# 7.4 Power  (Page 6/8)

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A crate is being pushed across a rough floor surface. If no force is applied on the crate, the crate will slow down and come to a stop. If the crate of mass 50 kg moving at speed 8 m/s comes to rest in 10 seconds, what is the rate at which the frictional force on the crate takes energy away from the crate?

160 J/s

Suppose a horizontal force of 20 N is required to maintain a speed of 8 m/s of a 50 kg crate. (a) What is the power of this force? (b) Note that the acceleration of the crate is zero despite the fact that 20 N force acts on the crate horizontally. What happens to the energy given to the crate as a result of the work done by this 20 N force?

Grains from a hopper falls at a rate of 10 kg/s vertically onto a conveyor belt that is moving horizontally at a constant speed of 2 m/s. (a) What force is needed to keep the conveyor belt moving at the constant velocity? (b) What is the minimum power of the motor driving the conveyor belt?

a. 10 N; b. 20 W

A cyclist in a race must climb a $5\text{°}$ hill at a speed of 8 m/s. If the mass of the bike and the biker together is 80 kg, what must be the power output of the biker to achieve the goal?

## Challenge problems

Shown below is a 40-kg crate that is pushed at constant velocity a distance 8.0 m along a $30\text{°}$ incline by the horizontal force $\stackrel{\to }{F}.$ The coefficient of kinetic friction between the crate and the incline is ${\mu }_{k}=0.40.$ Calculate the work done by (a) the applied force, (b) the frictional force, (c) the gravitational force, and (d) the net force.

If crate goes up: a. 3.46 kJ; b. −1.89 kJ; c. −1.57 kJ; d. 0; If crate goes down: a. −0.39 kJ; b. −1.18 kJ; c. 1.57 kJ; d. 0

The surface of the preceding problem is modified so that the coefficient of kinetic friction is decreased. The same horizontal force is applied to the crate, and after being pushed 8.0 m, its speed is 5.0 m/s. How much work is now done by the force of friction? Assume that the crate starts at rest.

The force F ( x ) varies with position, as shown below. Find the work done by this force on a particle as it moves from $x=1.0\phantom{\rule{0.2em}{0ex}}\text{m}$ to $x=5.0\phantom{\rule{0.2em}{0ex}}\text{m}\text{.}$

8.0 J

Find the work done by the same force in [link] , between the same points, $A=\left(0,0\right)\phantom{\rule{0.2em}{0ex}}\text{and}\phantom{\rule{0.2em}{0ex}}B=\left(2\phantom{\rule{0.2em}{0ex}}\text{m},2\phantom{\rule{0.2em}{0ex}}\text{m}\right)$ , over a circular arc of radius 2 m, centered at (0, 2 m). Evaluate the path integral using Cartesian coordinates. ( Hint: You will probably need to consult a table of integrals.)

Answer the preceding problem using polar coordinates.

35.7 J

Find the work done by the same force in [link] , between the same points, $A=\left(0,0\right)\phantom{\rule{0.2em}{0ex}}\text{and}\phantom{\rule{0.2em}{0ex}}B=\left(2\phantom{\rule{0.2em}{0ex}}\text{m},2\phantom{\rule{0.2em}{0ex}}\text{m}\right)$ , over a circular arc of radius 2 m, centered at (2 m, 0). Evaluate the path integral using Cartesian coordinates. ( Hint: You will probably need to consult a table of integrals.)

Answer the preceding problem using polar coordinates.

24.3 J

Constant power P is delivered to a car of mass m by its engine. Show that if air resistance can be ignored, the distance covered in a time t by the car, starting from rest, is given by $s={\left(8P\text{/}9m\right)}^{1\text{/}2}{t}^{3\text{/}2}.$

Suppose that the air resistance a car encounters is independent of its speed. When the car travels at 15 m/s, its engine delivers 20 hp to its wheels. (a) What is the power delivered to the wheels when the car travels at 30 m/s? (b) How much energy does the car use in covering 10 km at 15 m/s? At 30 m/s? Assume that the engine is 25% efficient. (c) Answer the same questions if the force of air resistance is proportional to the speed of the automobile. (d) What do these results, plus your experience with gasoline consumption, tell you about air resistance?

a. 40 hp; b. 39.8 MJ, independent of speed; c. 80 hp, 79.6 MJ at 30 m/s; d. If air resistance is proportional to speed, the car gets about 22 mpg at 34 mph and half that at twice the speed, closer to actual driving experience.

