For a drag force of the form F = - bv, what are the units of b?

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A 1.5-kg block rests on top of a 7.5-kg block. The cord and pulley have negligible mass, and there is no significant friction anywhere.

(a) What force F must be applied to the bottom block so the top block accelerates to the right at 2.6 m/s^{2} ?

(b) What is the tension in the connecting cord?

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A fisherman in a boat is using a "10-lb test" fishing line. This means that the line can exert a force of 45 N without breaking (1 lb = 4.45 N).

(a) How heavy a fish can the fisherman land if he pulls the fish up vertically at constant speed?

(b) If he accelerates the fish upward at 2.1 m/s^{2} , what maximum weight fish can he land?

(c) Is it possible to land a 15-lb trout on 10-lb test line? Why or why not?

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A 7700-kg helicopter accelerates upward at 0.75 m/s^{2} while lifting a 1300-kg frame at a construction site.

(a) What is the lift force exerted by the air on the helicopter rotors?

(b) What is the tension in the cable (ignore its mass) that connects the frame to the helicopter?

(c) What force does the cable exert on the helicopter?

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A wet bar of soap (m= 150 g) slides freely down a ramp 3.1 m long inclined at 9.0 ^{}.

How long does it take to reach the bottom?

How would this change if the soaps mass were 300 g?

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A heavy steel cable of length *ℓ* and mass M passes over a small massless, frictionless pulley. If a length hangs on one side of the pulley (so *ℓ* - y hangs on the other side):

(a) Calculate the acceleration of the cable as a function of y.

(b) Assuming the cable starts from rest with length y_{0} on one side of the pulley, determine the velocity v_{f} at the moment the whole cable has fallen from the pulley.

(c) Evaluate v_{f} for y_{0} = 2/3*ℓ*. [*Hint*: Use the chain rule, dv/dt = (dv/dy)(dy/dt), and integrate.]

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A block is given an initial speed of 4.6 m/s up the 26 degree plane shown in the figure. How far up the plane will it go? How much time elapses before it returns to its starting point? Ignore friction.

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The block shown in the figure has mass m=7.5 kg and lies on a fixed smooth frictionless plane tilted at an angle ^{}=23.0 to the horizontal.

Determine the acceleration of the block as it slides down the plane.

If the block starts from rest 13.0 m up the plane from its base, what will be the blocks speed when it reaches the bottom of the incline?
Caption: Block on inclined plane.

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A skateboarder, with an initial speed of 2.4 m/s , rolls virtually friction free down a straight incline of length 20 m in 3.3 s .

At what angle *
* is the incline oriented above the horizontal?

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Uphill escape ramps are sometimes provided to the side of steep downhill highways for trucks with overheated brakes.

For a simple 13 ^{} upward ramp, what length would be needed for a runaway truck traveling 150 km/h ? Note the large size of your calculated length. (If sand is used for the bed of the ramp, its length can be reduced by a factor of about 2.)

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Two snowcats in Antarctica are towing a housing unit to a new location, as shown in the figure . The sum of the forces **F**_{A} and **F**_{B} exerted on the unit by the horizontal cables is parallel to the line L, and F_{A}=4600 N .

Determine F_{B}.

Determine the magnitude of **F**_{A} + **F**_{B}.

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A window washer pulls herself upward using the bucket-pulley apparatus shown in the figure.

(a) How hard must she pull downward to raise herself slowly at constant speed? The mass of the person plus the bucket is 76 kg.

(b) If she increases this force by 16%, what will her acceleration be? The mass of the person plus the bucket is 76 kg.

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A 650-N force acts in a northwesterly direction.

A second 650-N force must be exerted in what direction so that the resultant of the two forces points westward?

Illustrate your answer with a vector diagram.

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(a) What is the weight of a 66-kg astronaut on Earth?

(b) What is the weight of a 66-kg astronaut on the Moon (g = 1.7 m/s^{2} )?

(c) What is the weight of a 66-kg astronaut on Mars (g = 3.7 m/s^{2} )?

(d) What is the weight of a 66-kg astronaut in outer space traveling with constant velocity?

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At t = 0 a batter hits a baseball with an initial speed of 28 m/s at a 55 ^{} angle to the horizontal. An outfielder is 85 t = 0 from the batter at t = 0 and, as seen from home plate, the line of sight to the outfielder makes a horizontal angle of 22 m with the plane in which the ball moves (as shown in the figure).

What direction must the fielder take to catch the ball at the same height from which it was struck? Give the angle with respect to the outfielders line of sight to home plate.

What speed must the fielder take to catch the ball at the same height from which it was struck?
Assume that the outfielder’s time for running is the same as the time of flight of the ball.

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A ball is shot from the top of a building with an initial velocity of 19 m/s at an angle = 43 ^{} above the horizontal.

What are the horizontal and vertical components of the initial velocity?

If a nearby building is the same height and 60 m away, how far below the top of the building will the ball strike the nearby building?

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A batter hits a fly ball which leaves the bat 0.95 m above the ground at an angle of 61 ^{} with an initial speed of 30 m/s heading toward centerfield. Ignore air resistance.

How far from home plate would the ball land if not caught?

The ball is caught by the centerfielder who, starting at a distance of 105 m from home plate, runs straight toward home plate at a constant speed and makes the catch at ground level. Find his speed.

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A rock is kicked horizontally at 15 m/s from a hill with a 45 ^{} slope .

How long does it take for the rock to hit the ground?

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You are driving south on a highway at 25 m/s (approximately 55 mi/h) in a snowstorm. When you last stopped, you noticed that the snow was coming down vertically, but it is passing the windows of the moving car at an angle of 36 ^{} to the horizontal.

Estimate the speed of the snowflakes relative to the car.

Estimate the speed of the snowflakes relative to the ground.

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A basketball is shot from an initial height of 2.4 m with an initial speed v_{0} =12 m/s directed at an angle _{0} = 35 ^{} above the horizontal.

How far from the basket was the player if he made a basket?

At what angle to the horizontal did the ball enter the basket?

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A child runs down a 12° hill and then suddenly jumps upward at a 15° angle above horizontal and lands 1.4 m down the hill as measured along the hill. What was the child’s initial speed?

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A boat is traveling where there is a current of 0.20 m/s east. To avoid some offshore rocks, the boat must clear a buoy that is NNE (22.5) ^{} and 2.8 km away. The boats speed through still water is 2.2 m/s .

If the boat wants to pass the buoy 0.16 km on its right, at what angle relative north should the boat head?

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A boat can travel 2.30 m/s in still water.

If the boat points its prow directly across a stream whose current is 1.60 m/s , what is the magnitude of the velocity of the boat relative to the shore?

What will be the position of the boat, relative to its point of origin, after 7.00 s ? Assume that the positive x and y axes are directed downstream and away from the shore, respectively.

What is the angle of the velocity of the boat relative to the shore?

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A projectile is launched from ground level to the top of a cliff which is 195 m away and 135 m high (as shown in the figure).If the projectile lands on top of the cliff 6.8 s after it is fired, find the initial velocity of the projectile ( (a)magnitude and (b)direction ). Neglect air resistance.

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A particle has a velocity of **v** = ( - 2.0**i** + 3.5t**j**) m/s. The particle starts at **r** = (1.5**i** - 3.1**j**) m at t = 0.

Give the position as a function of time.

What is the shape of the resulting path?

Give the acceleration as a function of time.

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