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Physics: Acceleration, Order of magnitude, Velocity, and Newton

A helium-filled balloon for a birthday party is being brought home in a car. As the car accelerates away from a stoplight, in which direction does the balloon move relative to the car? Explain.

Estimate how many 20 cm x 20 cm tiles it would take to tile the floor and three sides of a shower stall. The stall has a square floor, which is 16 square feet, and five-foot walls. Show your work. Also, discuss the purpose for order-of-magnitude calculations.

A man drops a baseball from the edge of a roof of a building. At exactly the same time, another man pitches a baseball vertically up toward the man on the roof in such a way that the ball just barely reaches the roof. Does the ball from the roof reach the ground before the ball from the ground reaches the roof, or is it the other way around? Explain your reasoning.

Reversing the algebraic sign on the velocity vector reverses the direction of motion. Is the same statement true for the acceleration vector? Explain your reasoning

To attain the maximum range, a projectile has to be launched at 45 degrees if the landing spot and the launch spot are at the same height (neglecting air-resistance effects). Explain how the relation between the vertical and the horizontal components of the initial velocity affects the projectile range

When a dog gets wet, it shakes its body from head to tail to shed the water. Explain, in terms of Newton's first law, why this works.

You hold your hands out in front of you and catch a bowling ball dropped from a foot above your hands. No problem. If, instead, you were to hold your hands about half an inch above the floor, and try the same catch, you would have a painful experience. Why? (Don't try this at home!)

In the Jurassic Park sequel, The Lost World, a man tries to keep a large vehicle from going over a cliff by connecting a cable from his Jeep to the vehicle. The man then puts the Jeep in gear and spins the rear wheels. Do you expect that spinning the tires will increase the force exerted by the Jeep on the vehicle? Why or why not.

A ski boat moves with constant velocity. Is the net force acting on the boat doing work? Explain why or why not? Also, explain why kinetic energy is a consideration when assessing constant velocity.

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A helium-filled balloon for a birthday party is being brought home in a car. As the car accelerates away from a stoplight, in which direction does the balloon move relative to the car? Explain.
Sol: The balloon would move backwards, i.e., opposite to the direction of the speeding of the car. This is because while the string with which the balloon is held moves forward, due to the inertia of its mass, the balloon continues to stay in its position of rest for some time (Newton's First Law of motion).

Estimate how many 20 cm x 20 cm tiles it would take to tile the floor and three sides of a shower stall. The stall has a square floor, which is 16 square feet, and five-foot walls. Show your work. Also, discuss the purpose for order-of-magnitude calculations.
Sol: Area of base = 16*16 ft2 = 256 ft2
Area of the four walls = 4*(16*5) = 320 ft2
Total area = 576 ft2 = 576*(30*30) cm2 = 518400 cm2
Number of tiles needed = 518400 cm2/400 cm2 = 1296 tiles.
Order of magnitude form allows representing very large ...

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