A mass m = 2.75 kg is at the end of a horizontal spring on a frictionless horizontal surface. The mass is oscillating with an amplitude A= 4.5 cm and a frequency f = 0.25 Hz Part (a)  Write an equation for the spring constant k. Part (b)  Calculate the spring constant k, in Newtons per meter.  Part (c)  Write an equation for the total mechanical energy, E, of the motion. Your expression should be in terms of the variables in the original problem statement.

A simple pendulum has a period of 2.7 s and an amplitude of 5.0 cm. The mass of the bob is 5 g. Calculate the maximum kinetic energy of the pendulum and give your answer micro Joules (μJ).

A pendulum with a length of 0.75 m and a mass of 4 kg is swinging consistently swinging back and forth without losing any energy to its environment. The maximum velocity the pendulum can achieve is 2 m/s. Calculate the kinetic energy of the pendulum.

A mass resting on a horizontal, frictionless surface is attached to one end of a spring; the other end is fixed to a wall. It takes 3.0 JJ of work to compress the spring by 0.13 mm . If the spring is compressed, and the mass is released from rest, it experiences a maximum acceleration of 12 m/s2m/s2.  Find the value of the mass. Express your answer to two significant figures and include the appropriate units.

A horizontal spring attached to a wall has a force constant of k = 780 N/m. A block of mass m = 1.90 kg is attached to the spring and rests on a horizontal, frictionless surface as in the figure below. www x=0 x = x;/2 m x = x₁ (a) The block is pulled to a position x; = 7.00 cm from equilibrium and released. Find the elastic potential energy stored in the spring when the block is 7.00 cm from equilibrium and when the block passes through equilibrium. x (cm) Elastic Potential Energy (J) 7.00 0 (b) Find the speed of the block as it passes through the equilibrium point. m/s (c) What is the speed of the block when it is at a position x;/2 = 3.5 cm? m/s (d) Why isn't the answer to part (c) half the answer to part (b)?

A spring with spring constant k has an unstretched length L . A block of mass m is pushed against the spring to compress it to the unknown position x = A. The block is not attached to the spring and the ground is frictionless. Another force acts on the block, attracting it to the point x = 0, with a magnitude c /x2, where c is a known constant. The block is released from rest. Obtain an algebraic equation for the compressed position x = A, such that the block escapes from the attractive force. (To escape means it will go all the way to infinity where it will have zero velocity.)

N 2. A horizontal spring is compressed by 25.0 cm. A 640.0 g box is then placed against the spring and then released. After travelling 3.15 m from the release point, the speed of the mass is 5.68 m/s. The coefficient of friction is 0.34. What is the spring constant of the spring? mi Tum Tm =

The figure blow shows the kinetic energy of a simple pendulum versus its angle θ from the vertical.  Note the energy units are in milli-joules.  The vertical axis is set by Ks=4mJ and the mass of the pendulum bob is 0.200 kg.  Determine the length of the pendulum in meters.  Use g = 9.8 N/kg.

A block with a mass of 30.0 kilograms (kg) is held against a spring with a force constant of k = 1.25×105 N/m. The spring is initially compressed 17.5 centimeters (cm) from equilibrium. Then the block is released, setting it into motion. The block initially slides along a frictionless surface, but then it encounters a 1.50 meter long rough patch where the coefficient of kinetic friction is 0.134. It then slides down a frictionless ramp, which is tilted at an angle of 19.5 degrees and has a length of 2.50 meters. How fast is the block moving when it reaches the bottom of the ramp? Give your answer in meters per second (m/s). Hint: use WNC = ΔK + ΔU.

A crane lifts a 268 kg crate a height of 12.4 m in a time of 80.0 s at a constant speed. What is the crane's power? Select one: 41.5 W Ob. 4.08 x 102 W O c. 3.32 x 10³ W O d. 3.26 x 104 W a. The time required for one complete oscillation of a vibrating object is called