(a). Derive an expression for the change of potential energy of the block near the surface of the Earth. m Diagram (a) (b)A block of mass 2.0 kg moves with a velocity v towards a spring as shown in diagram (b). 000000000 Diagram (b) The block compresses the spring by 2.0 cm as shown in diagram (c). Given that the force constant of the spring is 1000 N m¹¹. Calculate the velocity, v of the block if (i) the surface is smooth. v = 0 2.0 cm Diagram (c) (ii) the surface is rough and the frictional force between the block and the surface is 3.0 N.

Use Diagram 1 below to answer the following questions. Assume the speed at Position 1 is 10 m/s, the mass of the roller coaster car is 250 kg, the track is frictionless, and that no work is done by air resistance. Position 3 is higher than Position 4, but lower than Position 1. 3 35 m 15 m 2. hat is the kinetic energy of the roller coaster car at Position 2? 三 三 DELL

3. If a block of mass m starts from rest at position 3 as shown below, with the spring of stiffness k compressed a distance Ax3, and slides across the frictionless plane X=0 what is its speed at position 2? (Hint: use conservation of energy.) Note: This problem gives no numbers, so don't put in numbers to do this problem. Of course you can on your scratch paper, if you want to, but for the work on this test, you need to leave it as an algebraic problem. а. V2 = b. If the block continues to slide up the frictionless incline, what is the height, h, at which it stops before sliding back down? h =

As shown in the figure below, a spring having an initial unstretched length of fo is stretched by a force F applied at its end. The stretched length is . By Hooke's law, the force is linearly related to the spring extension by F = k(t - to) where k is the stiffness. 20 Unstretched spring www. (l-lo) If stiffness is constant, evaluate the work done, in J, if lo = 3 cm, l₁ = 6 cm, l₂ = 15 cm, and the stiffness is k = 2 x 104 N/m.

please answer the following the kinetic, potential and total energy of a baseball having a mass of 0.145kg held 10 meters above the ground. The baseball was released under the influence of gravity on Earth and freefalls to the ground.  Write the kinetic, potential and total energy of the baseball at the point the baseball hits the earth. What is the baseball’s final speed when it impacts the ground using the principles of Energy Conservation?

A 20m rope is hanging over the edge of a 50m building. Attached to the end is 2 kg bucket carrying 30kg of sand. There is a whole in the bucket that allows the sand to leak out at 0.5 kg/m. Disregarding the rope, how much work is done lifting the bucket to the top of the building? Show all work. Include units. Method of solving: fnint(), rounded to nearest whole number or Fundamental Theorem. Your choice

A block of weight -300 N sits on a frictionless inclined plane, which makes an angle 31.0 with respect to the horizontal, as shown in the figure (Figure 1)A force of magnitude F-155 N appied parallel to the incine, is just sufficient to pull the block up the plane at constant speed Figure 1 of 1 Part A The block moves up an incline with constant speed. What is the total work Wal done on the block by all forces as the block moves a distance Lw3.20 m up the incline? Include only the work done after the block has started moving at constant speed, not the work needed to start the block moving from rest. Express your answer numerically in joules. View Available Hint(s) W Submit Part 8 W₁- ΠΟΙ ΑΣΦ Subm 5 What is the work done on the block by the force of gravity as the block moves a distance L3.20 m up the incline Express your answer numerically in joules. View Avaliable Hint VAX Review Constants Periodic Table J 3