A block is released from the top of a frictionless incline plane as pictured above. If the total distance travelled by the block is 1.2 m to get to the bottom, calculate how fast it is moving at the bottom using Conservation of Energy.(incline 20 degrees mass of block is 2.5kg)
the vertical height traveled is 1.2 sin20°
PE lost is KE gained, so
mgh = 1/2 mv^2
gh = 1/2 v^2
you have g and h, so get v.
2.83
To calculate the speed of the block at the bottom of the incline using the principle of Conservation of Energy, we need to consider the changes in potential and kinetic energy.
1. Determine the potential energy at the top of the incline:
Since the incline is frictionless and the height is not given, we can use the formula for gravitational potential energy:
Potential Energy (PE) = mass (m) * gravity (g) * height (h)
However, instead of calculating the height directly, we can utilize the angle of the incline to determine the height component along the incline.
Height (h) = vertical displacement (d) * sin(angle)
Given that the total distance traveled by the block is 1.2 m, which is the sum of the vertical and horizontal displacements:
d = 1.2 m
Using trigonometry, we can find the vertical displacement:
Vertical displacement (d_vertical) = d * sin(angle)
2. Calculate the kinetic energy at the bottom of the incline:
At the bottom of the incline, all potential energy is converted into kinetic energy.
Kinetic Energy (KE) = ½ * mass (m) * velocity^2
To solve for the velocity at the bottom, we need to relate the potential energy at the top to the kinetic energy at the bottom.
According to the conservation of energy principle:
Potential Energy at the top (PE_top) = Kinetic Energy at the bottom (KE_bottom)
Therefore:
m * g * h = ½ * m * v^2
3. Solve for velocity (v):
Rearrange the equation to solve for v:
v = sqrt((2 * g * h))
Let's plug in the values:
m = 2.5 kg (mass of the block)
g = 9.8 m/s^2 (acceleration due to gravity)
angle = 20 degrees
First, calculate the height (h) using the given angle and the total distance traveled:
h = d * sin(angle) = 1.2 m * sin(20 degrees)
Substitute the calculated value of h into the velocity equation:
v = sqrt((2 * 9.8 m/s^2 * h))
Now calculate the height (h) and plug it back into the equation to find the velocity at the bottom of the incline.