A toy cannon uses a spring to project a 5.23-g soft rubber ball. The spring is o

Question

A toy cannon uses a spring to project a 5.23-g soft rubber ball. The spring is originally compressed by 4.94 cm and has a force constant of 8.09 N/m. When the cannon is fired, the ball moves 14.5 cm through the horizontal barrel of the cannon, and the barrel exerts a constant friction force of 0.032 4 N on the ball. (a) With what speed does the projectile leave the barrel of the cannon? 8.64 Incorrect: Your answer is incorrect. Make certain you have correctly converted all of the centimeter and gram quantities to MKS units. m/s (b) At what point does the ball have maximum speed? 4.54 Correct: Your answer is correct. cm (from its original position) (c) What is this maximum speed? 1.79 Correct: Your answer is correct. m/s

Explanation / Answer

Here ,

m = 5.23 g

m = 0.00523 Kg

x = 4.94 cm

x = 0.0494 m

force constant , k = 8.09 N/m

d = 14.5 cm = 0.145 m

f = 0.032 N

a)

let the speed of projectile is v

Using work energy theorum

0.5 * m * v^2 = 0.5 *k * x^2 - f * d

0.5 * 0.00523 * v^2 = 0.5 * 8.09 * 0.0494^2 - 0.032 * 0.145

solving for v

v = 1.414 m/s

the speed of projecitle launch is 1.414 m/s

b)

the maximum speed of ball is at the location when the spring is uncompressed

x = 4.54 cm

c)

for the maximum speed is v

Using work energy theorum

0.5 * m * v^2 = 0.5 *k * x^2 - f * d

0.5 * 0.00523 * v^2 = 0.5 * 8.09 * 0.0494^2 - 0.032 * 0.0454

sovling for v

v = 1.794 m/s

the speed of the ball is 1.794 m/s

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