rolls down a hill, the slope of the hill affects both the speed and acceleration of the ball. If the hill is steeper, the ball will experience a greater acceleration since the force of gravity will act more directly in the direction of the slope.
However, as the ball rolls down the hill and gains speed, its acceleration will start to decrease. This is because the force of gravity remains constant, but the opposing force of friction gradually increases as the ball gains speed. Eventually, the force of friction matches the force due to gravity, and the ball reaches a terminal velocity where its acceleration becomes zero.
To identify the hill where the ball rolls down with increasing speed and decreasing acceleration, we need to consider the slope and the presence of external forces such as friction. It is crucial to analyze the specific characteristics of each hill to determine the desired scenario.
99. If you drop an object, the acceleration towards the ground is given by the acceleration due to gravity, which is approximately 10 m/s^2 (assuming we are near the surface of the Earth and neglecting air resistance).
Now, if you throw the object downward instead of just dropping it, its initial velocity will be greater than zero. However, the acceleration after leaving your hand will still be 10 m/s^2. The additional initial velocity will not affect the acceleration due to gravity. Therefore, the acceleration of the object after leaving your hand will be the same as when you dropped it – 10 m/s^2.
100. In the previous question, we assumed that air resistance is ignored. However, in reality, air resistance does exist and affects the motion of objects moving through the air. When an object moves through the air, air resistance generates a force opposite to the direction of motion.
If the object thrown downward through the air encounters significant air resistance, it can reduce the net force acting on the object. As a result, the acceleration will be less than the 10 m/s^2 due to gravity alone, especially as the object's speed increases.
Factors like the shape, mass, and surface area of the object can influence the amount of air resistance it experiences. For example, an aerodynamic object or a lighter object with a smaller surface area will typically experience less air resistance and therefore have less impact on its acceleration.