roblems from Chapter 7 blem 7.35 Part A Consants A 20 g rille buet uwveing 230 m

Question

roblems from Chapter 7 blem 7.35 Part A Consants A 20 g rille buet uwveing 230 m/s embeds itsefl isa 40-kg pendukum hanging on a 29 mlong string which rakas the penduum seing upward n an arc (Figure 1) Detemine the vertical component ol the pendulum's maximum displacoment Express your answer to two significant figures and include the appropriate units tne is Submit Figure Dctarmine the hortz:ental cornp hent of the rendauma niaeimum dSerlacenent Express your aswe to two sigiant iures and eclade tie appropriste unts O Type here to search

Explanation / Answer

The resolution of the question sheet is not very clear. As I can read –

mass of the bullet m? = 26 g = 0.026 kg

m? = mass of the pendulum = 4.0 kg
v = speed of the bullet = 230 m/s
L = length of the pendulum = 2.9 m
g = acceleration by gravity = 9.8 m/s²

And we have to find out the -

Dx = horizontal displacement = ?
Dy = vertical displacement = ?

The combined mass of the pendulum with bullet is:
M = m? + m? = 4.026 kg

Now, the speed of the combined mass just after impact is:
V = m? v / M = (0.026*230) / 4.026 = 1.49 m/s

The maximum vertical displacement of the combined mass is:
Dy = V² / 2g = (1.49^2) / (2*9.81) = 0.112 m

The maximum horizontal displacement of the combined mass is:
Dx = ?(L² - (L - Dy)²) = sqrt[2.9^2 – (2.9 – 0.112)^2] = sqrt[8.41 – 7.77] = 0.80 m

Therefore –

Answer of Part A = 0.112 m

and answer of Part B = 0.80 m

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