If the cart weighs 3.9kg and the cart starts at a height of 7.8m, what is the final velocity of the cart?
To calculate the final velocity of the cart, you need to use the principles of energy. The potential energy of the cart at the beginning is equal to its kinetic energy at the end.
The potential energy (PE) of an object is given by the formula:
PE = mgh
Where:
m is the mass of the object (3.9 kg)
g is the acceleration due to gravity (approximately 9.8 m/s²)
h is the height of the object (7.8 m)
Now, the initial potential energy (PEi) is equal to the final kinetic energy (KEf). The formula for kinetic energy (KE) is:
KE = (1/2)mv²
Where:
m is the mass of the object (3.9 kg)
v is the final velocity of the object (what we want to find)
Setting PEi = KEf, we have:
mgh = (1/2)mv²
Now, we can cancel out the mass (m) from both sides of the equation:
gh = (1/2)v²
Rearranging the equation to solve for v:
v² = 2gh
Finally, taking the square root of both sides, we can find the final velocity (v):
v = √(2gh)
Now, plug in the given values:
v = √(2 * 9.8 m/s² * 7.8 m)
After calculating this expression, you'll find the final velocity of the cart.