Question Video: Identifying an Equation for Gravitational Potential Energy | Nagwa Question Video: Identifying an Equation for Gravitational Potential Energy | Nagwa

# Question Video: Identifying an Equation for Gravitational Potential Energy Physics • First Year of Secondary School

## Join Nagwa Classes

The quantity β is the vertical displacement of an object from a given position. The quantity πΈ is the objectβs gravitational potential energy. Which of the following formulas correctly shows the relationship between β, πΈ, the mass of the object, and the acceleration of the object by gravity? [A] πΈ = π/πβ [B] πΈ = ππβ [C] πΈ = ππ/β [D] πΈ = π/πβ [E] πΈ = βπ/π

02:50

### Video Transcript

The quantity β is the vertical displacement of an object from a given position. The quantity πΈ is the objectβs gravitational potential energy. Which of the following formulas correctly shows the relationship between β, πΈ, the mass of the object, and the acceleration of the object by gravity? (A) πΈ equals π over π times β, (B) πΈ equals π times π times β, (C) πΈ equals π times π divided by β, (D) πΈ equals π divided by π times β, and (E) πΈ equals β times π divided by π.

Letβs imagine a situation where we have ground level, and weβll call that where β is equal to zero. And that at some height weβll call β above ground level, we have an object where that object has a mass π. Because this mass is in a gravitational field whose acceleration is represented by lowercase π pointing downward, we can describe a quantity πΈ which represents the gravitational potential energy of this mass. This energy depends on the mass π, and it also depends on the height β and on the acceleration due to gravity π.

Notice that four out of our five answer options (A), (C), (D), and (E) all have an inverse relationship between this energy πΈ and one of the three variables. For example, answer choice (A) claims that πΈ is inversely proportional to π and β. Answer choice (D) claims that πΈ is inversely proportional to π times β. Regardless of the variable or variables in the denominators of these fractions, each one claims that thereβs at least one of π or π or β, which, if it increases, πΈ will decrease. Returning to our scenario, we can think about whether itβs likely that this is true.

For example, say that the mass π of our object increased. What effect would this have on the gravitational potential energy of our object? Everything else being equal, a greater mass will have a greater gravitational potential energy. This means that answer option (D) is off our list. Now letβs imagine that instead of the mass of our object increasing, its height above ground level increases. If this happened, if β went up, then so would the gravitational potential energy of our object. That object is now higher up in a gravitational field. This means that πΈ is not inversely proportional to β. That eliminates answer choice (A) as well as answer choice (C).

Finally, letβs imagine that for a given height above ground level and for an object of a given mass, the acceleration due to gravity π is increased in strength. What effect would that increase have on the objectβs gravitational potential energy? Would πΈ tend to decrease, stay the same, or increase as a result? The greater the acceleration due to gravity π becomes, the greater the gravitational potential energy of an object that exists in that strong field. Therefore, πΈ and π are not inversely related, but rather directly related. This eliminates answer option (E) from consideration. An objectβs gravitational potential energy is proportional to its mass, to its height above some reference, and to the acceleration due to gravity. We choose answer option (B).

## Join Nagwa Classes

Attend live sessions on Nagwa Classes to boost your learning with guidance and advice from an expert teacher!

• Interactive Sessions
• Chat & Messaging
• Realistic Exam Questions