The Physics
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Opus in profectus

Force & Mass

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Practice

practice problem 1

A supertanker doesn't come with brakes. Using engines alone, it takes a loaded supertanker 13 km (8 miles) to stop. A typical vessel of this class has a gross mass of about 150 million kilograms (150 thousand tons) and a cruising speed of 50 kph (30 mph). Determine the average stopping force applied to the ship.

solution

This problem lends itself well to standard techniques. State the given quantities and convert them to SI units as needed. Solve the appropriate equation of motion to get the acceleration. Substitute this expression into Newton's Second Law and solve. (It can also be solved using the work-energy theorem — as it will be in a later section of this book. Both methods lead to exactly the same answer — as they should.)

Δs =  13,000 m
m =  150 × 106 kg
v =  0 m/s
v0 =  50,000 m/3,600 s = 13.888… m/s
F =  ??
   
v2 = v02 + 2aΔs  ⇒  a =  v02
s
F =  ma =  mv02
s
F =  (150 × 106 kg)(13.888… m/s)2
2(13,000 m)
F =  1,112,892 N = 1.1 MN  
 

The first sentence of this question came from an article in the Chicago Tribune dated 6 April 2001, "Strait with No Equal Has New Danger." Moral of the story: Yield to the supertanker when you're sailing the Bosphorus.

practice problem 2

A person stands in an elevator weighing a cheeseburger with a kitchen scale. (It could happen.) The mass of the cheeseburger is 0.150 kg. The scale reads 1.14 N.
  1. Draw a free body diagram showing all the forces acting on the cheeseburger.
  2. Determine the weight of the cheeseburger.
  3. Determine the magnitude and direction of the net force on the cheeseburger.
  4. Determine the magnitude and direction of the elevator's acceleration.
  5. At the time the person in the elevator is weighing the cheeseburger, the elevator's instantaneous velocity is upward. Is the speed of the elevator increasing, decreasing, or remaining constant at this moment? Justify your answer.

solution

Answer it.

practice problem 3

Write something different.

solution

Answer it.

practice problem 4

Write something completely different.

solution

Answer it.