Consider a linear spring, as in [link] (a), with mass M uniformly distributed along its length. The left end of the spring is fixed, but the right end, at the equilibrium position $x=0,$ is moving with speed v in the x -direction. What is the total kinetic energy of the spring? ( Hint: First express the kinetic energy of an infinitesimal element of the spring dm in terms of the total mass, equilibrium length, speed of the right-hand end, and position along the spring; then integrate.)

What is the equation illustrating Williamsons ether synthesis
what is simple harmonic motion
examples: vibrating prongs of a tuning fork and a guittar string.
Salman
It is a repetitive periodic motion of a system about an equilibrium position
Felix
SHM is the repitition process of to and fro motion.
Younus
SHM is the motion in which the restoring force is directly proportional to the displacement of body from its mean position and is opposite in direction to the displacement. From Hooke's law F=-kx
Kushal
SHM is the motion in which the restoring force is directly proportional to the displacement of body from its mean position and is opposite in direction to the displacement. From Hooke's law F=-kx
Kushal
what is a wave?
show that coefficient of friction of solid block inclined at an angle is equivalent to trignometric tangent of angle
DAVID
Wave is the transfer of energy due to the periodic vibration of the particles in the medium.
Kushal
wave is the transfer of energy
Vindora
Wave is the transfer of particles in a fluid or any way.
Younus
thanks for that definition.
Hi everyone please can dere be motion without force?
Lafon
no...
Enyia
Thanks
Lafon
hi
Omomaro
whats is schrodinger equation
Omomaro
l went spiral spring
Xalat
what is position?
position is simply where you are or where you were
Shii
position is the location of an object with respect to a two or three dimensional axes or space.
Bamidele
Can dere be motion without force?
Lafon
what is the law of homogeinity?
two electric lines of force never interested each other. why?
if two electric lines of force intersect eachother then their will be two tangent at a point which represent the two forces which is impossible.
Amar
proof that for BBC lattice structure 4r\root 5 and find Apf for the BBC structure
what is physics?
physics is deine as the specific measrument of of volume, area,nd distances...
Olakojo
if a string of 2m is suspended an an extended 3m elasticity is been applied.... is hooks law obeyed?
Enyia
if a string of 2m is suspended an an extended 3m elasticity is been applied.... is hooks law obeyed?
Enyia
yes
Alex
proof that for a BBC lattice structure a= 4r/ root 5 find the APF for the BBC structure
Eric
if a string of 2m is suspended an an extended 3m elasticity is been applied.... is hooks law obeyed?
tell me conceptual quetions of mechanics
I want to solve a physical question
ahmed
ok
PUBG
a displacement vector has a magnitude of 1.62km and point due north . another displacement vector B has a magnitude of 2.48 km and points due east.determine the magnitude and direction of (a) a+ b and (b) a_ b
quantum
George
a+b=2.9
SUNJO
a+b
Yekeen
use Pythogorous
Dhritwan
A student opens a 12kgs door by applying a constant force of 40N at a perpendicular distance of 0.9m from the hinges. if the door is 2.0m high and 1.0m wide determine the magnitude of the angular acceleration of the door. ( assume that the door rotates freely on its hinges.) please assist me to d
Mike
what is conditions met to produce shm
what is shm
Manzoor
shm?
Grant
Why is Maxwell saying that light is an electromagnetic wave?
Bong
1st condition; It(th e BBC's system) must have some inertia which will enable it to possess Kinetic energy 2. must be able to store potential energy
Calleb
I meant "the system" not the BBC'S....."
Calleb
Manzoor
kindly tell us the name of your university
Manzoor
GUlam Ishaq Khan INSTITUTE of engineering science
ali
Department of Environment Ionian University Zante Greece
why light wave travel faster than sounds
Why light travel faster than sounds?
ALI
Light travel faster than sound because it does not need any medium to travel through.
alhassan
when an aeroplane flies....why it does not fall on the earth?
Frazali
As an aeroplane moves, it hits a wind,we have the wind flowing at the upper and lower zone of the aeroplane, the one that is moving on the upper zone moves at a greater speed than that of the lower zone, this creates a low pressure on the upper zone and a greater pressure at the lower zone.
Kipkoech
which thing of aeroplane moves it upward?
Frazali
good question
Manzoor
Barataa
am pleased to join the group
Nesru
yea
caleb
It a privilege to be here
olajire
hi
Awode
hello
Manzoor
Light speed is more than sound speed. C=3×10*8m/s V=320-340 m/s
siva
A body of mass 2kg slides down a rough plane inclined to horizontal at 30degrees. find the energy that is wasted as a result of friction if the co-efficient of kinetic f