A modern-day zeppelin holds 9,770 m3 of helium. Compute its maximum payload at sea level. (Assume the helium and air to be at 0°C and 1 atm.)
N=
12. A boat (with a flat bottom) and its cargo weigh 6,400 N. The area of the boat’s bottom is 5 m2. How far below the surface of the water is the boat’s bottom when it is floating in water?
m=
13. A scale reads 378 N when a piece of iron is hanging from it. What does it read (in N) when it is lowered so that the iron is submerged in water?
N=
14. A dentist’s chair with a person in it weighs 2000 N. The output plunger of a hydraulic system starts to lift the chair when the dental assistant’s foot exerts a force of 44 N on the input piston. Neglecting any difference in the heights of the piston and the plunger, what is the ratio of the area of the plunger to the area of the piston?
Aplunger/Apiston =
15. The wing of an airplane has an average cross-sectional area of 13 m2 and experiences a lift force of 91,000 N. What is the average difference in the air pressure between the top and bottom of the wing?
N/m2=
16. Air flows through a heating duct with a square cross-section with 9-inch sides at a speed of 4.1 ft/s. Just before reaching an outlet in the floor of a room, the duct widens to assume a square cross-section with sides equal to 15 inches. Compute the speed of the air flowing into the room (in ft/s), assuming that we can treat the air as an incompressible fluid.
ft/s=
17. A metal bowl with a weight of 1.45 N is placed in a larger kitchen container filled with olive oil. How much olive oil must the bowl displace in order to float? For reference, the mass density of olive oil is about 910 g/liter and its weight density is about 8.92 N/liter. Please give your answer in liters.
liters=

On the night of a Full Moon, Mary decides to do an experiment with gravity. At midnight, she climbs into her backyard tree house, leans out the window, and holds an acorn as high as she can. She lets go and is disappointed to see the acorn plummet back down to Earth.
1. Why did the acorn fall to Earth instead of rising up to the Moon? ______________________
_________________________________________________________________________
2. Give two reasons why we feel Earth’s gravity more strongly than the Moon’s gravity.
_________________________________________________________________________
_________________________________________________________________________
image3.jpg Gizmo Warm-up
From acorns to apples, gravity causes nearly any object to fall to Earth’s surface. Gravity also causes the Moon to orbit Earth and Earth and the other planets to orbit the Sun. The Gravitational Force Gizmo™ allows you to explore the factors that influence the strength of gravitational force.
To begin, turn on the Show force vector checkboxes for objects A and B. The arrows coming from each object are vectors that represent gravitational force. The length of each vector is proportional to the force on each object.
1. Move object A around. As object A is moved, what do you notice about the direction of the two force vectors? __________________________________________________________
2. How do the lengths of the two vectors compare? __________________________________
3. Drag object A closer to object B. How does this change the gravitational force between the two objects? ______________________________________________________________
Activity A:
Gravity and mass
Get the Gizmo ready:
· Turn on Show vector notation for each object.
· Check that each object’s mass (mA and mB) is set to 10.0 × 105 kg.
image5.png
Question: How does mass affect the strength of gravitational force?
1. Form hypothesis: How do you think the masses of objects A and B will affect the strength of the gravitational force between them? __________________________________________
_________________________________________________________________________
2. Predict: How do you think the gravitational force between two objects will change if the mass of each object is doubled? ____________________________________________________
3. Measure: Turn on Show grid. Place object A on the x axis at -20 and object B on the x axis at 20. The force on object A is now 0.0417i + 0j N. That means that the force is 0.0417 newtons in the x direction (east) and 0.0 newtons in the y direction (north).
A. What is the magnitude of the force on object A? |FA| = _______________________
B. What is the magnitude of the force on object B? |FB| = _______________________
4. Gather data: You can change the mass of each object by clicking in the text boxes. For each mass combination listed in the table below, write magnitude of the force on object A. Leave the last two columns of the table blank for now.
mA (kg)
mB (kg)
|FA| (N)
Force factor
mA × mB (kg2)
10.0 × 105 kg
10.0 × 105 kg
10.0 × 105 kg
20.0 × 105 kg
20.0 × 105 kg
20.0 × 105 kg
20.0 × 105 kg
30.0 × 105 kg
5. Calculate: To determine how much the force is multiplied, divide each force by the first value, 0.0417 N. Round each value the nearest whole number and record in the “Force factor” column.
Next, calculate the product of each pair of masses. Fill in these values in the last column. Compare these numbers to the “Force factor” numbers.
(Activity A continued on next page)
Activity A (continued from previous page)
6. Analyze: How much does the force increase if each mass is doubled? _________________
_________________________________________________________________________
7. Analyze: How do the force factors compare to the products of the masses? _____________
_________________________________________________________________________
_________________________________________________________________________
8. Apply: What would you expect the force to be if the mass of object A was 50.0 × 105 kg and the mass of object B was 40.0 × 105 kg? ________________________________________
Check your answer with the Gizmo.
9. Draw conclusions: How do the masses of objects affect the strength of gravitational force?
_________________________________________________________________________
_________________________________________________________________________
_________________________________________________________________________
10. Summarize: Fill in the blank: The gravitational force between two objects is proportional to the _________________________ of the masses of the objects.
11. Apply: Suppose an elephant has a mass of 1,800 kg and a person has a mass of 75 kg. If the strength of gravitational force on the person was 735 N, what would be the gravitational force on the elephant? (Assume both the person and elephant are on Earth’s surface.)
_________________________________________________________________________
Show your work:
Activity B:
Gravity and distance
Get the Gizmo ready:
· Turn on Show distance.
