Updated 1/18/19

For these problems start by creating a force picture and being sure you know what two objects are engaged in creating each force. This won't seem critical at this point but it will be helpful in future problems so enjoy the practice. If an object is speeding up or slowing down use your knowledge of motion diagram or graphs to determine the direction of the acceleration vector.

1) A block is hung in the middle of the elevator by a string from the ceiling. Create a force picture showing the forces acting on the block. Identify 'thing 1' and 'thing 2' for each of the forces -- working from our classroom definition of a force For each of the situations below state which force(s) is(are) larger. They may be equal.

i) The elevator is at rest.

ii) The elevator is moving upward at increasing speed.

iii) The elevator is moving upward at decreasing speed.

iv) The elevator is moving upward at constant speed.

v) The elevator is moving downward at decreasing speed.

vi) The elevator is moving downward at constant speed.

[Fs=Fg, >,<,=,>,=]

2) Sorry -- this is like 6 sequential questions in one! Create a force picture for a skydiver before their parachute/parafoil opens. Assume they are travelling straight down at the time of your sketch. What can you say about the balance of the forces before and after the skydiver reaches terminal velocity? Identify 'thing 1' and 'thing 2' for each force in your drawing. Which forces change when the parachute opens and the skydiver is slowing down? A little while after the parachute has opened what is the relationship between the forces when the skydiver is coming down at a constant velocity? Is the upward force on the parachute bigger, smaller, or the same as the upward force on the skydiver falling at terminal velocity? What happens to a skydiver on the moon there is essentially no atmosphere? How do you expect the terminal velocity on Mars to be different (or not) and explain your reasoning?

[upward smaller, same, ..., upward increases, becomes the same, same, no v_T, faster ]

3) A flatbed truck is driving down a level street at a constant velocity. Sitting in the middle of the bed of the truck is a box. Make a force picture of the forces you think are acting on the box. Identify 'thing 1' and 'thing 2' for each force in your drawing. Newton's 1st Law says that the net force (the vector sum of all the forces on your picture) must be 0 if the object is moving at constant velocity. Is this consistent with your picture? Would your force picture change is the box were sitting on an air hockey table (no friction) on the bed of the truck? What happens to your force picture in each case if the truck starts to slow down?

[things, depends on your picture, no, yes - friction in one case]

 

In each of the following problems please be aware that I fantasize that you are following the problem solving framework for Newton's Laws. Practice making the sketch a reasonable size and being very clear about your coordinate system. Circle the object (also known as the system) that you are interested in and be very clear about thing 1 and thing 2 as you choose to put forces on the force picture.

4) A 700 kg pallet of equipment is hanging from the 25 m long cable of a crane. What is the tension in the cable under each of the following circumstances? Be sure to do a freebody diagram (force picture). The tension is the force that a rope/cable to the object at one end.

i) The pallet is stationary.

ii) The pallet is moving consistently upward at 5 m/s

iii) The pallet is accelerating upward at 5 m/s²

iv) The pallet is accelerating downward at 2 m/s²

[7kN, 7 kN, 10.5 kN, 5.6 kN]

5) An empty plane has a mass of 3.0^.10⁴ kg and a takeoff acceleration of 1.20 m/s². What is the minimum force the jet engines must provide to accelerate the plane? Only consider forces in the horizontal direction (since the others are balanced) and ignore air resistance and frictional losses. Be sure to do a freebody diagram.

[36 kN]

6) A group of folks are riding in a hot air balloon 60 m above the ground. The total mass of the balloon and its occupants is 300 kg. The balloon is stationary in the air due to the upward buoyant force of the hot air. Do a freebody diagram of the balloon. If the buoyant force remains constant what mass of sand must be thrown overboard so that the balloon acquires an upward acceleration of 0.5 m/s²?

[14 kg]

7) A 40 kg child athlete is hanging from a rope by her hands. In a sudden display of strength she accelerates up the rope at 3 m/s². What is the tension in the rope before and after she starts her acceleration?

[520 N]

8) (Calc) The location of a 100 g particle is given by the expression

y= 8 t³ - 3t + 14 (in meters).

What is the net force on the particle at t = 2.0 s? Think about the mathematical relationship between position and acceleration from MTH 251!

[9.6 N]

9) There are two principle drag forces acting on a car externally. These are the rolling resistance and the air drag. F_rolling is given by the expression F_rolling = c_rr^.m^.g where crr is called the coefficient of rolling resistance. For a typical car c_rr is roughly 0.015 and has no units. The other is the drag force due to the air. F_{air drag} is given by the expression F_{air drag} = 0.5^.ρ^.v^2.C_D^.A . In this expression ρ is the density of the air (1.2 kg/m³), v is the speed of the car in m/s, and A is the cross sectional area of the car (it's silhouette from the front). C_D is the drag coefficient which is about 0.3 for all standard cars. What are the units of C_D? For a car with a mass of 1500 kg and a cross sectional area of 4 m² what is the speed at which F_rolling=F_{air drag}? What is the speed at which 5F_rolling=F_{air drag}?

[dimensionless, 18 m/s, 40 m/s]