Question

a lemon with mass 0.3 kg falls out of a tree from a height of 1.8 m. how much mechanical energy does the lemon have just before it hits the ground? (assume there is no air resistance.)

a. 5.3 j
b. 3.9 j
c. 7.4 j
d. 6.2 j

Explanation:

Step1: Recall mechanical - energy conservation

In the absence of air - resistance, mechanical energy is conserved. Just before hitting the ground, the lemon's mechanical energy \(E\) is equal to its initial potential energy \(U\) (since initial kinetic energy \(K_i = 0\) as it starts from rest).

Step2: Use the potential - energy formula

The formula for gravitational potential energy is \(U = mgh\), where \(m\) is the mass, \(g\) is the acceleration due to gravity (\(g=9.8\ m/s^{2}\)), and \(h\) is the height.
Substitute \(m = 0.3\ kg\), \(g = 9.8\ m/s^{2}\), and \(h = 1.8\ m\) into the formula:
\[U=mgh=0.3\times9.8\times1.8\]
\[U = 5.292\ J\approx5.3\ J\]

Answer:

A. 5.3 J