3. A 60 kg snowboarder begins to slide down the hill 50 m high on a smooth surface with a radius curvature of 80 m. The next section (AB) is a 20 m flat rough track with u = .3, at the end of which there is an elastic barrier with k 1000 N/m. a. Find her speed at point A. b. How much work is done by frictional force? What is the maximum compression of the spring? d. Find the rate of heat dissipation along the section AB. e. How long does it take to cover the section AB? с. h k A В
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- A sledder with a total mass 40.0 kg (including the sled) slides down a 10.0m hill that is 20◦ from the horizontal. i. Let the coefficient of kinetic friction be µK = 0.2. The velocity at the bottom of the hill is 5.5 m/s. What is the kinetic energy of the sledder at the bottom of the hill?ii. How much energy is lost due to friction?A box of mass 4.0 kg hangs by a cable from the ceiling of an elevator. The elevator is moving up at a steady speed of 5.0 m/s for 8.0 m. Use g = 10 m/s2. Consider the system is the box and the Earth. Match the answers with questions.In the movie Monty Python and the Holy Grail a cow is catapulted from the top of a castle wall over to the people down below. The gravitational potential energy is set to zero at ground level. The cow is launched from a spring of spring constant 1.9 x104 N/m that is expanded 0.5 m from equilibrium. The castle is 9.8 m tall and the mass of the cow is 600 kg. a. What is the gravitational potential energy of the cow at the top of the castle? J b. What is the elastic spring energy of the cow before the catapult is released? J c. What is the speed of the cow right before it lands on the ground? m/s Hint: For Parts a. and b., use the relevant formulas for gravitational and elastic potential energy, respectively. For Part c., use conservation of energy, noting that initially the cow is at rest so the initial energy is all potential while the final energy is all kinetic.
- 2. A 900 kg elevator is raised by an electric motor up from the basement to the third floor, a vertical distance of 9.9 m, over the course of 5 s. There's a friction force of 125 N between the elevator and the elevator shaft. A. Draw a free body diagram of the elevator. Which forces are conservative? Which forces are dissipative? Which are external? B. How much potential energy does the elevator gain as its lifted? C. What is the work done by friction on the elevator? Is it positive or negative?A student pushes a baseball of m = 0.15kg down onto the top of a vertical spring that has its lower end fixed to a table, compressing the spring a distance of d = 0.16 meters froms its equailibrium length. The springs constant of the spring constant k = 610 N/m. Let the gravitional potential energy be zero at the position of the baseball in the compressed spring. a. what is the maximum height, h, in meters, that the ball reaches above the equilibrium point? b. What is the ball's velocity, in meters per second, at half of the maximum height relative to the equilibrium pointC 4. A box is being pulled across a rough floor with a force P. What can you say about the work done by pulling force, normal force, friction, and gravitational force? 0, W by normal force > 0, Wby friction 0, Why normal force 0, W by normal force= D. Wby pulling force <0, Why normal force = 0, W by friction <0, W by gravitational force = 0 0, W by friction <0. Wby gravitational force = 0
- A particle of mass m moves along the x-axis. Its potential energy at any point x is, V(x) = Vox²e¬z². Vo = constant. %3D a. Find the force on the particle. b. Find all the points on the x-axis where the particle can be in equilibrium. Determine whether each equilibrium point is stable or unstable. Sketch the potential energy and label the equilibrium points.A daredevil on a motorcycle leaves the end of a ramp with a speed of 33.2 m/s as in the figure below. If his speed is 31.0 m/s when he reaches the peak of the path, what is the maximum height that he reaches? Ignore friction and air resistance. m A daredevil on a motorcyle is at the end of a ramp that is sloped up to the right. An arrow parallel to the ramp's surface is above the daredevil. A dotted-line path traces the trajectory of the daredevil. The path extends up to the right, initially parallel to the surface of the ramp, and decreases in slope until it reaches a maximum, whereupon it extends down to the right with increasing slope magnitude. The vertical distance between the maximum and the highest point of the ramp is h. A horizontal arrow points to the right above the maximum.A2.0-kg mass is projected vertically upward from ground level with an initial speed of 30 m/s. e mass rises to a maximum height of 35 m above ground level. What is the change in mechanical energy of the mass caused by air resistance between the point of projection and the point of maximum height?
- A crate with mass m = 33.3 kg being pushed up an incline that makes an angle φ = 22.7 degrees with horizontal. The pushing force is horizontal, with magnitude P, and the coefficient of kinetic friction between the crate and the incline is μ = 0.358. Consider the work done on the crate as it moves a distance d = 5.32 m at constant speed. a. What is work done by the pushing force, in joules? b. What is the work done by friction, in joules? c. What is the work done by gravity, in joules? d. What is the net work, in joules?a spring has a spring constant k of 140n/m. a 150 g block is placed against the spring and compressed 16 cm. a0 when the block is released how high up the slope does it rise? b) what is the kinetic energy at the highest point? c) what is the potential energy at the highest point.A spring is used to launch a box along the frictionless track shown below. The spring constant is 345 N/m and the spring is initially compressed by 15.6 cm. The mass of the box is 80.8 g. Point Z is 46.4 cm vertically below the launch point. a. What is the potential energy held in the spring before it is launched? J b. Using Conservation of Energy, what is the speed of the box as it passes point Z? m/s