1. Ben Travlun carries a 200-N suitcase up three flights of stairs (a height of 10.0 m) and then pushes it with a horizontal force of 50.0 N at a constant speed of 0.5 m/s for a ho... 1. Ben Travlun carries a 200-N suitcase up three flights of stairs (a height of 10.0 m) and then pushes it with a horizontal force of 50.0 N at a constant speed of 0.5 m/s for a horizontal distance of 35.0 meters. How much work does Ben do on his suitcase during this entire motion? 2. A bookshelf has five shelves, each 40 centimeters apart. If Roger lifts a 2.8-kilogram dictionary at a constant velocity from the second shelf to the fifth shelf, how much work does he do? 3. What two things must happen in order for you to do work? 4. What can a Joule also be written as? 5. Give an example of a time someone thinks they are working really hard, but actually aren't working at all?

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Understand the Problem

Here's a breakdown of the questions:

Question 11 involves calculating the total work done by Ben on his suitcase, considering both the vertical lift and the horizontal push. We need to compute the work done against gravity while lifting the suitcase and the work done by the horizontal force over the given distance. The total work is then the sum of these two components.

Question 12 asks us to determine the work done by Roger when lifting a dictionary from the second to the fifth shelf. We calculate the total distance the dictionary is lifted and then use the formula for work done against gravity to find the amount of work done.

Question 13 asks for two conditions needed to 'do work' from a physics point of view.

Question 14 relates to what a Joule represents in terms of fundamental units.

Question 15 asks for an example of someone expending energy, but not accomplishing any measurable change from a scientific view point.

Answer

11. $3750 \, \text{J}$ 12. $32.928 \, \text{J}$ 13. A force must be applied and there must be displacement in the direction of the force. 14. $\text{kg} \cdot \frac{\text{m}^2}{\text{s}^2}$ 15. Pushing against a stationary wall.
Answer for screen readers
  1. $3750 , \text{J}$
  2. $32.928 , \text{J}$
  3. A force must be applied and there must be displacement in the direction of the force.
  4. $\text{kg} \cdot \frac{\text{m}^2}{\text{s}^2}$
  5. Pushing against a stationary wall.

Steps to Solve

  1. Calculate the work done lifting the suitcase

Work is defined as force times distance. When lifting the suitcase, the force is the weight of the suitcase, and the distance is the height it is lifted.

$W_{lifting} = F \cdot d = 200 , \text{N} \cdot 10.0 , \text{m} = 2000 , \text{J}$

  1. Calculate the work done pushing the suitcase horizontally

Again, work is force times distance. Here, the force is the horizontal force applied, and the distance is the horizontal distance.

$W_{pushing} = F \cdot d = 50.0 , \text{N} \cdot 35.0 , \text{m} = 1750 , \text{J}$

  1. Calculate the total work

The total work done is the sum of the work done lifting and the work done pushing.

$W_{total} = W_{lifting} + W_{pushing} = 2000 , \text{J} + 1750 , \text{J} = 3750 , \text{J}$

  1. Determine the distance the dictionary is lifted

The dictionary is lifted from the second shelf to the fifth shelf, which is a total of $5 - 2 = 3$ shelf distances. Each shelf is 40 cm apart. Convert centimeters to meters by dividing by 100.

Distance between shelves = $40 , \text{cm} = 0.4 , \text{m}$ Total distance $= 3 \cdot 0.4 , \text{m} = 1.2 , \text{m}$

  1. Calculate the force required to lift the dictionary

The force required to lift the dictionary at a constant velocity is equal to its weight. Weight is mass times the acceleration due to gravity ($g = 9.8 , \text{m/s}^2$).

$F = mg = 2.8 , \text{kg} \cdot 9.8 , \text{m/s}^2 = 27.44 , \text{N}$

  1. Calculate the work done lifting the dictionary

Work is force times distance.

$W = F \cdot d = 27.44 , \text{N} \cdot 1.2 , \text{m} = 32.928 , \text{J}$

  1. State the conditions needed to do work

In physics, work is done when a force causes a displacement. Therefore, you need:

  1. A force must be applied.

  2. The object must move in the direction of the force.

  3. Express a Joule in fundamental units

A Joule is a unit of energy, and it can be expressed in terms of fundamental units (kilograms, meters, and seconds).

$1 , \text{Joule} = 1 , \text{N} \cdot \text{m} = 1 , \frac{\text{kg} \cdot \text{m}}{\text{s}^2} \cdot \text{m} = 1 , \text{kg} \cdot \frac{\text{m}^2}{\text{s}^2}$

  1. Give an example of expending energy without doing work

An example of someone expending energy but not doing work is pushing against a stationary wall. You are applying a force and using energy, but since the wall doesn't move, no work is done.

  1. $3750 , \text{J}$
  2. $32.928 , \text{J}$
  3. A force must be applied and there must be displacement in the direction of the force.
  4. $\text{kg} \cdot \frac{\text{m}^2}{\text{s}^2}$
  5. Pushing against a stationary wall.

More Information

The concept of work in physics is very specific. It requires both a force and a displacement in the direction of the force. If either of these is missing, no work is done in the physics sense, even if it feels like you are working hard.

Tips

  • For question 11, a common mistake is to forget to include both the work done lifting the suitcase and the work done pushing it horizontally.
  • For question 12, forgetting to convert centimeters to meters can also lead to an incorrect answer. Also, one could forget to calculate the net distance between shelves, instead using a single shelf distance in their calculations.

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