Classical Mechanics

# Mixed Conservative and Non-Conservative Forces - Problem Solving

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

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

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

A roller-coaster of mass $$M= 2000 \text{ kg}$$ has a speed of $$v_1 = 10 \text{ m/s}$$ as it goes over the top of a $$15$$-meter-high hill. Then it goes over a another hill of height $$10$$ meters, and at the crest of that hill, the roller-coaster is moving at $$v_2 = 13 \text{ m/s}.$$ How much work did friction do on the coaster during its movement between the two hills?

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

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

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

An object with mass $$m = 1 \text{ kg}$$ at the top of a $$h = 7 \text{ m}$$ 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 $$2 \text{ m}$$ in length. The object comes straight down the hill, over the spot of friction at the bottom, hits and presses the the damping spring $$20 \text{ cm}$$ in the process. If the spring constant is $$k = 2 \times 10^2 \text{ N/m},$$ what is the magnitude of kinetic friction between the object and flat section.

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

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