Show that the energy required to move circular motion at a fixed frequency is im the radius of the circular path. What is t direction and magnitude) required to m on a horizontal plane at 2450 Hz?

As shown in the figure below, two masses m, = 4.70 kg and m, which has a mass 80.0% that of m,, are attached to a cord of negligible mass which passes over a frictionless pulley also of negligible mass. If m, and m, start from rest, after they have each traveled a distance h = 1.60 m, use energy content to determine the following. (a) the speed (in m/s) v of the masses m/s (b) the magnitude (in N) of the tension T in the cord

need Answer only for (d)

A block of mass, m = 0.5 kg is used to compress a spring with a spring con- 78.4 N/m a distance x from it's resting point. The block is then stant, k released and travels towards a circular loop of radius, R = 1.5 m. The loop and the surface as frictionless except for the region, of length 2.5 m, defined by AB which has a coefficient of friction, µk = 0.3. Determine the minimum compression of the spring that allows for the block to just make it through the loop-to-loop at point C (Hint: This problem is best done by starting at the end and working backwards). R k A В

At the end of a graduation ceremony, graduates fling their caps into the air. Suppose a 0.120-kg cap is thrown straightupward with an initial speed of 7.85 m>s, and that frictional forces can be ignored. (a) Use kinematics to find the speedof the cap when it is 1.18 m above the release point. (b) Show that the mechanical energy at the release point is the sameas the mechanical energy 1.18 m above the release point.

answer vii) onwards and dont use chatgpt thank you!

A mass m = 2kg has an initial kinetic energy K = 9J.  The mass is under a constant force F = 1N. and moves from X(0) = 2 to X(tf) = 18m at a terminal time tf. Find the work done (W) by the force, the kinetic energy (K(tf)), and, the initial speed (v1 at X(0)) and the terminal speed ( v2 at X(tf)) of the mass at the terminal time