Exam 6: Energy of a System

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 speeds at the instant of launch is

Positive work can be done

A 2.0-kg projectile moves from its initial position to a point that is displaced 20 m horizontally and 15 m above its initial position.How much work is done by the gravitational force on the projectile?

If the scalar (dot)product of two vectors is negative,it means that

A 1.5-kg object moving along the x axis has a velocity of +4.0 m/s at x = 0.If the only force acting on this object is shown in the figure,what is the kinetic energy of the object at x = +3.0 m?

For the potential $U = 2 x ^ { 2 } - 8 x$ ,find the stable equilibrium point,if any.

The horizontal surface on which the block slides is frictionless.The speed of the block before it touches the spring is 6.0 m/s.How fast is the block moving at the instant the spring has been compressed 15 cm? k = 2.0 kN/m

A 30-kg child sitting 5.0 m from the center of a merry-go-round has a constant speed of 5.0 m/s.While she remains seated in the same spot and travels in a circle,the work the seat performs on her in one complete rotation is

A force acting on an object moving along the x axis is given by F_x = (14x-3.0x²)N where x is in m.How much work is done by this force as the object moves from x = -1 m to x = +2 m?

Two vectors $\overrightarrow { \mathrm { A } }$ and $\vec { B }$ are given by $\overrightarrow { \mathbf { A } } = 4 \hat { \mathbf { i } } + 8 \hat { \mathbf { j } }$ and $\overrightarrow { \mathbf { B } } = 6 \hat { \mathbf { i } } - 2 \hat { \mathbf { j } }$ .The scalar product of $\overrightarrow { \mathrm { A } }$ and a third vector $\overrightarrow { \mathrm { C } }$ is -16.The scalar product of $\vec { B }$ and $\overrightarrow { \mathrm { C } }$ is +18.The z component of $\overrightarrow { \mathrm { C } }$ is 0.What is the magnitude of $\overrightarrow { \mathrm { C } }$ ?

The only force acting on a 1.8-kg body as it moves along the x axis is given by F_x = -(3.0x)N,where x is in m.If the velocity of the body at x = 0 is v_x = +8.0 m/s,at what value of x will the body have a velocity of +4.0 m/s?

Two vectors $\overrightarrow { \mathrm { A } }$ and $\vec { B }$ are given by $\overrightarrow { \mathbf { A } } = 5 \hat{ \mathbf { i } } + 6 \hat { \mathbf { j } } + 7 \hat{ \mathbf { k } }$ and $\overrightarrow { \mathbf { B } } = 3 \hat { \mathbf { i } } - 8 \hat { \mathbf { j } } + 2 \hat { \mathbf { k } }$ .If these two vectors are drawn starting at the same point,what is the angle between them?

A 2.5-kg object falls vertically downward in a viscous medium at a constant speed of 2.5 m/s.How much work is done by the force the viscous medium exerts on the object as it falls 80 cm?

The force a spring exerts on a body is a conservative force because

Cubical blocks of mass m and side l are piled up in a vertical column.The total gravitational potential energy of a column of three blocks is

If the resultant force acting on a 2.0-kg object is equal to $( 3 \tilde { \mathbf { i } } + 4 \tilde { \mathbf { j } } )$ N,what is the change in kinetic energy as the object moves from $( 7 \tilde { \mathbf { i } } - 8 \tilde { \mathbf { j } } )$ m to $( 11 \hat { \mathbf { i } } - 5 \hat { \mathbf { j } } )$ m?

If $\overrightarrow { \mathbf { A } } \cdot \overrightarrow { \mathbf { C } } = - 7.5$ , $\overrightarrow { \mathbf { A } } = 3 \hat { \mathbf { i } } - 4 \hat { \mathbf { j } }$ ,and $| \overrightarrow { \mathbf { c } } | = 6.5$ ,what is the angle between the two vectors when they are drawn starting from the same point?

A 2.0-kg block slides down a frictionless incline from point A to point B.A force (magnitude P = 3.0 N)acts on the block between A and B,as shown.Points A and B are 2.0 m apart.If the kinetic energy of the block at A is 10 J,what is the kinetic energy of the block at B?

A block is pushed across a rough horizontal surface from point A to point B by a force (magnitude P = 5.4 N)as shown in the figure.The magnitude of the force of friction acting on the block between A and B is 1.2 N and points A and B are 0.5 m apart.If the kinetic energies of the block at A and B are 4.0 J and 5.6 J,respectively,how much work is done on the block by the force P between A and B?

Two identical springs with spring constant 50 N/m support a 5.0 N weight as in the picture below.What is the change in length of each spring when the weight is hung on the springs?