As shown in the figure above, a force of 300 N pulls the box shown to the right 70 o above the horizontal and a force of 250 N pulls the box to the right 20 o below the horizontal. In units of N, what is the net force in the horizontal direction due to the sum of the two forces?
a. 338 b. 132 c. 103 d. 367 e. 550
Soln.: Fx = 300 N * cos70 + 250 N * cos20 = 338 N
A 0.5 kg object moving at 30 m/s runs into a stationary object, mass=2 kg. The collision is elastic. What is the velocity of the target (the 2 kg mass) after the collision? Units of m/s
a. 12 b. 3 c. 6 d. 9 e. 15
Soln.: conserve p and E. pi=15 kgm/s, Ei=225 J (=1/2 mv2)
pf=pi = 0.5v1f + 2v2f Ei=Ef=0.25v1f2 + 1v2f2. Since we want v2f, eliminate v1f using the momentum eqn.: v1f=(15 kgm/s-2v2f)/0.5 Put this in the energy equation:
P=VI=220V * 20 A = 4400 W. This amount of power used for 2 hours is 8.8 kilowatt hours, or $0.88. So not a major cost. 7. Your car has tires with a radius of 14 inches. How many rpm (revolutions per minute) does a tire have to be rotating to have you traveling 40 miles/hour (forgive the units, but these mean more to you.)
a. 480 b. 130 c. 790 d. 2.1 e. 1300
v=ωr. Need r=14 inches in feet = 14/12 ft, need v=40 mi/hr in feet/sec = 40mi/hr*5280ft/mi/3600sec/hr =58.67 ft/s, so ω=58.67 ft/s/1.166 ft=50.3 rad/s. To convert to rev/s = (rad/s) / 2 (since there are 2 radians per revolution), so tires are going 8 rev/s or 480 rpm. This may sound slow if you have a tachometer in your car, but you have gears in your differential between the tires and the motor, so the motor turns around about 3 times for every one revolution of your tires.
8. Ignoring air resistance, how long does it take an object initially at rest to fall to the ground from a height of 100 m? (about a 30 story building) (units of seconds)
a. 4.5 b. 1.5 c. 2.5 d. 3.5 e. 5.5 y-y0 = -100 m = v0y* t (but v0y=0) + ½ at2, but a=-9.8 m/s2, so t=4.5 s