Exam 7: Conservation of Energy

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 speed of the rope when it just slides off the peg?

Two unequal masses hang from either end of a massless cord that passes over a frictionless pulley. Which of the following is true about the gravitational potential energy (U) and the kinetic energy of the system (K) after the masses are released from rest?

A woman on a bicycle traveling at 10 m/s on a horizontal road stops pedaling as she starts up a hill inclined at 3.0º to the horizontal. If friction forces are ignored, how far up the hill does she travel before stopping?

You drive a golf ball from A and it travels to B. The weight of the ball is w. The decrease in its potential energy is given by

A roller coaster starts from rest at point A. If you ignore friction and take the zero of potential energy to be at C,

According to Quantum Chromodynamics, the force that keeps quarks confined within a proton (or neutron) increases as the separation between the individual quarks increases. Which statement below best represents this scenario?

A woman runs up a flight of stairs. The gain in her gravitational potential energy is U. If she runs up the same stairs with twice the speed, what is her gain in potential energy?

Use the figure to the right to answer the next problems. An object of mass m = 100 g slides down without rolling a rough incline from a height H = 60 cm. At h = 30 cm, the object flies off the incline. The coefficient of kinetic friction is 0.4, and the angle $\theta$ = 30 ^$\circ$ . -What is the speed of the object just after it leaves the ramp?

You ride a roller coaster car of mass 1500 kg down a frictionless track a distance H = 23m above the bottom of a loop as shown. If the loop is 15 m in diameter, the downward force of the rails on your car when it is upside down at the top of the loop is

A 10-kg box is at the top of a 5-m plane inclined at 37º with the horizontal. The box starts from rest and slides down the plane. The coefficient of kinetic friction is 0.20. The magnitude of the change in the potential energy of the box is

The potential energy function for a conservative force acting in the x direction is shown in the figure on the right. Where would the particle experience a force directed to the right?

Calculate the work done by a force, , around a closed path, first going from P₁ (1,1) to P₂ (4,4) along path a and returning along path b.

When an electron in a hydrogen atom jumps from n = 2 to n = 1, the photon emitted is of frequency f = 4.572 $\times$ 10¹⁴ Hz. What is the energy of the photon?

A mass m is released from a height 75 cm from the right-hand side of the track shown in the diagram at right. There is only friction acting on mass along the horizontal portion 30 cm either side of the midpoint O, with a kinetic coefficient of friction of $\mu$ _k = 0.4. Determine how high it reaches the second time it passes over to the left side, and in which direction is it moving when it stops?

The total mechanical energy of any system is

The surface shown in the figure is frictionless. If the block is released from rest, it will compress the spring at the foot of the incline

A body falls through the atmosphere (consider air resistance) gaining 20 J of kinetic energy. How much gravitational potential energy did it lose?

Use the figure to the right to answer the next problems. An object of mass m = 100 g slides down without rolling a rough incline from a height H = 60 cm. At h = 30 cm, the object flies off the incline. The coefficient of kinetic friction is 0.4, and the angle $\theta$ = 30 ^$\circ$ . -According to the mass-energy relationship, how much energy is released if 1 kg of matter were converted to energy?

Newtonian mechanics, compared to Einstein's Special Relativity is valid if

A 5-kg blob of putty is dropped from a height of 10.0 m above the ground onto a light vertical spring the top of which is 5 m above the ground. If the spring constant k = 200 N/m and the blob compresses the spring by 1.50 m, then find the amount of energy lost in sound and thermal energy.