Problem 4. In figure below the horizontal surface on which the block slides is frictionless and the mass of the object is 2.0 kg. The speed of the block before it touches the spring is 6.0 m/s. (a) Find the potential energy of the spring when it has been compressed 15 cm. k = 2000 N/m. (b) How fast is the block moving at the instant the spring has been compressed 15 cm? xxxxxxxx 2.0 kg

1.A particle of mass 6-kg moves under the influence of the force F(x)=(4√x)F(x)=(4x) N. If its speed at x=2.0x=2.0 m is v=7v=7 m/s, what is its speed at x=7.0x=7.0 m? v =  m/s 2. A 102-kg man is skiing across level ground at a speed of 14.5 m/s when he comes to the small slope 1.8 m higher than ground level shown in the following figure. If the skier coasts up the hill, what is his speed when he reaches the top plateau? Assume friction between the snow and skis is negligible.v=v=  m/s What is his speed when he reaches the upper level if an 80-N frictional force acts on the skis?v=v=  m/s

A block with mass m = 12 kg rests on a frictionless table and is accelerated by a spring with spring constant k = 4599 N/m after being compressed a distance x1 = 0.45 m from the spring’s unstretched length. The floor is frictionless except for a rough patch a distance d = 2.7 m long. For this rough path, the coefficient of friction is μk = 0.41.  1) How much work is done by friction as the block crosses the rough spot? 2) Instead, the spring is only compressed a distance x2 = 0.117 m before being released. How far into the rough path does the block slide before coming to rest? 3) What distance does the spring need to be compressed so that the block will just barely make it past the rough patch when released?

If a spring is stretched 2.2 cm by a suspended object having a mass of 0.40 kg, what is the force constant of the spring? How much work is done by the spring on the object as it stretches through this distance? Evaluate the work done by the gravitational force on the object (in J).