Question 1 The Breakthrough Starshot project aims to accelerate tiny Starchips t

Question

Question 1

The Breakthrough Starshot project aims to accelerate tiny Starchips to 20% of the speed of light using light sails.
Answer the following questions.

a. Assuming that a Starchip and its sail has a total mass of 1.00 gram, what will its momentum be when it is moving at 20.0% of the speed of light? Neglect relativistic effects.

b. If the area of the Starchip's sail is 0.100 m2, what must the radiation pressure be to accelerate the Starchip to 20% of the speed of light in 1.00 × 103 seconds?

c. What is the intensity of the EM wave necessary to provide the radiation pressure?

A. 6.00×103 kgm/s B. 6.00×102 kgm/s C. 6.00×104 kgm/s D. 6.00×105 kgm/s E. 6.00×106 kgm/s

Explanation / Answer

a) To do this, let's pass the mass in g to kg:
m = 1 g * 1 kg/1000 g = 0.001 kg

Now, the momentum at 20% speed of light will be:

M = 0.001 kg * (3x108 m/s) * 0.20
M = 6x104 kg m/s

b) The pressure has units of Pascal, and the equivalence of these units are:
1 Pa = 1 N/m2
1 N = 1 kg m/s2

We already have the momentum, which has units of kg m/s so, let's calculate the force or newton with the given time:
F = 6x104 / 1000 = 60 N

p = 60/0.1 = 600 N/m2 or 600 Pa

c) The units of the intensity are Watts or W, and 1 W = 1 kg m2/s3 then:
P = p * c
P = 600 * 3x108
P = 1.8x1011 W / 0.1 m2
P = 1.8x1012 W/m2

And 1 MW is 1x106 W so:
P = 1.8x1012 W * 1 MW/1x106 W = 1.8x106 MW/m2

Hope this helps

Related Questions

Navigate

• Browse (All)
• Browse Q
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.