A cart rolls down a hill, if the cart weighs 8.7kg and the cart starts at a height of 3.0m, what is the final velocity of the cart?
Oh and the starting velocity is 0 just to let you know
To find the final velocity of the cart, we can use the principle of conservation of mechanical energy. The initial potential energy of the cart at height h is given by:
PE_initial = m * g * h
where:
m = mass of the cart (in kg)
g = acceleration due to gravity (approximately 9.8 m/s^2)
h = initial height of the cart (in meters)
In this case, the mass of the cart is 8.7 kg and the initial height is 3.0 m. Substituting these values:
PE_initial = (8.7 kg) * (9.8 m/s^2) * (3.0 m)
= 254.22 Joules
According to the conservation of mechanical energy, the potential energy is converted into kinetic energy as the cart rolls down the hill. The final kinetic energy of the cart is given by:
KE_final = (1/2) * m * v^2
where:
v = final velocity of the cart (in m/s)
Since there is no loss of energy due to factors like friction or air resistance, the potential energy is completely converted to kinetic energy. Therefore, we can equate the initial potential energy to the final kinetic energy:
PE_initial = KE_final
Substituting the values:
254.22 Joules = (1/2) * (8.7 kg) * v^2
Now we can solve for v:
v^2 = (2 * 254.22 Joules) / (8.7 kg)
v^2 = 58.45 Joules / kg
v = sqrt(58.45 Joules / kg)
Using a calculator, we find that the final velocity of the cart is approximately 7.651 m/s (rounded to three decimal places).
Therefore, the final velocity of the cart is approximately 7.651 m/s.