The air-track carts in (Figure 1) are sliding to the right at 1.0 m/s. The sprin

Question

The air-track carts in (Figure 1) are sliding to the right at 1.0 m/s. The spring between them has a spring constant of 110 N/m and is compressed 4.3 cm . The carts slide past a flame that burns through the string holding them together

A. What is the speed of 100-g cart?

Express your answer to two significant figures and include the appropriate units.'

B. What is the direction of the motion of 100- cart?

C. What is the speed of 300-g cart?

Express your answer to two significant figures and include the appropriate units.

D. What is the direction of the motion of 300- cart?

Explanations would be helpful.

Explanation / Answer

a)

m1 = mass of left cart = 100 g = 0.1 kg

m2 = mass of right cart = 300 g = 0.3 kg

v1 = velocity of left cart towards left after string burns

v2 = velocity of right cart towards right after string burns

V = velocity of combination towards right before string burns

taking velocity in right as positive

using conservation of momentum

(m1 + m2) V = m1 v1 + m2 v2

(0.1 + 0.3)(1) = 0.1 v1 + 0.3 v2

v2 = (0.4 - (0.1) v1)/(0.3)                                     eq-1

using conservation of energy

(0.5) (m1 + m2) V2 + (0.5) k x2 = (0.5) m1 v21 + (0.5) m2 v22

(m1 + m2) V2 + k x2 = m1 v21 + m2 v22

(0.4) (1)2 + (110) (0.043)2 = (0.1) v21 + (0.3) (0.4 - (0.1) v1)2/(0.3)2

v1 = 2.24 m/s

using eq-1

v2 = (0.4 - (0.1) v1)/(0.3)

v2 = (0.4 - (0.1) (2.24))/(0.3) = 0.59 m/s

b)

since velocity v1 is positive , hence direction is towards right

c)

using eq-1

v2 = (0.4 - (0.1) v1)/(0.3)

v2 = (0.4 - (0.1) (2.24))/(0.3) = 0.59 m/s

d)

towards right

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