1.a ball with a mass 2kg rests on an incline with an angle of 10 degrees. The ball is released to roll down the incline plane neglecting all friction:
Determine the following:
A.the loss in potential energy after it has rolled 12m.
B.the velocity after it has rolled 12m.
C.the original height that the ball has rolled from in order to reach the bottom of the slope at 20m/s
I need anser
To determine the answers to the given questions, we can use the principles of mechanical energy conservation and the equations of motion.
A. The loss in potential energy after the ball has rolled 12m can be calculated using the equation for gravitational potential energy:
Potential Energy = Mass x Gravity x Height
In this case, the mass of the ball is given as 2kg, and the height can be determined using trigonometry and the distance traveled (12m) along the inclined plane. The height can be calculated as follows:
Height = Distance Traveled x sin(θ)
where θ is the angle of the incline (10 degrees). Plugging in the values, we get:
Height = 12m x sin(10 degrees)
After calculating the height, you can find the loss in potential energy by multiplying the height by the mass and the acceleration due to gravity (9.8 m/s^2).
B. To determine the velocity after the ball has rolled 12m, you can use the principle of conservation of mechanical energy. The total mechanical energy of the ball at any point is the sum of its potential energy (PE) and kinetic energy (KE):
Total Mechanical Energy = PE + KE
Since there is no friction, the loss in potential energy is completely converted into kinetic energy as the ball rolls down the incline. The equation for kinetic energy is:
Kinetic Energy = 0.5 x Mass x Velocity^2
We need to solve for velocity, so we can rewrite the equation as:
Velocity = sqrt((2 x (Total Mechanical Energy - PE)) / Mass)
Substituting the values for total mechanical energy, potential energy, and mass, you can calculate the velocity.
C. To determine the original height from which the ball was rolled in order to reach the bottom of the slope with a velocity of 20m/s, we can use the equation for kinetic energy as mentioned earlier:
Kinetic Energy = 0.5 x Mass x Velocity^2
Rearranging the equation to solve for height, we get:
Height = (Velocity^2) / (2 x g)
where g is the acceleration due to gravity (9.8 m/s^2).
By substituting the given values for velocity and g, you can calculate the original height.