Exam 8: Conservation of Energy

A spring (k = 200 N/m)is suspended with its upper end supported from a ceiling.With the spring hanging in its equilibrium configuration,an object (mass = 2.0 kg)is attached to the lower end and released from rest.What is the speed of the object after it has fallen 4.0 cm?

A 1.6-kg block slides down a plane (inclined at 25° with the horizontal)at a constant speed of 2.0 m/s.At what rate is the frictional force changing the mechanical energy of the block?

While running,a person dissipates about 0.6 J of mechanical energy per step per kilogram of body mass.If a 60-kg person runs with a power of 70 Watts during a race,how fast is the person running? Assume a running step is 1.5 m long.

As a result of friction between internal parts of an isolated system

The speed of a 4.0-kg object is given by v = (2t)m/s,where t is in s.At what rate is the resultant force on this object doing work at t = 1 s?

As an object moves from point A to point B only two forces act on it: one force is nonconservative and does −30 J of work,the other force is conservative and does +50 J of work.Between A and B,

A 3.0-kg mass is dropped from the edge of a 50-m tall building with an initial speed of zero.The mass strikes the ground with a downward velocity of 25 m/s.Find the change in mechanical energy of the mass caused by air resistance between the point where it is dropped and the point where it strikes the ground?

Two masses,M_A and M_B,with M_B = 2M_A,are released at the same time and allowed to fall straight down.Neglect air resistance.When we compare their kinetic energies after they have fallen equal distances,we find that

Objects A and B,of mass M and 2M respectively,are each pushed a distance d straight up an inclined plane by a force F parallel to the plane.The coefficient of kinetic friction between each mass and the plane has the same value μ_k.At the highest point,

A 1.2-kg mass is projected up a rough circular track (radius = 0.80 m)as shown.The speed of the mass at point A is 8.4 m/s,and at point B,it is 5.6 m/s.What is the change in mechanical energy between A and B caused by the force of friction?

The solution to a problem is the equation below.Which description best fits this solution?

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?

A 0.04-kg ball is thrown from the top of a 30-m tall building (point A)at an unknown angle above the horizontal.As shown in the figure,the ball attains a maximum height of 10 m above the top of the building before striking the ground at point B.If air resistance is negligible,what is the value of the kinetic energy of the ball at B minus the kinetic energy of the ball at A (K_B − K_A)?

A 2.0-kg block slides down a plane (inclined at 40° with the horizontal)at a constant speed of 5.0 m/s.At what rate is the gravitational force on the block doing work?

A spring with spring constant k = 800 N/m is compressed 12 cm from its equilibrium position.A spring with spring constant k = 400 N/m has the same elastic potential energy as the first spring when its extension is

A 6.0-kg block slides along a horizontal surface.If µ_k = 0.20 for the block and surface,at what rate is the friction force changing the mechanical energy of the block at an instant when its speed is 4.0 m/s?

Two masses,M_A and M_B,with M_B = 2M_A,are released at the same time and allowed to fall straight down.Neglect air resistance.When we compare their kinetic energies after they have fallen for equal times,we find that

A champion athlete can produce one horsepower (746 W)for a short period of time.If a 70-kg athlete were to bicycle to the summit of a 500-m high mountain while expending power at this rate,she would have used at least ____ J of energy.

A 20-kg mass is fastened to a light spring (k = 380 N/m)that passes over a pulley as shown.The pulley is frictionless,and the mass is released from rest when the spring is unstretched.After the mass has dropped 0.40 m,what is its speed?

A 70-kg high jumper leaves the ground with a vertical velocity of 6.0 m/s.How high can he jump?