Question

a lantern hanging in a barn has a gpe of 295.6 j when it is 5.6 m above the ground. what is the mass of the lantern?

Explanation:

Step1: Write the formula for gravitational potential energy (GPE)

The formula for GPE is \(GPE = mgh\), where \(m\) is mass, \(g\) is the acceleration due to gravity (\(g = 9.8\ m/s^{2}\)), and \(h\) is height.

Step2: Rearrange the formula to solve for mass (\(m\))

From \(GPE = mgh\), we can solve for \(m\) as \(m=\frac{GPE}{gh}\).

Step3: Substitute the given values into the formula

We are given \(GPE = 295.6\ J\), \(h = 5.6\ m\), and \(g = 9.8\ m/s^{2}\).

$$m=\frac{295.6}{9.8\times5.6}$$

$$m=\frac{295.6}{54.88}$$

$$m = 5.4\ kg$$

Answer:

The mass of the lantern is \(5.4\ kg\).