9702_s22_qp_11 Question 8

Water flows out of a pipe and hits a wall. 

When the jet of water hits the wall, it has horizontal velocity v and cross-sectional area A. 

The density of the water is ρ. The water does not rebound from the wall. 

What is the force exerted on the wall by the water? 

A  ρv/A 

B  ρv/A²  

C  ρAv 

D ρAv²

ANSWER: D

The Physics Behind answer

• The work done on the wall by a volume of water is equal to the change in kinetic energy of water that volume during collision.
• The following are some formulas and other concepts needed:
• change in kinetic energy ΔE_k = 1/2 mv² - 0
• work done W = average F x d = 1/2 Fd
• density ρ = m/V
• volume V = Ad
• Note that we use W = Fd only when the F is constant. However, in the case of the water described above, the force varies at constant rate. So we take the average.
• Based on bullet 1 and the formulas in bullet 2,

ΔE_k = W

1/2 mv² = 1/2 Fd

mv² = Fd

ρVv² = Fd

Therefore, F = ρAvv²