Question

solve. show your solutions.
problem 1: a 5 kg backpack is placed on a shelf 2.5 m above the floor. what is the gravitational potential energy of the backpack? (6 points)
problem 2: a 10 kg box is lifted and gains 490 j of gravitational potential energy. how high was the box lifted? (6 points)
problem 3: a ladder supports an object with 196 j of gravitational potential energy when it is 4 m above the ground. what is the mass of the object? (6 points)

Explanation:

Problem 1

Step1: Recall the formula for gravitational potential energy

The formula for gravitational potential energy is $PE = mgh$, where $m$ is the mass, $g$ is the acceleration due to gravity (we use $g = 9.8\ m/s^2$), and $h$ is the height.

Step2: Substitute the given values into the formula

Given $m = 5\ kg$, $g = 9.8\ m/s^2$, and $h = 2.5\ m$. Substitute these into the formula: $PE=5\times9.8\times2.5$.

Step3: Calculate the result

First, calculate $5\times9.8 = 49$. Then, calculate $49\times2.5 = 122.5$.

Step1: Recall the formula for gravitational potential energy

The formula is $PE = mgh$, and we need to solve for $h$. Rearranging the formula for $h$, we get $h=\frac{PE}{mg}$.

Step2: Substitute the given values

Given $PE = 490\ J$, $m = 10\ kg$, and $g = 9.8\ m/s^2$. Substitute into the formula: $h=\frac{490}{10\times9.8}$.

Step3: Calculate the result

First, calculate $10\times9.8 = 98$. Then, calculate $\frac{490}{98}=5$.

Step1: Recall the formula for gravitational potential energy

The formula is $PE = mgh$, and we need to solve for $m$. Rearranging the formula for $m$, we get $m=\frac{PE}{gh}$.

Step2: Substitute the given values

Given $PE = 196\ J$, $g = 9.8\ m/s^2$, and $h = 4\ m$. Substitute into the formula: $m=\frac{196}{9.8\times4}$.

Step3: Calculate the result

First, calculate $9.8\times4 = 39.2$. Then, calculate $\frac{196}{39.2}=5$.

Answer:

The gravitational potential energy of the backpack is $122.5\ J$.

Problem 2