- #1

Bigworldjust

- 54

- 0

## Homework Statement

In a physics lab experiment, a compressed spring launches a 40g metal ball at a 25 degree angle. Compressing the spring 17cm causes the ball to hit the floor 1.6m below the point at which it leaves the spring after traveling 5.3m horizontally.

What is the spring constant?

Express your answer using two significant figures.

## Homework Equations

y = x tan Φ + ½ g (x/(Vo cos Φ))²

½ m Vo² - ½ k (Δx)² = 0

## The Attempt at a Solution

x = Vo t cos Φ

t = x/(Vo cos Φ)

y = Vo t sin Φ + ½ g t²

y = Vo(x/(Vo cos Φ)) sin Φ + ½ g (x/(Vo cos Φ))²

y = x tan Φ + ½ g (x/(Vo cos Φ))²

-1.6 = 5.3 tan 25° + ½ (-9.8)(5.3/Vo)² sec² 25°

Vo = 6.41541 m/s

according to conservation of energy,

ΔE = 0

½ m Vo² - ½ k (Δx)² = 0

½ (0.040)(6.41541)² - ½ k (0.17)² = 0

k = 56.9654 N/m

Since the question asked for two significant figures I put in 57, and I got it wrong with an explanation saying that it was close to the answer but I may have made an error in significant figures or approximation. Could someone please tell me where my slight error is? Thank you!