# Force & Mass

## Problems

### practice

- 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.
- 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.
- Draw a free body diagram showing all the forces acting on the cheeseburger.
- Determine the weight of the cheeseburger.
- Determine the magnitude and direction of the net force on the cheeseburger.
- Determine the magnitude and direction of the elevator's acceleration.
- 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.

- Write something different.
- Write something completely different.

### conceptual

- As a rocket rises its acceleration increases. Why does this happen? (Assume that the acceleration due to gravity and air resistance are nearly constant during the ascent.)

### numerical

- Before a transparent material can be approved for use as a windshield in an airplane, it must first pass the "bird-impact resistance" test. A genuine (dead) or artificial chicken is accelerated to aircraft cruising speeds from the mouth of an air cannon and aimed at the windshield prototype. If the material shows any significant form of damage it fails the test. Each part of this problem contains an except from a USAF News Agency report.
- "Aircrews… find nothing funny about bird strikes. A strategically placed feathered bullet can wreak the same amount of damage as a laser-guided missile. The impact of a four-pound bird at 500 mph lasts less than a thousandth of a second, but can generate forces exceeding 100,000 pounds." Verify this statement; that is, that show that such a collision would indeed exert the force claimed.
- "They fire gelatin-molded, artificial birds weighing four pounds apiece, out a compressed air, 30 foot barrel cannon, which can shoot at speeds up to 900 mph. Three lasers and photodetectors measure the artificial chicken's velocity, while three cameras shoot the impact at 6,000 frames per second." Calculate the force exerted by the cannon on the chicken.

- An 11.3 g bullet leaves the muzzle of a 61 cm rifle with a horizontal velocity of 922 m/s. It strikes a target 457 m away with a horizontal velocity of 650 m/s. Determine…
- the acceleration of the bullet in the rifle
- the force of the propellant on the bullet in the rifle
- the horizontal acceleration of the bullet after it left the rifle barrel
- the aerodynamic drag on the bullet after it left the rifle barrel
- the time it took the bullet to travel the distance between the muzzle and the target
- how far the bullet fell by the time it hit the target

- An open parachute provides an upward drag force of 855 N to a 56 kg skydiver.
- Draw a free body diagram showing all the forces acting on the skydiver.
- Determine the weight of the skydiver.
- Determine the magnitude and direction of the net force on the skydiver.
- Determine the magnitude and direction of the skydiver's acceleration.
- Determine the speed of the skydiver ten seconds after the parachute opened if her initial velocity was 60 m/s.

### statistical

- The table below shows some of the best and worst performing cars in an emergency braking test.
Emergency braking test Source: Road & Track make

modelweight/mass initial speed braking distance (lb) (kg) (mph) (m/s) (ft) (m) Mercedes-Benz

E550 Coupe3810 1728 80 35.8 252 76.8 Porsche

911 GT33075 1395 80 35.8 186 56.7 Volkswagen

Golf GTI 3-dr3370 1529 60 26.8 143 43.6 Alfa Romeo

8C Competizione3495 1585 60 26.8 105 32.0 - For all four cars, determine the…
- braking acceleration
- braking force

- Which car is "the best"? Why did you choose this car?

- For all four cars, determine the…
- lab-f.txt

A group of physics students measured the acceleration of a laboratory cart pulled across a table by a string tied to a falling weight. They varied the weight on the string, but kept the total mass of the system constant. Perform a linear fit on this data and use the slope to determine the mass of the system. - lab-m.txt

A group of physics students measured the acceleration of a laboratory cart pulled across a table by a string tied to a falling weight. They varied the mass of the cart, but kept the weight on the end of the string constant.- Transform the data so that a linear fit can be performed.
- Use the slope to determine the net force on the system.
- The students performing this experiment used standard laboratory weights. What is the most probable mass of the weight on the end of the string?