Question

A brass weight has a ring on the top of it. You attach a strong but massless rope to the ring and lift it directly upward so that it accelerates with a constant acceleration of 24.0 m/s2 . When it reaches a velocity of 1.60 m/s, you drop the rope and the mass continues to move. What is the maximum height the block reaches before it starts to fall back to the ground?

A. 0.131 m

B. 0.184 m

C. 0.254 m

D. 0.368 m

E. 0.508 m

Answer 1

consider the motion of block when it is being lifted up

a = acceleration = 24 m/s²

V_o = initial velocity = 0 m/s

V_f = final velocity when rope is dropped = 1.60

Y₁ = distance travelled before rope is dropped

using the equation

V_f² = V_o² + 2 a Y

1.60² = 0² + 2 (24) Y₁

Y₁ = 0.053 m

consider the motion of block after rope is dropped

a = acceleration = - 9.8 m/s²

V_o = initial velocity = 1.6 m/s

V_f = final velocity at the highest point = 0

Y₂ = distance travelled after rope is dropped

using the equation

V_f² = V_o² + 2 a Y

0² = 1.60² + 2 (-9.8) Y

Y₂ = 0.131 m

maximum height = H_max = Y₁ + Y₂ = 0.053 + 0.131 = 0.184