A ball with mass of 2kg rolls from rest , down an incline of 10° neglecting friction. Calculate the kinetic energy after it has roll 12m
We can first find the gravitational potential energy of the ball at the top of the incline, which we can then convert to kinetic energy as the ball rolls down the incline.
Potential energy (PE) at the top is given by PE = m * g * h, where m is the mass, g is the acceleration due to gravity (approximated as 9.8 m/s^2), and h is the height of the incline.
We can find h using the sine function, as h = sin(θ) * L, where θ is the angle of the incline and L is the length of the incline. Plugging in the values, we get:
h = sin(10°) * 12 m
h ≈ 0.173648 * 12 m
h ≈ 2.08378 m
Now we can find the potential energy:
PE = 2 kg * 9.8 m/s^2 * 2.08378 m
PE ≈ 40.96312 J (joules)
Since we are neglecting friction, when the ball reaches the bottom of the incline, all of this potential energy will have been converted to kinetic energy:
KE = PE
KE ≈ 40.96312 J
So the kinetic energy of the ball after it has rolled 12 meters is approximately 40.96 joules.
To calculate the kinetic energy of the ball after it has rolled 12m down the incline, we can follow these steps:
Step 1: Calculate the gravitational potential energy at the starting position:
Gravitational Potential Energy (GPE) = mass * gravity * height
Since the ball is at rest, its GPE at the starting position is given by:
GPE = mass * gravity * height
= 2 kg * 9.8 m/s^2 * 0
= 0 J
Step 2: Calculate the change in gravitational potential energy:
Change in GPE = GPE at end position - GPE at starting position
= 0 J - 0 J = 0 J
Step 3: Calculate the change in kinetic energy:
Change in Kinetic Energy = Change in GPE
Since the friction is neglected in this scenario, the change in kinetic energy is equal to the change in gravitational potential energy.
Step 4: Calculate the final kinetic energy:
Initial Kinetic Energy = Change in Kinetic Energy + Initial Gravitational Potential Energy
Substituting the values:
Initial Kinetic Energy = 0 J + 0 J
= 0 J
Therefore, the kinetic energy of the ball after it has rolled 12m down the incline is 0 Joules.
To calculate the kinetic energy of the ball after it has rolled 12m, we need to use the formula:
Kinetic energy (KE) = 1/2 * mass * velocity^2
First, let's find the final velocity of the ball after rolling down the incline.
We can use the principle of conservation of energy. The potential energy (PE) the ball gains while rolling down the incline is converted into kinetic energy (KE). The formula for potential energy is:
Potential energy (PE) = mass * gravity * height
In this case, the height is equivalent to the vertical displacement of the ball, which can be calculated using the given angle of the incline and the distance rolled.
Height = (Distance rolled)*(sin(angle))
Height = 12m * sin(10°) = 2.08m (approximately)
Now, we can calculate the potential energy (PE) gained by the ball:
PE = (mass * gravity * height)
PE = (2kg * 9.8m/s^2 * 2.08m) = 40.77 Joules (approximately)
Since there is no friction, the entire potential energy is converted into kinetic energy.
So, the kinetic energy (KE) after rolling 12m is equal to the potential energy gained:
KE = PE
KE = 40.77 Joules (approximately)
Therefore, the kinetic energy of the ball after rolling 12m is approximately 40.77 Joules.