If the cart weighs 8.7kg and the cart starts at a height of 3m, what is the final velocity of the cart?
the starting velocity is 0
to clear any confusion, the cart rolls down a hill
To find the final velocity of the cart, we can use the principle of conservation of energy. Here's the step-by-step process to calculate the final velocity:
Step 1: Determine the potential energy at the starting height.
The potential energy (PE) of an object at height h is given by the equation PE = mgh, where m is the mass, g is the acceleration due to gravity (9.8 m/s^2), and h is the height.
In this case, the mass (m) of the cart is 8.7 kg, and the height (h) is 3 m. So, the potential energy at the starting height can be calculated as:
PE_start = m * g * h = 8.7 kg * 9.8 m/s^2 * 3 m.
Step 2: Convert the potential energy at the starting height to kinetic energy at the final velocity.
According to the conservation of energy, the potential energy at the starting height is converted to kinetic energy (KE) at the final velocity.
So, KE_start = PE_start.
KE_start = m * g * h.
Step 3: Calculate the final kinetic energy using the mass and velocity.
The kinetic energy (KE) of an object is given by the equation KE = 0.5 * m * v^2, where v is the final velocity.
In this case, the mass (m) of the cart is 8.7 kg.
So, KE_final = 0.5 * m * v^2.
Step 4: Equate the starting kinetic energy to the final kinetic energy.
Since the potential energy is converted to kinetic energy, we can equate the initial kinetic energy (KE_start) to the final kinetic energy (KE_final).
KE_start = KE_final.
m * g * h = 0.5 * m * v^2.
Step 5: Solve for the final velocity.
Rearrange the equation and solve for v:
v^2 = (2 * g * h).
v = sqrt(2 * g * h).
Step 6: Substitute the known values and calculate the final velocity.
Substitute g = 9.8 m/s^2 and h = 3 m into the equation:
v = sqrt(2 * 9.8 m/s^2 * 3 m).
Calculating the square root and simplifying, we get:
v ≈ sqrt(58.8) ≈ 7.67 m/s.
Therefore, the final velocity of the cart is approximately 7.67 m/s.