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If the order of the barges of the preceding exercise is reversed so that the tugboat pulls the 3.00 × 10 3 -kg barge with a force of 20.0 × 10 3 N , what are the acceleration of the barges and the tension in the coupling cable?

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An object with mass m moves along the x -axis. Its position at any time is given by x ( t ) = p t 3 + q t 2 where p and q are constants. Find the net force on this object for any time t .

m (6 pt + 2 q )

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A helicopter with mass 2.35 × 10 4 kg has a position given by r ( t ) = ( 0.020 t 3 ) i ^ + ( 2.2 t ) j ^ ( 0.060 t 2 ) k ^ . Find the net force on the helicopter at t = 3.0 s .

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Located at the origin, an electric car of mass m is at rest and in equilibrium. A time dependent force of F ( t ) is applied at time t = 0 , and its components are F x ( t ) = p + n t and F y ( t ) = q t where p , q , and n are constants. Find the position r ( t ) and velocity v ( t ) as functions of time t .

v ( t ) = ( p t m + n t 2 2 m ) i ^ + ( q t 2 2 ) j ^ and r ( t ) = ( p t 2 2 m + n t 3 6 m ) i ^ + ( q t 3 60 m ) j ^

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A particle of mass m is located at the origin. It is at rest and in equilibrium. A time-dependent force of F ( t ) is applied at time t = 0 , and its components are F x ( t ) = p t and F y ( t ) = n + q t where p , q , and n are constants. Find the position r ( t ) and velocity v ( t ) as functions of time t .

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A 2.0-kg object has a velocity of 4.0 i ^ m/s at t = 0 . A constant resultant force of ( 2.0 i ^ + 4.0 j ^ ) N then acts on the object for 3.0 s. What is the magnitude of the object’s velocity at the end of the 3.0-s interval?

9.2 m/s

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A 1.5-kg mass has an acceleration of ( 4.0 i ^ 3.0 j ^ ) m/s 2 . Only two forces act on the mass. If one of the forces is ( 2.0 i ^ 1.4 j ^ ) N, what is the magnitude of the other force?

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A box is dropped onto a conveyor belt moving at 3.4 m/s. If the coefficient of friction between the box and the belt is 0.27, how long will it take before the box moves without slipping?

1.3 s

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Shown below is a 10.0-kg block being pushed by a horizontal force F of magnitude 200.0 N. The coefficient of kinetic friction between the two surfaces is 0.50. Find the acceleration of the block.

An illustration of a 10.0 kilogram block being pushed into a slope by a horizontal force F. The slope angles up and to the right at an angle of 30 degrees to the horizontal and the force F points to the right.
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As shown below, the mass of block 1 is m 1 = 4.0 kg, while the mass of block 2 is m 2 = 8.0 kg . The coefficient of friction between m 1 and the inclined surface is μ k = 0.40 . What is the acceleration of the system?

Block 1 is on a ramp inclined up and to the right at an angle of 37 degrees above the horizontal. It is connected to a string that passes over a pulley at the top of the ramp, then hangs straight down and connects to  block 2. Block 2 is not in contact with the ramp.

5.4 m/s 2

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A student is attempting to move a 30-kg mini-fridge into her dorm room. During a moment of inattention, the mini-fridge slides down a 35 degree incline at constant speed when she applies a force of 25 N acting up and parallel to the incline. What is the coefficient of kinetic friction between the fridge and the surface of the incline?

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A crate of mass 100.0 kg rests on a rough surface inclined at an angle of 37.0 ° with the horizontal. A massless rope to which a force can be applied parallel to the surface is attached to the crate and leads to the top of the incline. In its present state, the crate is just ready to slip and start to move down the plane. The coefficient of friction is 80 % of that for the static case. (a) What is the coefficient of static friction? (b) What is the maximum force that can be applied upward along the plane on the rope and not move the block? (c) With a slightly greater applied force, the block will slide up the plane. Once it begins to move, what is its acceleration and what reduced force is necessary to keep it moving upward at constant speed? (d) If the block is given a slight nudge to get it started down the plane, what will be its acceleration in that direction? (e) Once the block begins to slide downward, what upward force on the rope is required to keep the block from accelerating downward?

a. 0.60; b. 1200 N; c. 1.2 m/s 2 and 1080 N; d. −1.2 m/s 2 ; e. 120 N

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Questions & Answers

Clay Matthews, a linebacker for the Green Bay Packers, can reach a speed of 10.0 m/s. At the start of a play, Matthews runs downfield at 43° with respect to the 50-yard line (the +x-axis) and covers 7.8 m in 1 s. He then runs straight down the field at 90° with respect to the 50-yard line (that is, in the +y-direction) for 17 m, with an elapsed time of 2.9 s. (Express your answers in vector form.) (a) What is Matthews's final displacement (in m) from the start of the play?
Justin Reply
A machine at a post office sends packages out a chute and down a ramp to be loaded into delivery vehicles. (a) Calculate the acceleration of a box heading down a 17.4° slope, assuming the coefficient of friction for a parcel on waxed wood is 0.100. (b) Find the angle of the slope down which this box could move at a constant velocity. You can neglect air resistance in both parts.
Austin Reply
what principle is applicable in projectile motion
Mkapa Reply
does rocket and satellite follow the same principle??? which principle do both of these follow???
Abhishek Reply
According to d'Broglie's concept of matter waves matter behaves like wave and the wavelength is h/p. but actually there is not only a wave but a wave packet wich is defined by a wave function and that wave function can defines everything about the particle but restricted by the uncertainty principle
Ravi Reply
what phenomenon describes Matter behave as a wave???
SHAKIRU Reply
simple definition of wave
Prajwal Reply
hello
Carls Reply
can anyone help me with this problem
Carls
A projectile is shot at a hill, the base of which is 300 m away. The projectile is shot at 60°60° above the horizontal with an initial speed of 75 m/s. The hill can be approximated by a plane sloped at 20°20° to the horizontal. Relative to the coordinate system shown in the following figure, the equation of this straight line is y=(tan20°)x−109.y=(tan20°)x−109. Where on the hill does the projectile land?
Carls
what is velocity
Abel Reply
hi, Musa,this moment a lateral
Arzoodan Reply
what is moment
Musa Reply
about projectile
Indra Reply
dimesion is defined as a measureable extent of particular kind such as breadth mass
Amruta Reply
Dimension is a quantity which give us direction of any vector unit like velocity
H.M.Ahmad Reply
what is dimension
Practice Key Terms 2

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Source:  OpenStax, University physics volume 1. OpenStax CNX. Sep 19, 2016 Download for free at http://cnx.org/content/col12031/1.5
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