Exam 6: Energy of a System

A 2.0-kg body moving along the x axis has a velocity v_x = 5.0 m/s at x = 0.The only force acting on the object is given by F_x = (-4.0x)N,where x is in m.For what value of x will this object first come (momentarily)to rest?

Negative work can be done

The same constant force is used to accelerate two carts of the same mass,initially at rest,on horizontal frictionless tracks.The force is applied to cart A for twice as long a time as it is applied to cart B.The work the force does on A is W_A;that on B is W_B.Which statement is correct?

As a particle moves along the x axis it is acted upon by a single conservative force given by F_x = (20 - 4.0x)N where x is in m.The potential energy associated with this force has the value +30 J at the origin (x = 0).What is the value of the potential energy at x = 4.0 m?

Carts A and B have equal masses and travel equal distances D on side-by-side straight frictionless tracks while a constant force F acts on A and a constant force 2F acts on B.Both carts start from rest.The velocities $\overrightarrow { \mathbf { v } }$ _A and $\overrightarrow { \mathbf { v } }$ _B of the bodies at the end of distance D are related by

If $\overrightarrow { \mathrm { A } }$ = 5.0, $\vec { B }$ = 8.0,and $\alpha$ = 30 $\degree$ ,determine the scalar product of the two vectors shown.

The force of static friction exerted on an automobile's tires by the ground

A 10-kg block on a horizontal frictionless surface is attached to a light spring (force constant = 0.80 kN/m).The block is initially at rest at its equilibrium position when a force (magnitude P = 80 N)acting parallel to the surface is applied to the block,as shown.What is the speed of the block when it is 13 cm from its equilibrium position?

If $\overrightarrow { \mathbf { A } } = 7 \tilde { \mathbf { i } } - 6 \hat { \mathbf { j } } + 5 \hat { \mathbf { k } }$ , $| \overrightarrow { \mathbf { B } } | = 7$ ,and the angle between $\overrightarrow { \mathrm { A } }$ and $\vec { B }$ (when the two are drawn starting from the same point)is 60 $\degree$ ,what is the scalar product of these two vectors?

The graph below shows how the force on a 0.500 kg particle varies with position.If the particle has speed $v = 2.23 \frac { \mathrm { m } } { \mathrm { s } }$ at x = 0.00 m,what is its speed in m/s when x = 8.00 m?

A conservative force on a particle moving along the x axis is given by $\overrightarrow { \mathbf { F } } = \left( 3 x ^ { 2 } - 2 x \right) \tilde{ \mathbf { i } }$ .Which of the following is a potential that is associated with this force?

Two balls,A and B,of mass m and 2m respectively,are carried to height h at constant velocity,but B rises twice as fast as A.The work the gravitational force does on B is

If vectors $\overrightarrow { \mathrm { A } }$ and $\vec { B }$ have magnitudes 12 and 15,respectively,and the angle between the two when they are drawn starting from the same point is 110 $\degree$ ,what is the scalar product of these two vectors?

The work $\overrightarrow { \mathbf { F } } _ { sp} \cdot d ~\overrightarrow { { x } }$ done by the force exerted by the spring on a mass attached to the end of the spring when the mass has displacement d $\overrightarrow { \mathbf { x } }$ is

Equal amounts of work are performed on two bodies,A and B,initially at rest,and of masses M and 2M respectively.The relation between their speeds immediately after the work has been done on them is

A 5.0-kg object is pulled along a horizontal surface at a constant speed by a 15-N force acting 20 $\degree$ above the horizontal.How much work is done by this force as the object moves 6.0 m?

As a 1.0-kg object moves from point A to point B,it is acted upon by a single conservative force which does -40 J of work during this motion.At point A the speed of the particle is 6.0 m/s and the potential energy associated with the force is +50 J.What is the potential energy at point B?

How much work is done by a person lifting a 2.0-kg object from the bottom of a well at a constant speed of 2.0 m/s for 5.0 s?

The force an ideal spring exerts on an object is given by F_x =-kx,where x measures the displacement of the object from its equilibrium (x = 0)position.If k = 60 N/m,how much work is done by this force as the object moves from x = -0.20 m to x = 0?

Two clowns are launched from the same spring-loaded circus cannon with the spring compressed the same distance each time.Clown A has a 40-kg mass;clown B a 60-kg mass.The relation between their kinetic energies at the instant of launch is