Questions – Terminal velocity 1. The diagram shows a parachutist falling to the ground at constant velocity. Which statement is correct about forces F1 and F2? A F1 is equal to 2F2. B F1 is equal to F2. C F1 is larger than F2 but smaller than 2F2. D F1 is smaller than F2. 2. What happens as a body falls at a terminal velocity? A Air resistance is equal to the weight of a body. B Air resistance is higher than the weight of the body. C The weight of a body decreases. D The weight of a body increases. 3. Below is a skydiver dropped from a plane and the graph representing his journey. (Moses Notes) (a) Name the force Y and X acting on the skydiver. (2) (b) The sizes of the two forces named in a) changes as the diver falls. Compare the two forces after 10s. (1) (c) Determine the skydiver's acceleration during the first five seconds. (2) (d) What is the speed of the diver after 20s? (1) (e) When did the diver reach terminal velocity? (1) (f) Calculate the diver's acceleration between 30s and 40s. (2) (g) Indicate on the graph, how the graph should be if the sky diver is falling in the vacuum. (1)
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1. What is another term for the fluid resistance force exerted on an object when it falls through air? a. Drag b. Gravity c. Weight d. Viscosity 2. Without air resistance, an object in free fall.... a. will fall at the same speed (velocity) during the entire fall. b. will accelerate at a constant rate during the fall c. will speed up (accelerate) until it reaches a final top speed. d. will accelerate at a rate that depends on its mass 3. The air resistance force on a dropped object will tend to a. reduce the acceleration of an object as it falls. b. not affect the acceleration of the object. c. increase the acceleration of the object. d. first increase, then decrease the acceleration of the object. 4. In the Square Law fit, the units shown are not correct. Starting with the SI units of force (1N = 1 kg m/s^2) and the relation FD=Av^2, what are the correct SI units (i.e. using powers of kg, m, s) of the constant A? a. kg m s^-2 b. kg/m c. kg m d. kg/s 5. If you triple the speed of an object through the air, without changing anything else, the drag force changes by a factor of a. 1 (i.e. is unchanged) b. 9 c. 3 d. 1/3 6. Two skydivers are floating down under separate identical parachutes. Skydiver B's mass is double that of skydiver A (perhaps because they have a passenger strapped to them). The ratio of their terminal speeds vTB/vTA is predicted to be a. 2 (B descends twice as fast as A) b. 1 (B descends at the same speed as A) c. √2 = 1.4 (B descends 40% faster) d. 1/√2 = 0.71 (B descends 30% slower)
Umar Sohail Q.
(III) The force of air resistance (drag force) on a rapidly falling body such as a skydiver has the form $F_{\mathrm{D}}=-k v^{2},$ so that Newton's second law applied to such an object is $$m \frac{d v}{d t}=m g-k v^{2},$$ where the downward direction is taken to be positive. (a) Use numerical integration to estimate (within 2$\% )$ the position, speed, and acceleraton, from $t=0$ up to $t=15.0 \mathrm{s},$ for a $75-\mathrm{kg}$ skydiver who starts from rest, assuming $k=0.22 \mathrm{kg} / \mathrm{m} .$ (b) Show that the diver eventually reaches a steady speed, the terminal speed, and explain why this happens. (c) How long does it take for the skydiver to reach 99.5$\%$ of the terminal speed?
(III) The force of air resistance (drag force) on a rapidly falling body such as a skydiver has the form $F_{\mathrm{D}}=-k v^{2},$ so that Newton's second law applied to such an object is $$ m \frac{d v}{d t}=m g-k v^{2} $$ where the downward direction is taken to be positive. (a) Use numerical integration [Section $2-9]$ to estimate (within $2 \%$ ) the position, speed, and acceleraton, from $t=0$ up to $t=15.0 \mathrm{~s},$ for a $75-\mathrm{kg}$ skydiver who starts from rest, assuming $k=0.22 \mathrm{~kg} / \mathrm{m}$ (b) Show that the diver eventually reaches a steady speed, the terminal speed, and explain why this happens. (c) How long does it take for the skydiver to reach $99.5 \%$ of the terminal speed?
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