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Feb 12 Discussion

Feb 12 Discussion. Force and Newton’s Second Law problems. Designing an elevator.

ainsley-barton
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Feb 12 Discussion

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  1. Feb 12 Discussion Force and Newton’s Second Law problems

  2. Designing an elevator • Because of your physics background, you are asked to choose the cable strength necessary to safely support an elevator. The cab of the elevator has a mass of 1200 kg and its passenger capacity is 800 kg. The maximum acceleration (up or down) of the elevator is to be 2.0 m/s2. • Hint: when two objects accelerate together, they can be treated as a single combined mass from the point of view of external forces and Newton’s Second Law.

  3. Designing an elevator • The cab of the elevator has a mass of 1200 kg and its passenger capacity is 800 kg. The maximum acceleration (up or down) of the elevator is to be 2.0 m/s2. • The greatest tension occurs when the elevator is accelerating upward. The cable must support the total weight is the weight of the elevator plus the passengers plus additional force to accelerate the total mass upward.

  4. Towing • A 5000 kg truck can produce a maximum force on a dry road so that the road pushes back hard enough to accelerate the truck at 2.4 m/s2. The truck is to tow a trailer with a mass of 10000 kg. What is the maximum acceleration for the truck/trailer combination? • Hint: when two objects accelerate together, they can be treated as a single combined mass from the point of view of external forces and Newton’s Second Law.

  5. Towing • A 5000 kg truck can produce a maximum force on a dry road so that the road pushes back hard enough to accelerate the truck at 2.4 m/s2. The truck is to tow a trailer with a mass of 10000 kg. What is the maximum acceleration for the truck/trailer combination?

  6. Pulling a car out of the mud • Your car is stuck in the mud. You have a rope and a place to tie it securely to the car. You try pulling on it to free the car, but cannot pull hard enough to get the car’s drive wheels out of the muddy rut. You decide to see if taking physics allows you to solve real-world problems…

  7. The set up • First, of course, you get out some paper and draw the free body diagram: consider the balance of forces on the midpoint of the rope.

  8. The set up • First, of course, you get out some paper and draw the free body diagram: consider the balance of forces on the midpoint of the rope.

  9. How much force? You decide to estimate the tension you will get. You realize that it also depends on how hard you can pull against therope. Draw the free-body diagram for yourself. What limits the force you can exert on the rope?A) your arm strengthB) maximum static friction force from the groundC) the weight of the carD) the strength of the tree

  10. How much force? You decide to estimate the tension you will get. You realize that it also depends on how hard you can push against therope. Draw the Free-body diagram for yourself. What limits the force you can exert on the rope?A) B) maximum static friction force-that’s the only other horizontal force acting on youC) D)

  11. How much tension? • Assuming that the maximum static friction force is on the order of your weight (500-1000 N, for most people), and the angle of the rope is similar to the diagram (5-10 degrees), how much tension can you produce? A) 300 NB) 3000 NC) 30000 ND) 300000 N The weight of one ton is about 20000 N.

  12. How much tension? • Assuming that the maximum static friction force is on the order of you weight, and the angle of the rope is similar to the diagram (5-10 degrees), how much tension can you produce? y A) B) 3000 NC) D) x q The forces balance in the x-direction due to the symmetry. For the forces to balance in the y-direction, the tension needs to satisfy:

  13. Truck stopping a plane • In a recent television ad for a pickup truck, a cargo plane carrying the truck lands, the truck rolls down a ramp out the back of the plane onto the ground, and we see that the truck and plane are still connected by a chain. The truck’s brakes to bring the plane and the truck to rest. What should we be impressed about here?

  14. Forces on the truck • What is the direction of the acceleration of the truck? Consider the forces on the truck. Draw the free body diagram. • Which is greater, A) the force of the road on the truck, or B) the force of the chain on the truck, orC) are they the same?

  15. Forces on the truck • What is the direction of the acceleration of the truck? • Consider the forces on the truck. Draw the free body diagram. • Which is greater, A) the force of the road on the truck, since the acceleration is opposite from the velocity, the force on the car from the road must be greater!B) C)

  16. Force on the plane • Which is greater? A) the force of the road on the truck or B) the force of the chain on the plane, orC) are they the same?

  17. Force on the plane • Which is greater? A) the force of the road on the truck or B) C) • Note that the force of the chain on the plane is the same magnitude as the force of the chain on the truck • What’s impressive?It’s not so much the amount of force involved, it’s the fact that the truck’s brakes didn’t burn up that was impressive.

  18. Braking a plane • Consider: a 3000 kg pickup stopping a 30000 kg plane. The plane lands at 50 m/s and the braking force from friction is no greater than 80% of the weight of the pickup. How far do they travel together while braking? (use g=10 m/s2)

  19. Braking a plane • Consider: a 3000 kg pickup stopping a 30000 kg plane. The plane lands at 50 m/s and the braking force from friction is no greater than 80% of the weight of the pickup. How far do they travel together while braking? • The magnitude of the braking force is fs=0.80(3000 kg)(10 m/s2)=24000 N • Taking v0 as positive, the braking acceleration isa=-fs/mtot=-(24000 N)/(33000 kg)=-0.73 m/s2 • The braking distance is given byvf2=v02+2a Dx or Dx=-v02/(2a)=-(50 m/s)2/(2(-0.73 m/s2))=1700 m!

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