A small rock with mass 0.225 kg is fastened to a massless string with length 0.870 m to form a pendulum. The pendulum is swinging so as to make a maximum angle of 50.0 degrees with the vertical. Air resistance is negligible.

a.) What is the speed of the rock when the string passes through the vertical position?

b.) What is the tension in the string when it makes an angle of 50.0 degrees with the vertical?

c.) What is the magnitude of the acceleration of the rock when it makes an angle of 50.0 degrees with the vertical?

d.) What is the tension in the string as it passes through the vertical?

A spring of force constant 300.0 N/m and unstretched length 0.220 m is stretched by two forces, pulling in opposite directions at opposite ends of the spring, that increase to 18.0 N.

a.) How long will the spring now be?

b.) How much work was required to stretch it that distance?