1) Billy Bob "Bubba" Hickman is driving along one day with a 34 kg bag of cattle feed in his pickup. The coefficient of static friction between the bag and the bed of the pickup is 0.35.
a) What is the maximum angle up an incline that he can drive before the box begins to slide?
b) Bubba is later driving on a level road at 34 m/s. He suddenly hits his brakes because Arnold the Armadillo is laying in the road ahead of him. The coefficient of kinetic friction between his tires and the road is 0.78. What is the shortest distance in which he can stop the truck without hitting Arnold?
2) Bubba pulls a cart of mass 20.3 kg with a uniform horizontal force at constant speed of 31.3 cm/s underneath a hopper that is dropping cattle feed onto the cart at a rate of 57.5 kg/s.
a) How much force is needed to keep the cart moving at a constant speed?
b) What power does Bubba supply in order to pull the cart at this constant speed?
3) A 223 gram mass is pressed against a spring on a horizontal frictionless surface. The mass is pushed until the spring has compressed a distance of 2.83 cm. The force needed to compress the spring is 523 N. The mass is then released and the spring pushes it away. Determine the speed of the mass as it is pushed away from the spring.
4) Bubba drives around an unbanked curve at a constant speed of 60mph. The radius of curvature of the curve is 318 feet.
a) If Bubba is driving as fast as possible without slipping, what is the coefficient of friction between Bubba's tires and the road? (Caution: Watch units.)
b) If Bubba has an object hanging from his mirror, what angle does it make with respect to the vertical as he goes around the curve?
5) Two objects are hanging from the ceiling of an elevator accelerating upward at 1.78 m/s2 . What are the tensions TA and TB in the two cords holding the masses?
6) Bubba throws a ball of mass 105g at a block hanging from the roof of his barn. The ball is moving at 7.72 m/s when it strikes the hanging block of mass 1.12kg. The ball sticks in the block. The block is initially hanging vertically on a 215cm long piece of string. After the ball strikes the block, the block then swings an angle of θ from the vertical.
a) What is the angle θ?
b) How much mechanical energy was lost during the collision?
7) A construction crane is used to lift a 142 kilogram mass vertically a distance of 5.71 meters in 3.35 seconds. The mass is initially sitting on the ground at rest, and it is lifted with a force providing a constant acceleration. The final speed of the mass is 3.41 m/s.
a) How much work is done in lifting this object?
b) What average power is supplied by the crane to lift this object?
8) The brand new Boeing 787 Dreamliner (787-8 variant) has two engines, each having a thrust of 280 kN. The aircraft, when fully loaded and fueled, has a mass of 228,000 kg. The aircraft has a minimum takeoff speed of 80.5 m/s. What is the shortest length runway on which this aircraft can take off? The aircraft starts from rest.
9) A small piece of ice of mass 35g slides down an incline with no friction. When it reaches the bottom of the incline, the ice goes over a hump having a radius of curvature of 25cm.
a) What is the maximum speed that the piece of ice can be moving as it goes over the hum without leaving the surface on which it is sliding?
b) How much higher than the hump would the ice have to have started in order for it to just fly off of the surface on the top of the hump?
10) Sheriff Bob is driving down the highway at 29.0 m/s in a 1630 kg police car. Bubba is driving his 2490 kg truck at 17.2 m/s along a road perpendicular to the highway, as shown below. Bubba is texting a friend on his phone instead of watching what he is doing, so he drives through a stop sign and slams into Bob's car. The two vehicles then become a tangled mass of metal and move as one object. Determine the speed and direction that they slide after the collision.