A 2-kg block is thrown upward from a point 20 m above the Earth's surface. At what height above the Earth's surface will the gravitational potential energy of the Earth - block system have increased by 500 J?
A) 5 m     B) 25 m      C) 45 m       D) 70 m        E) 270 m

U_g = mgy      U_{g initial} = 2*10*20    U_{g final} = 2*10*h = U_{g initial} + 500     2*10*h = 2*10*20 +500      h = 45
 

2. A 4-lb block slides along a horizontal frictionless surface at 8 ft/s. It is brought to rest by compressing a very long spring of spring constant (1/8) lb/ft. The maximum spring compression is:
A) 4 ft            B) 8 ft          C) 16 ft         D) 2 ft             E) 45 ft
K_i+U_si = ¹/₂mv²+0 =(because there are no nonconservative forces)=K_f+U_sf=  0+¹/₂kx^2
1/₂( ⁴/₃₂)8²  = ¹/₂kx²      = 8
3. A block is released form rest at point P and slides along the frictionless track shown. At point Q, its speed is


K_i+U_gi = 0+mgh₁ =(because there are no nonconservative forces)=K_f+U_gf = ¹/₂mv²+mgh₂
¹/₂mv²  =  mgh₁- mgh₂    so    v =