Exam 7: Conservation of Energy

A 5-kg mass with initial velocity 20 m/s slides along a frictionless horizontal surface then up a frictionless ramp (2 m long and at an angle 30 degrees to the horizontal) and onto a second horizontal surface. The block slides over a rough surface 15 m in length ( $\mu$ _k = 0.4) before moving again on a frictionless surface and then impacting upon an uncompressed spring. If the block compresses the spring a distance 2 m, what is the spring constant k for the spring?

The potential energy function for a conservative force acting in the x direction on a particle is shown below. The number of points where the net force on the particle is equal to zero are

A 4.0-kg block starts from rest and slides 5.0 m down a plane inclined at 60º to the horizontal. The coefficient of kinetic friction between the surface and the block is 0.20. The work done by friction on the block is

Assuming the incline to be frictionless and the zero of gravitational potential energy to be at the elevation of the horizontal line,

A mass m is released from a height 80 cm from the right-hand side of the track shown in the diagram at right. There is only friction acting along the horizontal portion 30 cm either side of the midpoint O with a kinetic coefficient of friction of $\mu$ _k = 0.4. Determine (i) how many times does the mass m pass through the midpoint O, and (ii) how far from the midpoint does it come to rest.

In magazine car tests an important indicator of performance is the zero to 60 mph (0 to 96.6 km/h) acceleration time. A time below 6 s is considered to be extremely quick. If a car with mass 1300 kg were dropped vertically from a great height, how long would it take to go from zero to 60 mph and what would the magnitude of the change in gravitational potential energy be during this time? (neglect air resistance)

A 75-kg man climbs the stairs to the fifth floor of a building, a total height of 16 m. His potential energy has increased by

Which of the following statements is true?

A spring with force constant k = 300 N/m is compressed 9.0 cm. What is the potential energy in the spring?

A mass, m, slides down a frictionless incline and hits a spring with spring constant k. Find the spring compression when the acceleration of the mass is zero.

Use the figure to the right for the next problems. A flexible rope of mass m and length L = L₁ + L₂, hangs over a frictionless peg, as shown in the figure. -What is the change in potential energy when the end of the rope just slides off the peg?

An electron has a rest mass of 0.511 MeV. From this information one can conclude that the rest mass of an electron is

A proton has a rest mass of 938 MeV. From this information one can conclude that the rest mass of a proton is

The block shown in the figure is sliding on a frictionless surface. Its speed when it reaches the level portion of the surface on which it is sliding will be

Use the figure to the right for the next problem. An object of mass m = 200 g slides down a frictionless ramp from a height H = 60 cm. Near the bottom of the ramp, the path changes into an arc of a circle with radius r = 20 cm. The arc has coefficient of kinetic friction $\mu$ _k = 0.4. The angle $\theta$ = 120 ^$\circ$ and points P₁ and P₂ which are the ends of the arc, are at the same height. -What is the speed of the object at point P₁?

Which of the following are units of mass?

Susana ascends a mountain via a short, steep trail. Sean ascends the same mountain via a long, gentle trail. Which of the following statements is true?

The rest mass of a proton is 1.67 $\times$ 10^-27 kg. From this information one can conclude that the rest energy of a proton is

Use the figure to the right for the next problem. An object of mass m = 200 g slides down a frictionless ramp from a height H = 60 cm. Near the bottom of the ramp, the path changes into an arc of a circle with radius r = 20 cm. The arc has coefficient of kinetic friction $\mu$ _k = 0.4. The angle $\theta$ = 120 ^$\circ$ and points P₁ and P₂ which are the ends of the arc, are at the same height. -What is the kinetic energy of the object at point P₂?

Which potential energy versus displacement curve best represents that of an extended spring?