The Hunger Games The movie The Hunger Games brought in about $152,000,000 in its

Question

The Hunger Games The movie The Hunger Games brought in about $152,000,000 in its opening weekend. Express this amount in (a) gigadollars and (b) teradollars. * BIO The Thickness of Hair A human hair has a thickness of about 85 mu m. What is this in (a) meters and (b) millimeters? The speed of light in a vacuum is approximately 0.3 Gm/s. Express the speed of light in meters per second. A Fast Computer IBM has a computer It calls the Blue Gene/1, that can do 136.8 tera calculations per second. How many calculations can It do in a nanosecond? CE Which of the following equations are dimensionally consistent? (a) x = 1/2at^2. (b) t = v/x, (c) t = (2x/a)^1/2. CE Which of the following quantities have the dimensions of a time? (a) x/v, (b) a/v, (c) (2x/a)^1/2, (d) v^2/a. CE Which of the following quantities have the dimensions of a distance? (a) vt, (b) 1/2at^2, (c) 2at, (d) v^2/a. CE Which of the following quantities have the dimensions of a speed? (a) 1/2at^2, (b) at, (c) (2x/a)^1/2, (d) (2ax)^1/2. Velocity is related to acceleration and distance by the following expression. v^2 = 2ax^D. Find the power p that makes this equation dimensionally consistent. Acceleration is related to distance and time by the following expression: a = 2xt^p. Find the power p that makes this equation dimensionally consistent. The time t required for an object to fall from rest through a height h is given by t = If Squareroot 2/g In this expression, g is the acceleration due to gravity. Find the power p that makes this equation dimensionally consistent. Newton's second law (to be discussed in Chapter 5) states that the acceleration a of an object is proportional to the force F acting on it, and Inversely proportional to its mass in. That is, a = F/m What are the dimensions of force? The time T required for one complete oscillation of a mass m on a spring of force constant k is T = 2 pi Squareroot m/k Find the dimensions k must have for this equation to be dimensionally correct. The speed of light to five significant figures is 2.9979 times 10^8 m/s. What Is the speed of light to three significant figures? A parking lot is 124.3 m long and 41.06 m wide. What is the perimeter of the lot?

Explanation / Answer

(5) The equations which are dimensionally correct are (a) and (c).

(6) The quantities with dimensions of time are (a) and (c).

(7) The quantities with dimensions of distance are (a), (b) and (d).

(8) The quantities with dimensions of speed are (b) and (d).

(9) The power of x should be 1.

(10) The power of t should be -2.

(11) The power of h should be 1/2.

(12) Dimension of force kg m/s^2

(13) The dimensions of force constant should be N/m.

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