Physics Midterm

Midterm Study Guide

Vocabulary

Conceptual Relationships

Motion

Projectiles

When an object is moving through the air under the influence of nothing but gravity, we call that a projectile. A rocket is not a projectile, because it has an internal fuel source continuing to affect its motion. A baseball is a projectile, because after it is thrown, or hit with a bat, the only thing making it move through the air the way it does is the pull of gravity.

We break down projectiles into two basic categories: Type 1 projectiles start out moving horizontally, whereas Type 2 projectiles start out at an angle. 

Type 1 projectiles fall from a higher up point, like a cliff or a roof, and move horizontally as they do so. 

The time it takes for a type 1 projectile to hit the ground depends on how high up it is, but can also be found if the horizontal distance and velocity are both known.

Type 2 projectiles initially are moving up, but due to gravity they slow down and eventually stop before reversing direction and moving back down towards the ground. All the while, they are moving horizontally at a constant speed, just like with Type 1s.

Sine and cosine functions can be used to find the vertical and horizontal parts of the projectile's motion.

Forces
Free Body (Force) Diagrams: The forces acting on an object can be drawn as arrows coming out of a mass in the middle.
The size and direction of the arrows are drawn to show how much force is being applied in which direction.

Forces that are up or down can be added or subtracted from each other because they are both vertical. 

The same is true for horizontal forces: leftward forces subtract and rightward forces add.

This is how the net force for each direction is found. If the forces add up to 0, then they are balanced, and the object does not accelerate in that direction. If the net force is not 0, then it can be divided by the mass of the object to find the acceleration on the object in that direction.

In this example, the forces in the vertical direction are the same size, but in opposing directions. This means that they are balanced, or in other words will add up to 0. This mass is not accelerating up or down.

If we were to add horizontal forces of different sizes, this would create an unbalanced net force. Because the net force is not zero, there must be an acceleration that is also not zero. In this case, it is two.

Work and Energy

Energy can be defined as the ability to do work. Work, in physics, is when a force is exerted on an object over a distance. The different kinds of energy represent this ability to do work in different ways. 

For elastic potential energy, if the spring is released from its displaced position, it will either push or pull on anything attached to it, ie exert a force over a distance. Because it is not currently exerting that force, we call the energy potential. 

Similarly, when an object is high above the ground, gravity has the potential to exert a force on the object to bring it falling towards the ground. 

For kinetic energy, we can think about what would happen if that moving object were to collide with something else. It would exert a force on that other thing! 

All energy is tied to the ability to exert a force over a distance.

When work is done, energy is transferred from one object to another. The total amount of energy does not change, if we account for the energy of both objects. This is what is meant by conservation of energy; energy is not created, nor is it destroyed. It’s just transferred from one form to another, or from one object to another.

If we’re focused on one object, then the work done on that object can make its energy increase or decrease, but only because that energy was already present somewhere else. That is why our full explanation of conservation of energy includes the term for work! It is not always reasonable to treat the place the energy came from or went to as part of the system we’re defining. 

The best example of this is when Friction does work on an object. This work, sometimes called thermal energy, happens when an object is on a surface that isn’t perfectly smooth. The resistance to motion creates heat between the object and the surface, and that heat gradually dissipates into the air. It isn’t practical to try to include the air as part of our system of objects, so we treat that energy as ‘lost’ to friction.

The key takeaway from this is that if there’s any energy that’s gone ‘missing’, it is typically friction that is the culprit.

