A 3.00-kg ball swings rapidly in a complete vertical circle of radius 2.00 m by a light string that is fixed at one end. The bal
1 answer:
Answer:
- The gravity does a work of - 117.6 Joules.
- The tension does not do work as the force is perpendicular to the direction of motion at any point in the trajectory.
Explanation:
The work done by the gravity simply is the difference in gravitational potential energy multiplied by -1:
where m is the mass of the ball, g is the acceleration due to gravity, is the final height and
is the initial height.
So, if the radius is 2.00 m, then the difference of height will be 4 meters:
As the tension is perpendicular to the velocity of the ball, the force is always perpendicular to the direction of motion. So, the differential of work will be:
You might be interested in
The expression commonly used for potential gravitational energy is just simplification. It is actually just the first term in Taylor expansion of the real expression.
In general, the potential energy of gravitational field is defined as:
Where G is universal gravitational constant, and r is the distance between the objects centers of mass. Negative sign represents the bound state.
Since we are not given the mass of the planet we have to calculate it.
This formula can be used for any planet. It gives you the gravitational acceleration on the planet's surface. We can use it to calculate the planet's mass:
Now we can calculate the potential energy of that cannonball when it reaches its maximum height.
When we plug in the numbers we get:
The potential energy has to be equal to the kinetic energy.
In general, the potential energy of gravitational field is defined as:
Where G is universal gravitational constant, and r is the distance between the objects centers of mass. Negative sign represents the bound state.
Since we are not given the mass of the planet we have to calculate it.
This formula can be used for any planet. It gives you the gravitational acceleration on the planet's surface. We can use it to calculate the planet's mass:
Now we can calculate the potential energy of that cannonball when it reaches its maximum height.
When we plug in the numbers we get:
The potential energy has to be equal to the kinetic energy.
Answer:
Average speed: 0.5 m/s. Average velocity: 0
Explanation:
Average speed is given by:
where
d is the total distance covered (the length, of one lap of the track, so d = 400 m)
t is the time taken to cover that distance (so, t = 800 s)
Substituting,
Instead, average velocity is defined as
where this time,
d is the displacement, which is the vector connecting the starting point to the final point of the motion
t is still the time taken (800 s)
However, in this case the walker starts and finishes his trip at the same point: therefore, the displacement is zero (d=0), and this means that the average velocity is zero as well.