Question

1. a box with a mass of 12.5 sits on the floor. how high would you need to lift it for it to have a gpe of 355j?
2. a cart at the top of a 300 m hill has a mass of 40 kg. what is the carts gravitational potential energy?

Explanation:

Question 4

Step1: Recall the formula for gravitational potential energy

The formula for gravitational potential energy (\(GPE\)) is \(GPE = mgh\), where \(m\) is the mass, \(g\) is the acceleration due to gravity (\(g = 9.8\ m/s^{2}\)), and \(h\) is the height. We need to solve for \(h\), so we can rewrite the formula as \(h=\frac{GPE}{mg}\).

Step2: Substitute the given values into the formula

Given \(GPE = 355\ J\), \(m = 12.5\ kg\), and \(g = 9.8\ m/s^{2}\).

$$h=\frac{355}{12.5\times9.8}$$

$$h=\frac{355}{122.5}$$

$$h\approx 2.9\ m$$

Step1: Use the formula for gravitational potential energy

The formula for gravitational potential energy is \(GPE=mgh\). Here, \(m = 40\ kg\), \(g = 9.8\ m/s^{2}\), and \(h = 300\ m\).

Step2: Substitute the values into the formula

$$GPE=40\times9.8\times300$$

First, calculate \(40\times9.8 = 392\).
Then, \(392\times300=117600\ J\)

Answer:

The height \(h\) is approximately \(2.9\ m\).

Question 5