Exam 7: 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?

For the potential , find the stable equilibrium point, if any.

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?

Positive work can be done

In a contest, two tractors pull two identical blocks of stone the same distance over identical surfaces. However, block A is moving twice as fast as block B when it crosses the finish line. Which statement is correct?

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 , , and , what is the angle between the two vectors when they are drawn starting from the same point?

The only force acting on a 2.0-kg body as it moves along the x axis is given by F_x = (12 − 2.0x) N, where x is in m. The velocity of the body at x = 2.0 m is 5.5 m/s. What is the maximum kinetic energy attained by the body while moving in the +x direction?

Each of two vectors, and , lies along a coordinate axis in the xy plane. Each vector has its tail at the origin, and the dot product of the two vectors is . Which possibility is correct?

If , , and the angle between and (when the two are drawn starting from the same point) is 60°, what is the scalar product of these two vectors?

A 10-kg block on a rough horizontal surface is attached to a light spring (force constant = 1.4 kN/m). The block is pulled 8.0 cm to the right from its equilibrium position and released from rest. The frictional force between the block and surface has a magnitude of 30 N. What is the kinetic energy of the block as it passes through its equilibrium position?

Planets go around the sun in elliptical orbits. The highly exaggerated diagram below shows a portion of such an orbit and the force on the planet at one position along that orbit. The planet is moving to the right. F_|| and are the components of the force parallel (tangential) and perpendicular (normal) to the orbit. The work they do is W_|| and . At the position shown

If the vectors and have magnitudes of 10 and 11, respectively, and the scalar product of these two vectors is −100, what is the magnitude of the sum of these two vectors?

If the resultant force acting on a 2.0-kg object is equal to N, what is the change in kinetic energy as the object moves from m to m?

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?

When a crate of mass m is dragged a distance d along a surface with coefficient of kinetic friction μ_k, then dragged back along the same path to its original position, the work done by friction is

Two eggs of equal mass are thrown at a blanket with equal velocity. Egg B hits the blanket but egg A hits the wall instead. Compare the work done on the eggs in reducing their velocities to zero.

A particle is subject to the potential . What is the value of the y component of the force on the particle at the point (x, y) = (2.0, 3.0)?

Two vectors and are given by and . The scalar product of and a third vector is −16. The scalar product of and is +18. The z component of is 0. What is the magnitude of ?

A block slides on a rough horizontal surface from point A to point B. A force (magnitude P = 2.0 N) acts on the block between A and B, as shown. Points A and B are 1.5 m apart. If the kinetic energies of the block at A and B are 5.0 J and 4.0 J, respectively, how much work is done on the block by the force of friction as the block moves from A to B?