Three different objects, all with different masses, are initially at rest at the bottom of a set of steps. Each step is of uniform height d. The mass of each object is a multiple of the base mass m: object 1 has mass 4.90m, object 2 has mass 1.46m, and object 3 has mass m. When the objects are at the bottom of the steps, define the total gravitational potential energy of the three-object system to be zero. If the objects are then relocated as shown, what is the new total potential energy of the system? Each answer requires the numerical coefficient to an algebraic expression. Each algebraic expression is given using some 3 combination of the variables m, g, and d, where g is the acceleration due to gravity. Enter only the numerical coefficient. (Example: If the answer is 1.23mgd, just enter 1.23)
Three different objects, all with different masses, are initially at rest at the bottom of a set of steps. Each step is of uniform height d. The mass of each object is a multiple of the base mass m: object 1 has mass 4.90m, object 2 has mass 1.46m, and object 3 has mass m. When the objects are at the bottom of the steps, define the total gravitational potential energy of the three-object system to be zero. If the objects are then relocated as shown, what is the new total potential energy of the system? Each answer requires the numerical coefficient to an algebraic expression. Each algebraic expression is given using some 3 combination of the variables m, g, and d, where g is the acceleration due to gravity. Enter only the numerical coefficient. (Example: If the answer is 1.23mgd, just enter 1.23)
College Physics
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ISBN:9781305952300
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Chapter1: Units, Trigonometry. And Vectors
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Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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![Three different objects, all with different masses, are initially at rest at the bottom of a set of steps. Each step is of uniform height \(d\). The mass of each object is a multiple of the base mass \(m\): object 1 has mass \(4.90m\), object 2 has mass \(1.46m\), and object 3 has mass \(m\). When the objects are at the bottom of the steps, define the total gravitational potential energy of the three-object system to be zero. If the objects are then relocated as shown, what is the new total potential energy of the system?
Each answer requires the numerical coefficient to an algebraic expression. Each algebraic expression is given using some combination of the variables \(m\), \(g\), and \(d\), where \(g\) is the acceleration due to gravity. Enter only the numerical coefficient. (Example: If the answer is \(1.23mgd\), just enter \(1.23\))
Diagram Explanation:
- Object 1 is initially at the bottom and is moved up to the third step.
- Object 2 is placed on the second step.
- Object 3 is placed on the first step.
- Each step has a uniform height \(d\).
\[ U_{g, \text{system}} = \boxed{\phantom{0}} \, mgd \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1dd80890-34f3-42a2-96e7-3fec6dc24d2c%2Fa45ea708-b491-4a30-9c47-23fed38b74ed%2Fwaivd78_processed.png&w=3840&q=75)
Transcribed Image Text:Three different objects, all with different masses, are initially at rest at the bottom of a set of steps. Each step is of uniform height \(d\). The mass of each object is a multiple of the base mass \(m\): object 1 has mass \(4.90m\), object 2 has mass \(1.46m\), and object 3 has mass \(m\). When the objects are at the bottom of the steps, define the total gravitational potential energy of the three-object system to be zero. If the objects are then relocated as shown, what is the new total potential energy of the system?
Each answer requires the numerical coefficient to an algebraic expression. Each algebraic expression is given using some combination of the variables \(m\), \(g\), and \(d\), where \(g\) is the acceleration due to gravity. Enter only the numerical coefficient. (Example: If the answer is \(1.23mgd\), just enter \(1.23\))
Diagram Explanation:
- Object 1 is initially at the bottom and is moved up to the third step.
- Object 2 is placed on the second step.
- Object 3 is placed on the first step.
- Each step has a uniform height \(d\).
\[ U_{g, \text{system}} = \boxed{\phantom{0}} \, mgd \]
![This portion of educational content involves understanding the potential energy of a system relative to a reference point. The formula for gravitational potential energy in this context is given by:
\[ U_{g, \text{system}} = \boxed{\phantom{space}} \, mgd \]
The task begins by considering potential energy calculated relative to the bottom of the stairs. You are asked to redefine the reference height such that the total potential energy of the system equals zero. Given this condition, you must determine how high above the bottom of the stairs the new reference height would be:
\[ \boxed{\phantom{space}} \, d \]
Next, you are tasked with finding another reference height, again measured from the bottom of the stairs. This time, the goal is to make sure that the highest two objects have the exact same potential energy:
\[ \boxed{\phantom{space}} \, d \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1dd80890-34f3-42a2-96e7-3fec6dc24d2c%2Fa45ea708-b491-4a30-9c47-23fed38b74ed%2F1t2eldu_processed.png&w=3840&q=75)
Transcribed Image Text:This portion of educational content involves understanding the potential energy of a system relative to a reference point. The formula for gravitational potential energy in this context is given by:
\[ U_{g, \text{system}} = \boxed{\phantom{space}} \, mgd \]
The task begins by considering potential energy calculated relative to the bottom of the stairs. You are asked to redefine the reference height such that the total potential energy of the system equals zero. Given this condition, you must determine how high above the bottom of the stairs the new reference height would be:
\[ \boxed{\phantom{space}} \, d \]
Next, you are tasked with finding another reference height, again measured from the bottom of the stairs. This time, the goal is to make sure that the highest two objects have the exact same potential energy:
\[ \boxed{\phantom{space}} \, d \]
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