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Q.78

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Physics for Scientists and Engineers: A Strategic Approach with Modern Physics
Found in: Page 158

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Short Answer

An object with cross section A is shot horizontally across frictionless ice. Its initial velocity is at . Air resistance is not negligible.

a. Show that the velocity at time t is given by the expression

b. A -wide, -high, car with a drag coefficient of hits a very slick patch of ice while going . If friction is neglected, how long will it take until the car’s speed drops to ? To ?

c. Assess whether or not it is reasonable to neglect kinetic friction.

a. derivation of the velocity at time

b. time taken for car to drop its speed is

c. Its absurd. so that kinetic friction were neglected.

See the step by step solution

Step by Step Solution

Step 1: Given information (part a)

cross section of the object

Initial velocity at

velocity at time

Coefficient of drag

density of air

mass of the object

Step 2: Explanation (part a)

From Newton's second law

The drag force is

Consider the negative sign for drag force as it acts opposite to the net force and equal the drag force.

Here

Therefore, we get

On integrating the above equation, we get

Conclusion: The expression for velocity at time has been derived.

Step 3: Given information (part b)

length of the car

height of the car

mass of the car

drag coefficient

Initial velocity

Final velocity

density of air

Step 4: Explanation (part b)

The velocity expression at time is given by

Plugging all the values in the above equation, we get

The time taken for the car to drop its speed

Step 5: Explanation (part c)

If we consider an object that moves by inertia with the drag or frictional force, the net force is not zero and the motion will be decelerated (non-uniform), and we will have to introduce new forces to make it uniform, which is absurd. That is why we neglect the mentioned forces.

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