Example 5.13 Friction in horizontal motionYou want to move a 500-N crate across a level floor. To start thecrate moving, you have to pull with a 230-N horizontal force.Once the crate "breaks loose" and starts to move, you can keep itmoving at constant velocity with only 200 N. What are the coeffi-cients of static and kinetic friction?Example 5.15 Minimizing kinetic frictionIn Example 5.13, suppose you meve the crate by pulling upwardon the rope at an angle of 30° above the horizontal. How hard mustyou pull to keep it moving with constant velocity? Assume thatMk = 0.40.Example 5.16 Toboggan ride with friction ILet's go back to the toboggan we studied in Example 5.10. Thewax has worn off, so there is now a nonzero coefficient of kineticfriction uk. The slope has just the right angle to make the tobogganslide with constant velocity. Find this angle in terms of w and HkExample 5.17 Toboggan ride with friction IIThe same toboggan with the same coefficient of friction as inExample 5.16 accelerates down a steeper hill. Derive an expres-sion for the acceleration in terms of g, a, uk, and w.

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You want to move a 500-N crate across a level floor. To start the crate moving, you have to pull with a 230-N horizontal force. Once the crate "breaks loose" and starts to move, you can keep it moving at constant velocity with only 200 N. What are the coeffi- cients of static and kinetic friction? Example 5.15 Minimizing kinetic friction In Example 5.13, suppose you move the crate by pulling upward on the rope at an angle of 30° above the horizontal. How hard must you pull to keep it moving with constant velocity? Assume that 0.40.

You want to move a 500-N crate across a level floor. To start the crate moving, you have to pull with a 230-N horizontal force. Once the crate "breaks loose" and starts to move, you can keep it moving at constant velocity with only 200 N. What are the coeffi- cients of static and kinetic friction? Example 5.15 Minimizing kinetic friction In Example 5.13, suppose you move the crate by pulling upward on the rope at an angle of 30° above the horizontal. How hard must you pull to keep it moving with constant velocity? Assume that 0.40.

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Newton's Second Law

Newton’s laws of motion describe the relationship between the motion of an object and forces acting on it. Newton’s law of motion has two types as follows:

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Question

Example 5.13 Friction in horizontal motion
You want to move a 500-N crate across a level floor. To start the
crate moving, you have to pull with a 230-N horizontal force.
Once the crate "breaks loose" and starts to move, you can keep it
moving at constant velocity with only 200 N. What are the coeffi-
cients of static and kinetic friction?
Example 5.15 Minimizing kinetic friction
In Example 5.13, suppose you meve the crate by pulling upward
on the rope at an angle of 30° above the horizontal. How hard must
you pull to keep it moving with constant velocity? Assume that
Mk = 0.40.
Example 5.16 Toboggan ride with friction I
Let's go back to the toboggan we studied in Example 5.10. The
wax has worn off, so there is now a nonzero coefficient of kinetic
friction uk. The slope has just the right angle to make the toboggan
slide with constant velocity. Find this angle in terms of w and Hk
Example 5.17 Toboggan ride with friction II
The same toboggan with the same coefficient of friction as in
Example 5.16 accelerates down a steeper hill. Derive an expres-
sion for the acceleration in terms of g, a, uk, and w.

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O Macmillan Learning Calculate the final speed vf of a 2.00-kg object that is pushed for 28.0 m by a 40.0-N force directed 30.0° below the horizontal on a level, frictionless floor, as shown in the figure. Assume the object starts from rest. Uf = m/s 30° F d 2.00 kg 12