Question

a 4 kg vase sits on a shelf at a height of 1.2 m. how much gravitational potential energy is added to the vase when it is lifted to a shelf of height 1.4 m?
a. 7.84 j
b. 54.9 j
c. 31.2
d. 47.0 j

Explanation:

Step1: Recall the formula for gravitational potential energy

The formula for gravitational potential energy is \(U = mgh\), where \(m\) is the mass, \(g\) is the acceleration due to gravity (\(g= 9.8\space m/s^{2}\)), and \(h\) is the height. The added gravitational potential energy \(\Delta U=mg\Delta h\).

Step2: Calculate the change in height

\(\Delta h=1.4 - 1.2=0.2\space m\)

Step3: Substitute values into the formula

Given \(m = 4\space kg\), \(g = 9.8\space m/s^{2}\), \(\Delta h=0.2\space m\). Then \(\Delta U=4\times9.8\times0.2\).
First, \(4\times9.8 = 39.2\), then \(39.2\times0.2=7.84\space J\)

Answer:

A. \(7.84\space J\)