Exam 7: Conservation of Energy

A 3-kg block sits on an incline where the top half of the incline has a coefficient of kinetic friction of 0.5 and the bottom half is frictionless. The angle of inclination is 35 degrees. If the block is released and travels 10 m along the rough part of the incline and then 10 m along the smooth part before it makes contact with the spring (k = 200 N/m), calculate the distance the spring is compressed.

A mass m is released from a height 60 cm from the right-hand side of the track shown in the diagram at right. There is only friction acting on the mass on the horizontal portion 35 cm either side of the midpoint O, with a kinetic coefficient of friction of $\mu$ _k = 0.5. Determine what is the velocity of the block the first time it passes through the midpoint, and on which side of the midpoint does it stop?

A hanging block A (m_A = 15 kg) is connected by a light cable and a pulley wheel to a second block B (m_B = 10 kg) situated at the bottom of a frictionless inclined plane with angle 30 ^$\circ$ to the horizontal. If the hanging block is released from rest 5 m above the ground, find the maximum distance that block B travels up along the inclined plane.

Which of the following statements is NOT correct?

Which of the following are units of energy?

If you drive at the posted speed limit of 70 mph on the interstate, what is the fraction of your speed compared to the speed of light?

The rest mass of an electron is 9.11 $\times$ 10^-31 kg. From this information one can conclude that the rest energy of an electron is

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

A child is sitting on the seat of a swing with ropes 10 m long. Her father pulls the swing back until the ropes make a 37º angle with the vertical and then releases the swing. If air resistance is neglected, what is the speed of the child at the bottom of the arc of the swing when the ropes are vertical?

A block of mass, m, is pushed up against a spring, compressing it a distance x, and is then released. The spring projects the block along a frictionless horizontal surface, giving the block a speed v. The same spring projects a second block of mass 4m, giving it a speed 3v. What distance was the spring compressed in the second case?

Calculate the work done by a force, , along the path (0,0) $\to$ P₁ (2,0) $\to$ P₂ (2,2).

Which of the following statements is true?

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 ^$\circ$ . -How far from the base of the elevated incline does the object hit the floor?

Release mass m on a string from rest at point A. As it passes the lowest point B, the tension in the string is

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 ^$\circ$ . -The minimum amount of energy released in an electron-positron annihilation is

When a hydrogen atom absorbs a photon with E = 4.089 $\times$ 10^-19 J, what is the frequency of the photon?

The reference point for gravitational potential energy

A block of mass m starts from position 1 and moves up a frictionless inclined plane with an initial speed v. At some later time the block has moved down the plane and at position 2 has a speed u. If a and b are the heights above the bottom of the plane, the magnitude of u can be determined from

When the potential energy U(r) is given as in Figure A, then the force is given in Figure B by curve

The block shown in the figure is sliding on a frictionless surface. Its speed when it has traveled 9 m along the horizontal surface will be