Two solid spheres of radius R and mass m are initially separated by a distance d such that the two centres of mass are separated by d+3R as shown below. The spheres are initially at rest, but the gravitational force  accelerates them towards each other until they collide. a) Calculate the initial mechanical energy of the system. b) Calculate the gravitational potential energy of the system at the moment they collide. c) Derive an expression for v. State carefully what physical law you are applying. d) Show that, in the limit d >> R, the velocity v is independent of d.

Circular Motion A 1 Kg bead is confined to move on a vertical circle of radius 2 meters. There is no friction between the bead and the circular track. The bead has a speed of 10 m/s when at the top of the circle at point "A", and the total mechanical energy of the bead is assumed to be constant as it moves around the circle. Assume it takes the bead 0.62 seconds to go counter-clockwise from point "A" to point "B" each cycle. 10 m/s 2m 1 Note: vector directions should be given as the "standard" angle with 0 <0 < 360 degrees 30° Calculate the magnitude of the average velocity (m/s) from "A" to "B" (based on the 0.62 seconds mentioned in the description).

C7 7.) The work that a force does by acting on an object is equal to what? a.) the product of momentum and force (in the direction of motion) b.) the product of force (in the direction of motion) and distance and is negative if the force and motion are in the same direction     c.) the product of force and distance without regard to direction d.) the product of force (in the direction of motion) and distance and is positive if the force and motion are in the same direction e.) the product of distance and kinetic energy

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1.A brick of mass m initially traveling at speed vo slows to a stop while sliding along a rough horizontal surface. m=7.5 kg, vo=25 m/s   a)What is the work done by the frictional force in stopping the brick? b)If the brick slides for 33 m before coming to rest, find μk, the coefficient of kinetic friction between the brick and the surface.       2.A variable force acts on a mass of 1.2 kg as it moves in one dimension along the x-axis.  The force is position-dependent and is given by the equation:  F(x) = (5 N/m) x + 3 N.  Assume there are no other forces acting on the mass.   a)How much work is done by this force in moving the mass from x = 1 m to x = 4 m? b)If the kinetic energy of the mass is 50 J at x = 1 m, what is the kinetic energy of the mass when it reaches x = 4 m? c)What is the velocity of the mass when it reaches x = 4 m?         4.A puck starts from rest at point A and slides on the frictionless path shown. It is launched horizontally off the end of the track and lands on…

rrrA solid spherical jewel rolls smoothly from rest down a ramp. The jewel descends a vertical height of 1.2m to reach the bottom of the ramp. The previous question asked "What is the jewel's speed at the bottom of the ramp?" Hint: This problem has nothing to do with elasticity as we did not formally cover that topic. All elastic energy terms are zero. List all terms that had a value of zero

Which one is answer ? A or B or C or D

5. Andy, who has a mass of 80 kg, is performing calf raises with just his bodyweight. During the rising part of the calf raise, his center of mass is displaced 0.1 m. What is the work done by Andy's calf muscles during the rising part of the a. calf raise? b. If Andy does the rising part in 0.5 seconds, how much power is produced by his calf muscles? c. What kind of contraction (concentric, eccentric, isometric) is occurring in Andy's calf muscles? Why?

QUESTION 8 Consider the four possible paths of a body moving through gravity as diagrammed below. Which of the following statements is true? Projectile A a. The work done by gravity is greatest for path B. b. The work done by gravity is greatest for path C. c. The work done by gravity is greatest for path D. d. The work done by gravity is the same for all four paths. e. The work done by gravity is greatest for path A.

Determine the final speed of the ball using conservation of energy considerations. But assume a frictionless surface for this problem