A 34.0 cm long pendulum with a 245-g bob swings through at an angle of 180 degrees. Choose the reference configuration as the point where the pendulum string is vertical. Assuming the pendulum remains taut, what is the gravitational potential energy of the pendulum bob-Earth system when the pendulum string makes an angle of a. 90 degrees with the vertical? and b. 40.5 degrees with the vertical? c. What is the gravitational potential energy of the pendulum bob-Earth system at the lowest point of the pendulum's motion?

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.

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A. Calculate the work done by the force of gravity when a 7.0 kg object is lifted to a height of 46.0 m above the ground.B. Calculate the velocity with which the object strikes the ground if dropped from that height, using the principle of conservation of energy.C. Calculate the kinetic energy (KE) and the potential energy (PE) of the object at apoint halfway on the path (i.e. at a height of 23.0 m) after it is dropped. To do this, you need to find the object's velocity at that position using an equation of motion. What is the total energy of the object at that point? Does this verify the principle of conservation of energy?

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 point

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 2kg package is moves up along a 10 m ramp AC inclined at 15' with an initial speed of 5 m/s. Knowing that the coefficient of sliding friction between the package and the incline is 0.2, answer the following questions: 10 m B 15° d 1. What force/s do/does NOT do any work on the package as it moves along the incline? 2. What is the work done by friction on the package as it moves a distance x along the incline? 3. What is the change in the kinetic energy from A to B if at position the package becomes zero? 4. What is the change in the potential energy from A to B if at position B the velocity of the package 5. What is the maximum distance that the package will move up the incline?

A 10.0kg cart is released from rest with no slack in the cable and with the string unstretched. The spring constant is 125 N/m. a). When m=0, the cart travelled 0.663m before coming to rest. Determine the work done on the spring. b). When m=2.0kg, the cart travelled 0.349m before coming to rest. Determine the work done on the spring.

A block of mass 2.28 kg starts sliding from rest down an incline plane for 25 cm. If the block has a velocity of 1.14 m/s, and the incline has an angle measured from the +x axis of 37 degrees then: a. How much work did kinetic friction do on the block? b. What is the coefficient of kinetic friction between the block and the incline?