Classical Mechanics

Conservation of Energy

Mixed Conservative and Non-Conservative Forces - Problem Solving

         

Consider the situation where a baseball player with mass m=76 kg m = 76 \text{ kg} slides to a stop on level ground. Using energy considerations, calculate the distance d d the baseball player slides, given that his initial speed is v=8 m/s v = 8 \text{ m/s} and the force of friction against him is a constant f=304 N. f= 304 \text{ N}.

In the above diagram, the bob A A of a pendulum with mass m=8 kg m = 8 \text{ kg} is released from height h=8 m. h = 8 \text{ m}. Because of air resistance, the speed of velocity at the lowest position is v=6 m/s. v = 6 \text{ m/s}. Find the loss in the total mechanical energy of the bob.

The gravitational acceleration is g=10 m/s2. g =10 \text{ m/s}^2.

A roller-coaster of mass M=2000 kg M= 2000 \text{ kg} has a speed of v1=10 m/s v_1 = 10 \text{ m/s} as it goes over the top of a 1515-meter-high hill. Then it goes over a another hill of height 1010 meters, and at the crest of that hill, the roller-coaster is moving at v2=13 m/s. v_2 = 13 \text{ m/s}. How much work did friction do on the coaster during its movement between the two hills?

The gravitational acceleration is g=10 m/s2. g= 10 \text{ m/s}^2.

A skier with mass m=77 kg m = 77 \text{ kg} coasts up an inclination with angle θ=45 \theta = 45 ^\circ and height h=0.5 m h = 0.5 \text{ m} at an initial speed of vi=12 m/s. v_i = 12\text{ m/s}. Find the square of her final speed at the top, given that the coefficient of kinetic friction between her skis and the snow is μ=0.5. \mu = 0.5.

The gravitational acceleration is g=10 m/s2. g = 10 \text{ m/s}^2.

An object with mass m=1 kg m = 1 \text{ kg} at the top of a h=7 m h = 7 \text{ m} tall hill starts to go down from rest. The downhill portion of the run is covered with frictionless material but the flat section at the base of the hill has a spot of friction 2 m 2 \text{ m} in length. The object comes straight down the hill, over the spot of friction at the bottom, hits and presses the the damping spring 20 cm 20 \text{ cm} in the process. If the spring constant is k=2×102 N/m, k = 2 \times 10^2 \text{ N/m}, what is the magnitude of kinetic friction between the object and flat section.

The gravitational acceleration is g=10 m/s2 g = 10 \text{ m/s}^2 and air resistance is negligible.

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