skateboards on a hill time speed kinetic energy and work
starting from rest angel and Brittany skateboard down a hill as shown. angel rides down the steep side while britney rides down the shallow side. Angel has more mass than Britney. assume that friction and air Resistance are negligible.
Is the speed at the bottom of the hill greater for angel, (ii)greater for Britney, or (iii) the same fir both skateboards?
Explain your reasoning
decrease in potential energy = gain in kinetic energy
so
v^2 is the same for both
To determine whether the speeds at the bottom of the hill are greater for Angel, greater for Britney, or the same for both skateboards, we need to analyze the factors that affect their speeds, namely time, speed, kinetic energy, and work.
Time: The time it takes for each skateboarder to reach the bottom of the hill depends on the inclination of the hill, but since the angles are not provided, we cannot compare their times directly.
Speed: The speed of an object is influenced by its mass and the force acting on it. In this scenario, Angel has more mass than Britney, which means Angel will experience a greater gravitational force. As a result, Angel will achieve a higher speed compared to Britney.
Kinetic Energy: Kinetic energy is directly proportional to the square of an object's speed but is independent of mass. Since Angel is expected to have a higher speed, Angel will have more kinetic energy than Britney.
Work: Work is directly related to the change in kinetic energy of an object. Work is equal to the force applied multiplied by the distance over which it is applied. Since both riders start from rest, they have the same initial kinetic energy. As a result, the work done by gravity on each rider will also be the same. However, since Angel has more mass, the same amount of work will result in a greater increase in Angel's kinetic energy compared to Britney's.
In conclusion, the speed at the bottom of the hill will be greater for Angel compared to Britney. Angel has more mass, which leads to a higher gravitational force, resulting in a greater acceleration and therefore a higher speed.
The speed at the bottom of the hill will be greater for Angel.
To understand why, let's analyze the situation using the concept of potential and kinetic energy.
1. Potential Energy: Skateboards on a hill have gravitational potential energy due to their elevated position. The potential energy is directly proportional to the height and mass of the skateboarders. Since Angel has more mass than Britney, she will have a higher potential energy compared to Britney at the start.
2. Kinetic Energy: As the skateboarders roll down the hill, their potential energy is converted into kinetic energy. The kinetic energy is directly proportional to the mass and squared velocity of the skateboarders. The higher the kinetic energy, the faster they will be moving.
Let's analyze both skateboarders separately:
- Angel: Since Angel has more mass and a higher potential energy at the start, this potential energy is converted into kinetic energy as she moves down the steep side of the hill. Therefore, Angel will have a higher kinetic energy and higher speed compared to Britney at the bottom of the hill.
- Britney: Britney has less mass and a lower potential energy compared to Angel. As she moves down the shallow side of the hill, her potential energy gets converted into kinetic energy. However, due to her lower initial potential energy, she will have a lower kinetic energy and, therefore, a lower speed compared to Angel at the bottom of the hill.
In conclusion, the speed at the bottom of the hill will be greater for Angel as she has more mass and a higher initial potential energy, resulting in a higher conversion of potential energy to kinetic energy and a higher final speed.