a 45 kg object slides down an uneven frictionless incline from rest without rotating. What is its speed after it travels 2.5 meters vertically
change in PE= change in KE
mgh=1/2 m v^2
v= sqrt 2gh
To find the speed of the object after it travels 2.5 meters vertically down the incline, we can use the principle of conservation of mechanical energy.
The potential energy (PE) of the object at the starting position (h1) is given by:
PE1 = m * g * h1
where m is the mass of the object (45 kg), g is the acceleration due to gravity (9.8 m/s^2), and h1 is the initial vertical height.
The kinetic energy (KE) of the object at the final position (h2) is given by:
KE2 = (1/2) * m * v^2
where v is the final velocity of the object.
Since there is no friction and the object does not rotate, the mechanical energy is conserved. Therefore,
PE1 = KE2
m * g * h1 = (1/2) * m * v^2
Here, h1 = 0 (since the object starts from rest), and we want to find v when the object reaches h2 = -2.5 m. Substituting these values:
0 = (1/2) * m * v^2
We can solve for v:
v^2 = 0
v = 0
Therefore, the speed of the object after it travels 2.5 meters vertically down the incline is 0 m/s.
To find the speed of the object after it travels a certain distance along an incline, we can use the principles of energy conservation. The object initially has gravitational potential energy due to its position on the incline, and as it moves down the incline, this energy is converted into kinetic energy.
To solve this problem, we'll need to consider the conservation of mechanical energy. The total mechanical energy of the object is the sum of its potential energy (PE) and kinetic energy (KE). Assuming the incline is frictionless and there is no loss of energy due to other factors, such as air resistance, the total mechanical energy of the object remains constant.
The formula for gravitational potential energy (PE) is given by:
PE = m * g * h
Where:
m = mass of the object (45 kg)
g = acceleration due to gravity (9.8 m/s^2)
h = vertical distance traveled (2.5 meters)
The formula for kinetic energy (KE) is given by:
KE = (1/2) * m * v^2
Where:
v = velocity (speed) of the object
Since the object starts from rest, its initial kinetic energy (KE initial) is zero, and its total mechanical energy is equal to the initial potential energy (PE initial).
Setting the initial potential energy equal to the final kinetic energy, we have:
PE initial = KE final
m * g * h = (1/2) * m * v^2
We can cancel out the mass (m) on both sides of the equation:
g * h = (1/2) * v^2
Now, we can solve for the speed (v):
v^2 = (2 * g * h)
Taking the square root of both sides:
v = sqrt(2 * g * h)
Plugging in the values:
v = sqrt(2 * 9.8 * 2.5)
v ≈ 7.85 m/s
Therefore, the speed of the object, after it travels 2.5 meters vertically down the incline, is approximately 7.85 m/s.