If the kinetic energy of a particle is doubled, by what factor has its speed increased?

(II) Recall from Chapter $4$. Example $4-14$, that you can use a pulley and ropes to decrease the force needed to raise a heavy load (see Fig. 7-22). But for every meter the load is raised, how much rope must be pulled up? Explain.

A car drives at steady speed around a perfectly circular track. (a) The car's acceleration is zero. (b) The net force on the car is zero. (c) Both the acceleration and net force on the car point outward. (d) Both the acceleration and net force on the car point inward. (e) If there is no friction, the acceleration is outward.

Estimate the work you do to mow a lawn $10 \mathrm{~m}$ by $20 \mathrm{~m}$ with a $50~\mathrm{cm}$-wide mower. Assume you push with a force of about $15 \mathrm{~N}$.

If the speed of a particle is halved, by what factor does its kinetic energy change ?

A 65.0-kg firefighter climbs a flight of stairs 20.0 m high. How much work is required?

A 6kg bucket of water is being pulled straight up by a string at a constant speed. I determined that the tension on the string was F = ma F = (6kg * 9.8 m/s2) , F = 58.8 N Now its asking At a certain point the speed of the bucket begins to change. The bucket now has an upward constant acceleration of magnitude 3 m/s2. What is the tension in the rope now? The correct answer was "about 78N" then Now assume that the bucket has a downward acceleration, with a constant acceleration of magnitude3 m/s2. Now what is the tension in the rope?

Forces $\vec { F _ { 1 } }$ and $\vec { F _ { 2 } }$ act at a point. The magnitude of $\vec { F _ { 1 } }$ is 9.00 N, and its direction is $60.0 ^ { \circ }$ above the x-axis in the second quadrant. The magnitude of $\vec { F _ { 2 } }$ is 6.00 N, and its direction is $53.1 ^ { \circ }$ below the x-axis in the third quadrant. (a) What are the x- and y-components of the resultant force? (b) What is the magnitude of the resultant force?

For each of the cases described below, sketch and label the total acceleration vector, the radial acceleration vector, and the tangential acceleration vector. $(a)$ A car is accelerating from $55 \mathrm{~km} / \mathrm{h}$ to $70 \mathrm{~km} / \mathrm{h}$ as it rounds a curve of constant radius. $(b)$ A car is going a constant $65 \mathrm{~km} / \mathrm{h}$ as it rounds a curve of constant radius. $(c)$ A car slows down while rounding a curve of constant radius.

When jumping, a flea rapidly extends its legs, reaching a takeoff speed of 1.0 m/s over a distance of 0.50 mm. a. What is the flea's acceleration as it extends its legs? b. How long does it take the flea to leave the ground after it begins pushing off?

A 145-g baseball is dropped from a tree 13.0 m above the ground. With what speed would it hit the ground if air resistance could be ignored?

Write a paragraph describing different forms of colonial rule. Be sure to define protectorate, direct rule, and indirect rule and to discuss specific examples

A person has a reasonable chance of surviving an automobile crash if the deceleration is no more than $30 \mathrm{~g}$'s. Estimate the force on a $65\,\mathrm{kg}$ person accelerating at this rate. What distance is traveled if brought to rest at this rate from $85 \mathrm{~km} / \mathrm{h}$?

Block A has a mass of 5 kg and is placed on the smooth triangular block B having a mass of 30 kg. If the system is released from rest, determine the distance B moves from point O when A reaches the bottom. Neglect the size of block A.