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

Answer 1

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.