Dynamics test

 

1)       A crane is being used to lift a 2000 kg box.  The maximum tension the crane cable can support is 22,000 N.

a.         Determine the weight of the box.

b.        Determine the greatest acceleration the crane can impart onto the box.

2)       You are driving your pick-up truck at 22 m/s.  In the bed of the pick-up, you have a large cardboard box.  Determine your shortest possible stopping distance without the box sliding if you are going uphill at a 12 degree angle.  The truck has a mass of 2,000 kg and the box has a mass of 150kg.  You are listening to Led Zeppelin at the time you are trying to stop.

a.         Draw a body diagram of this situation.

b.        Draw a free body diagram of this situation

c.         Solve the problem as stated above.

3)        A 12kg sign is supported over a road by two ropes.  Rope “A” is connected to the sign, and then is connected to a tall building that is 15 m away from the sign, and 5 m above the sign.  Rope “B” is connected to the other side of the sign and is connected to a building that is also 15 m away from the sign, and 8 m above the sign.  Determine the tension in the two ropes.

a.         Draw a body diagram of this problem

b.        Draw a free body diagram of this problem.

c.         Solve for the tension is rope “A”

d.        Solve for the tension in rope “B”

4)       Determine the weight of a 15 kg object.

 

 

Kinematics

 

 

  1. You are driving to a vacation spot (fill in your favorite spot) 223 miles away.  If you average 53 mi/hr, how long will it take you to get there (assuming no stops).

 

  1. Imagine you are driving on a straight road at a constant speed of 18 m/s (40 mi/hr).  A "friend" is following you at a distance of 9.14m (30 ft) also traveling at a constant speed, and maintaining a constant distance behind you.  You are chewing on gum, and it's getting stale.  You think it would be funny to "spit" the gum straight up in the air and have it land on their windshield.  How fast would the gum have to leave your mouth in order for the gum to hit the windshield? (Assume no air resistance.  In no way do I promote littering of any kind) 

 

  1. A pigeon starts flying north from York, and a train (EMD GP9…there you go Joel!!!) heads out of Enola heading south, both at the same time.  The Enola Yard and York are 30 miles (48,000 m) apart (not really, but close).  The pigeon flies low over the train tracks at a constant speed of 18 m/s, and the train starts out from rest and steadily accelerates at 0.05 m/s2.  Determine how far north the pigeon flies north until it has to fly up and over the train….or else…

 

  1. You throw a ball straight up in the air with a speed of 32m/s.  Where is the ball after a time of 3.2 seconds?

 

  1. You are standing on the edge of a cliff that is 12 m high.  You are holding a hand grenade with a 3 second fuse.  You wish the hand grenade to explode just as it hits the ground.  How fast and in what direction must you throw it for this to happen?

 

  1. For the train in #3, how long does it take to get to 10 m/s?

 

  1. (Information from Wikipedia regarding Kingda Ka at Six Flags/great Adventure: reaching 456 ft high and accelerating up to 128 miles per hour (206 km/h) in 3.5 seconds.  Six Flags is currently under chapter 11 bankruptcy, and Kingda Ka had some major malfunctions.)  Determine the acceleration of the train, in m/s2.

 

  1. When you throw a ball up in the air, determine the velocity at the top of the path

 

Work and Energy

 

1)       A 1200 kg is cruising down the road at 15 m/s.  Determine the work that must be done to stop the car.


2)       Conservation of energy (PE to KE) A roller coaster train is lifted to the top of a 22m hill by a chain pulling at 8 m/s.  Once over the top, the train then plummets back to the ground with a smooth arc, then into a circular loop with a radius of 6m.  Determine how fast the train will be going through the top of the loop.

3)       A 2 kg mass is dropped from a height of 3 m onto a spring that has a spring constant of 45 N/m.  Determine how far the spring is compressed in the process of stopping the 2 kg mass.


4)       Determine the power rating required of a motor that is powering a go-cart that has a total of resistive forces (air resistance, and other friction) of 220 N when traveling at 12 m/s.

5)       A spring with a spring constant of 20 N/m is stretched 2 m (Wow!!!  That’s far).  Using a graph, show the amount of work that is done.

6)       A pulley arrangement is used to lift a 158 kg mass. A person pulls 5 meters of rope as the mass raises 0.5 meters.  Determine the ideal mechanical advantage of this machine.


7)       A constant force of 12 N acts to move an object through a distance of 6 m. Once the object has moved through the 6 m, then the force increases steadily until a force of 20N is being applied.  While the force was increasing, the object moved through an additional 3 m.  Determine the work done while the object moved through the 9m distance.


8)       A 2 kg mass stretches a spring 12cm.  How far will a 3.5 kg mass stretch the spring?

 

 

 

Vector Test

 

Directions:  Solve the following problems, showing all work and circling your answer.  Each is worth 5 points.

 

1)       During a silly stunt in a Disney comedy movie, a crazed person is screaming (literally) down a hill and across a boat dock on a skateboard.  (The board is 0.6 m long).  Of course, the screaming person then flies off the end of the dock, which is 1.2 m above the water, into the water.  The person landed in the water 3.4 m from the end of the dock.

a.         How long was the person in mid-air from the moment they left the dock until they hit the water?

b.        How fast was the person traveling on the skateboard?

 

2)       You design a frame to hold a water balloon launcher so you are assured of a constant launch velocity of 26 m/s, and a fixed launch angle of 30 degrees. You are perched at the top of the cliff with your water balloon launcher.  A pick-up truck is parked at the base of the cliff, 25 m below you.  You desire to land a water balloon in the back of the pick-up truck as they drive away.  The pick-up truck leaves the area directly below the cliff and drives away from the cliff at a steady 30 mph, which is about 14m/s (assume the time to accelerate to 30 mph is negligible).

a.         How long after the water balloon is released do you have to wait to see if you hit it? (How long is it in the air?)

b.        Determine how far out from the base of the cliff the water balloon lands.

c.         How long after the truck leaves the base of the cliff do you have to wait to release the water balloon to hit the truck?

3)       A river is ˝ mile (800m) wide and flows at a constant rate of 2m/s (Yes, this is a little “ideal,” but would you really want to solve for a “real” situation?)   You leave the dock in your canoe, and wish to reach another dock that is 400m downstream in a time of 3 minutes.

a.         Determine your speed WRT water CROSSING the river.

b.        Determine your speed WRT land going downstream.

c.         When leaving the dock, determine the angle needed as measured from a line perpendicular from the river bank.

4)       (be careful with this one!!! It’s easy, but a little tricky).  A river is 1 mile wide, and flows at a constant 2 m/s.  You are in a boat that runs at 6 m/s WRT water.  You desire to travel upstream for a time of 30 minutes.  Assume that you travel close to the edge of the bank, as to not waste time traveling across the water.  Another boater approaches you heading downstream at a rate of 12 m/s WRT you.  Determine the speed of the water WRT land.

5)       Two baseball players are warming up prior to a game.  The players are standing about 10 meters apart, and each are throwing the ball so that it leaves their hand at about a 20 degree angle above the horizontal.  If they both consistently catch the ball just above their head, determine the speed the ball leaves their hand with each throw.