· Set mA and mB to 10.0 × 105 kg.
image2.jpg
Question: How does distance affect the strength of gravitational force?
1. Form hypothesis: How do you think the distance between objects A and B will affect the strength of the gravitational force between them? __________________________________
_________________________________________________________________________
2. Predict: How do you think the gravitational force between two objects will change if the distance between the objects is doubled? ________________________________________
3. Measure: Place object A on the x axis at -5 and object B on the x axis at 5.
A. What is the distance between the two objects? ________________________
B. What is the magnitude of the force on object A? |FA| = ________________________
4. Gather data: For each set of locations listed below, record the distance and the force on object A. Leave the last two columns blank for now.
Object A
Object B
Distance (m)
|FA| (N)
Force factor
image4.png 1
Distance2
(-5, 0)
(5, 0)
(-10, 0)
(10, 0)
(-15, 0)
(15, 0)
(-20, 0)
(20, 0)
5. Interpret: How does increasing the distance affect the force? _________________________
_________________________________________________________________________
6. Calculate: To calculate the force factor, divide each force by the original force (0.667 N). Write each force factor with three significant digits. Next, calculate the reciprocal of the square of each distance and fill in the last column of the table. Write each of these values with three significant digits as well. (The unit of 1/distance 2 is square meters, or m2.)
(Activity B continued on next page)
Activity B (continued from previous page)
7. Analyze: Compare the force factors to the 1/distance2 values in your table. What is the relationship between these values?
_________________________________________________________________________
_________________________________________________________________________
8. Apply: What would you expect the force to be if the distance was 50 meters? ____________
Use the Gizmo to check your answer.
9. Make a rule: Based on the measured force between objects that are 10 meters apart, how can you find the force between objects that are any distance apart?
_________________________________________________________________________
_________________________________________________________________________
10. Summarize: Fill in the blanks: The gravitational force between two objects is proportional to the ____________________ of the distance ____________________
11. Challenge: In activity A, you found that the gravitational force between two objects is proportional to the product of their masses. Combine that with what you have learned in this activity to complete the universal formula for the force of gravity below. (Hint: In the equation, G is a constant.) Check your answer with your teacher.
FGravity = G ×
12. On your own: Use the Gizmo to find the value of G in the formula above. List the value and describe how you found it below. The units of G are newton · meter2 ÷ kilograms2, or N·m2/kg2. Check your answer with your teacher.
G = _____________________
Show your work:

Q1. Cruz runs a bakery. She has an oven that bakes 20 cookies at a time. It takes 40 minutes on average
for her to bake a cookie. What is the average number of cookies Cruz bakes an hour?
Q2. Clare works at the front desk of DESB. Between 10:30am and 11:00am, 10 students stop by to ask
questions on average. It usually takes 3 minutes to answer a question. What is the average number of
students either waiting or asking questions to Clare at the front desk? (Be careful when you find the
flow rate for this question!)
Q3. Hayden commutes to school from Park City. It usually takes her 40 minutes to get to school. She
finds that there are, on average, 60 cars that travel to school each hour from Park City. What is the
average number of cars on the way to school from Park City?
Jake’s Beer, Bait, & Tackle Co. (Q4-Q6)
Jake’s Beer, Bait, & Tackle Co. is a small chain of fishing tackle stores in northern Minnesota. In 2009,
the company’s revenue was $4,300,000 and its cost of goods sold was $3,200,000. Assume 52 weeks and
365 days per year. Assume that the annual inventory holding cost for Jake’s is 40%.
Q4. Jake keeps only 5.5 days-of-supply of inventory on average because much of his inventory is live bait
and micro-brew beer, both of which have a short shelf life. What is his annual inventory turns? (Round
your answer to two decimal places)
Q5. Given that he has 5.5 days-of-supply of inventory on average, how much inventory does Jake
have on average (in $)?
Q6. What is the inventory holding cost (in $) of an item that costs Jake $20 and is sold to his customers
at $30? (Round your answer to two decimal places)
B&K Consulting (Q7-Q9)
B&K is a strategy consulting firm that divides its consultants into three classes: Associates, Managers,
and Partners. The firm has been stable in size for the last 30 years, and on average, there have been 200
Associates, 60 Managers, and 20 Partners.
The work environment at B&K is rather competitive. After four years of working as an Associate, a
consultant goes “either up or out”; that is, becomes a Manager or is dismissed from the company.
Similarly, after working as a Manager for six years, a Manager either becomes a Partner or is dismissed.
The company recruits MBAs as Associates; no hires are made at the Manager or Partner level.
Q7. How many new MBA graduates does B&K hire every year? (Hint: Think of the Associate stage
itself as a process and use Little’s law to find the number of MBA graduates that are hired each year.
The following picture may help.)
Q8. What percentage (in %) of new hires at B&K will become Managers (as opposed to being
dismissed after 4 years of working as an Associate)? (Hint: Think of the Manager stage itself as a
separate process and find how many managers should be appointment each year. The following picture
may help.)
Q9. Every year, 2 Managers are promoted to Partner level. How many years on average does a
Partner stay in the company as a Partner?
4 years
200 Associates ? Associates/year
6 years
60 Managers ? Managers/year
A Simple Process (Q10 – Q13)
Consider the following process that makes customized suits. When an order is placed, measurement is
taken, which takes 30 minutes to complete. After taking the measurement, materials are prepared and
cut, and this takes one hour. Once the materials are prepared and cut, the materials are sewed. Sewing
takes 2.5 hours on average per order. The process operates for 10 hours a day. The following picture
summarizes the process.
Q10. What is the capacity of the process in [suits/day]?