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physics exam 3
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Gravity
Terms in this set (14)
A truck with 0.420 m radius tires travels at 32.0 m/s. What is the angular velocity of the rotating tires in radians per second? What is this in rev/min?
76.2 rad/s
728 rpm
An ordinary workshop grindstone has a radius of 7.50 cm and rotates at 6500 rev/min. (a) Calculate the centripetal acceleration at its edge in meters per second squared and convert it to multiples of g. (b) What is the linear speed of a point on its edge?
(a) centripetal acceleration=3.47x10^4
multiples of g=3.55x10^3
(b) 51.1
What is the ideal banking angle for a gentle turn of 1.20 km radius on a highway with a 105 km/h speed limit (about 65 mi/h), assuming everyone travels at the limit?
4.14 degrees
Part of riding a bicycle involves leaning at the correct angle when making a turn, as seen in Figure 6.36. To be stable, the force exerted by the ground must be on a line going through the center of gravity. The force on the bicycle wheel can be resolved into two perpendicular components—friction parallel to the road (this must supply the centripetal force), and the vertical normal force (which must equal the system's weight). (a) Show that angle (as defined in the figure) is related to the speed v and radius of curvature r of the turn in the same way as for an ideally banked roadway—that is, angle=tan^-1v^2/rg (b) Calculate angle for a 12.0 m/s turn of radius 30.0 m (as in a race).
(a) inverse tan (v^2/rg)
(b) 26.1 degrees
Astrology, that unlikely and vague pseudoscience, makes much of the position of the planets at the moment of one's birth. The only known force a planet exerts on Earth is gravitational. (a) Calculate the gravitational force exerted on a 4.20 kg baby by a 100 kg father 0.200 m away at birth (he is assisting, so he is close to the child). (b) Calculate the force on the baby due to Jupiter if it is at its closest distance to Earth, some 6.29x10^11 m away. How does the force of Jupiter on the baby compare to the force of the father on the baby? Other objects in the room and the hospital building also exert similar gravitational forces. (Of course, there could be an unknown force acting, but scientists first need to be convinced that there is even an effect, much less that an unknown force causes it.)
(a) Ff=(GMm/r^2) = 7.01x10^-7
(b)0.521
Astronomical observations of our Milky Way galaxy indicate that it has a mass of about 8.0x10^11 solar masses. A star orbiting on the galaxy's periphery is about 6.0x10^4 light years from its center. (a) What should the orbital period of that star be? (b) If its period is 6.0x10^7 instead, what is the mass of the galaxy? Such calculations are used to imply the existence of "dark matter" in the universe and have indicated, for example, the existence of very massive black holes at the centers of some galaxies.
(a) 3x10^8
(b) 2x10^3
Suppose a car travels 108 km at a speed of 30.0 m/s, and uses 2.0 gal of gasoline. Only 30% of the gasoline goes into useful work by the force that keeps the car moving at constant speed despite friction. (See Table 7.1 for the energy content of gasoline.) (a) What is the force exerted to keep the car moving at constant speed? (b) If the required force is directly proportional to speed, how many gallons will be used to drive 108 km at a speed of 28.0 m/s?
(a) 6.7x10^2
(b) 1.9 gal
How much work is done by the boy pulling his sister 30.0 m in a wagon as shown in Figure 7.36? Assume no friction acts on the wagon.
1.30x10^3 J
(a) Calculate the force needed to bring a 950-kg car to rest from a speed of 90.0 km/h in a distance of 120 m (a fairly typical distance for a non-panic stop). (b) Suppose instead the car hits a concrete abutment at full speed and is brought to a stop in 2.00 m. Calculate the force exerted on the car and compare it with the force found in part (a).
(a) -2470 N
(b) 60.0
A 100-g toy car is propelled by a compressed spring that starts it moving. The car follows the curved track in Figure 7.39. Show that the final speed of the toy car is 0.687 m/s if its initial speed is 2.00 m/s and it coasts up the frictionless slope, gaining 0.180 m in altitude.
0.687 m/s
A 5.00x10^5 subway train is brought to a stop from a speed of 0.500 m/s in 0.400 m by a large spring bumper at the end of its track. What is the force constant k of the spring?
7.81x10^5 N/m
A 60.0-kg skier with an initial speed of 12.0 m/s coasts up a 2.50-m-high rise as shown in Figure 7.40. Find her final speed at the top, given that the coefficient of friction between her skis and the snow is 0.0800. (Hint: Find the distance traveled up the incline assuming a straight-line path as shown in the figure.)
9.46 m/s
Using energy considerations and assuming negligible air resistance, show that a rock thrown from a bridge 20.0 m above water with an initial speed of 15.0 m/s strikes the water with a speed of 24.8 m/s independent of the direction thrown.
24.8 m/s
(a) What is the available energy content, in joules, of a battery that operates a 2.00-W electric clock for 18 months? (b) How long can a battery that can supply 8.00x10^4 J run a pocket calculator that consumes energy at the rate of 1.00x10^-3 ?
(a) 9.46x10^7 J
(b) 2.54 y
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Verified questions
PHYSICS
A black, totally absorbing piece of cardboard of area $$ A = 2.0 cm^2 $$ intercepts light with an intensity of $$ 20 W/m^2 $$ from a camera strobe light. What radiation pressure is produced on the cardboard by the light?
PHYSICS
Write a program to model the 3D motion of a mass hanging from a spring. Find initial conditions for which $\vec{F}_\bot$ is zero and remains zero. Explain.
PHYSICS
As a mechanism for downward transitions, spontaneous emission competes with thermally stimulated emission (stimulated emission for which blackbody radiation is the source). Show that at room temperature (T=300 K) thermal stimulation dominates for frequencies well below $5 \times 10^{12} \mathrm{Hz}$, whereas spontaneous emission dominates for frequencies well above $5 \times 10^{12} \mathrm{Hz}$. Which mechanism dominates for visible light?
PHYSICS
The potential energy of a diatomic molecule (a two-atom system like $$ H_2 $$ or $$ O_2 $$ ) is given by $$ U = A/r^12 - B/r^6 $$ , where r is the separation of the two atoms of the molecule and A and B are positive constants. This potential energy is associated with the force that binds the two atoms together. (a) Find the equilibrium separation—that is, the distance between the atoms at which the force on each atom is zero. Is the force repulsive (the atoms are pushed apart) or attractive (they are pulled together) if their separation is (b) smaller and (c) larger than the equilibrium separation?
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