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1)A spring with a spring constant k = 50N/m has an unstretched length of 20cm. Find the work required to stretch the spring to a length of 30 cm.

I know the spring is being streched by 10 cm and that the work needed is equal to potential energy but I'm still stuck

2) A ball of mass 4 kg is thrown straight up in the earth's gravitational field with an initial speed v0 = 19 m/s.

a) What is the initial kinetic energy of the ball?

b) How much work does the gravitational force do on the ball if it goes up to a height h = 1.9 m?

c) c) What is the speed of the ball at a height h = 1.9 m?

for this last part I think it's KEfinal - KEinitial = Workg but I am not sure

3)A box slides across a frictionless floor with an initial speed v = 2.2 m/s. It encounters a rough region where the coefficient of friction is µk = 0.3.

a) What is the shortest length of rough floor which will stop the box?

b) If instead the strip is only 0.32 m long, with what speed does the box leave the strip?

4)An object of mass M = 4 kg slides from rest a distance d = 4 m down a frictionless inclined plane where it encounters a spring. It compresses the spring a distance D = 1.6 m before stopping. The inclined plane makes an angle q = 30° with the horizontal.

a) When the block just touches the spring, how much gravitational potential energy has it lost?

b) After the mass has fully compressed the spring, what is its total loss of gravitational potential energy? Give your answer as a postive number.

c) What is the value of the spring constant?

5)A man pulls a block of mass m = 15 kg up an incline at a slow constant velocity for a distance of d = 3.5 m. The incline makes an angle q = 28° with the horizontal. The coefficient of kinetic friction between the block and the inclined plane is µk = 0.1.

a) What is the work Wm done by the man?

At the top of the incline, the string breaks and the block, assumed to be at rest when the string breaks, slides down a distance d = 3.5 m before it reaches a frictionless horizontal surface. A spring is mounted horizontally on the frictionless surface with one end attached to a wall. The block hits the spring, compresses it a distance L = 0.7 m, then rebounds back from the spring, retraces its path along the horizontal surface, and climbs up the incline.

b) What is the speed v of the block when it first reaches the horizontal surface?

c) What is the spring constant k of the spring?

d) How far up the incline d1 does the block rebound?