Practice Problems:

Motion

1. A dog runs at 8 m/s for 15 seconds. How far did it run? (120m)
   
   

2. A train traveled 1,000 miles in 8 hours. How fast was it moving? (125mi/hr)
   
   

3. A car drives on cruise control at 60 miles/hr. It does this for 540 miles. How long was the car driving for? (9hrs)
   
   

4. An object initially at rest experiences an acceleration of 7 m/s². How much time will it take to achieve a velocity of 49 m/s? (7 seconds)
   
   

5. A bus initially traveling at 40 m/s accelerates at a constant rate of 3.5 m/s² over a distance of 50 m.  What is its speed after accelerating? (44m/s)
   
   

6. A hummingbird travels 50 m in 4 s. It had no initial velocity and experienced constant acceleration. What is the magnitude of the acceleration? (6.25m/s/s)
   
   

7. A shark reaches a speed of 34 m/s after accelerating for 11 seconds at a rate of 2 m/s/s. How fast was it moving before it accelerated? (12m/s)
   
   

8. When dropped, all objects fall towards the ground at a rate of about 32 ft/s/s. How many feet off of the ground would an object have to be dropped in order for it to fall for 4 seconds? (256 ft)
   
   

Projectiles

Type 1
1 A motorcycle rides off of an 80 m high cliff at 8 m/s. How far away from the base of the cliff should the stunt coordinators put the trampoline? (32m)

2. A rock is thrown horizontally off a roof at 6 m/s, and lands 18 m away from the base of the building. How tall is the building? (45m)

3 A frozen chicken is punted horizontally off of a 20 m high diving board, and lands 90 m from the base of the scaffolding. How fast was this chicken moving when it was kicked? (45m/s)

Type 2

4 A football is kicked off the ground at a 60 degree angle, and is initially moving at 30 m/s. 

How long will this football be in the air? (5.2 seconds)

How high up will it go? (34m)

How far away will it land? (78m)

Forces

1 A 12 kg mass accelerates at 6 m/s/s. How much force is being applied? (72N)

2 How much acceleration would be produced by applying a 260 N force to a 20 kg mass? (13m/s/s)

3 A sledgehammer hits a piece of wood with 256 N of force, accelerating it at 64 m/s/s. How large was this mass? (4kg)

4  A 4 kg box sits on a table, not moving.

First find the force of gravity acting on the object. (40N)

Then find the normal force. (40N)

Finally find the net force. Is there an acceleration? (0N, no)

5 A 5 kg cart is pushed through the snow with 70 Newtons of applied force. There is a coefficient of friction of 0.4

First find the force of gravity acting on the object. (50N)

Then find the normal force. (50N)

Use the normal force and coefficient of friction to find the force of friction. (20N)

Find the net force in both directions. (0N vertically, 50N horizontally)

Divide by the mass to find the acceleration. (10ms/s/s)

6  A 12 kg box is being pushed across a warehouse and accelerating at 4 m/s². There are 50 Newtons of force acting against this box due to friction.

First find the force of gravity and normal force. (120N)

Since we already know that there’s an acceleration, we can find the net force on the box. (48N)

And, since we know how much frictional force there is, we can use the net force to find the applied force from the push. (98N)
It is also possible to find the coefficient of friction by dividing the force of friction by the normal force. (0.42)

7  A 700 kg block of marble is pushed by a truck at a constant speed. If the coefficient of friction is only 0.2, what force is the truck applying?
First find the force of gravity and the normal force. (7000N)

Force of friction can be found using the normal force and coefficient of friction. (1400N)

The phrase “constant speed” means that the block is not accelerating.

This means the net force is zero, which helps find the applied force. (Fa=1400N)

Work and Energy

1. How much gravitational potential energy does a 9 kg object have if it is being held 25m above the ground? (2250 Joules)
   
   

2. How much kinetic energy does a 15 kg object have if it is moving at 4 m/s? (120 J)
   
   

3. How much work must be done to lift a box that weighs 120N 6m in the air? (720 J)
   
   

4. How fast will a 16 kg box of corndogs hit the ground if it is dropped from a height of 5m? (10 m/s)
   
   

5. How high up do you have to hold a 12 kg box of popcorn to make it hit the ground at 40 m/s? (80 m)
   
   

6. What will the speed of a 10 kg sled be when it is halfway down an 18 m high hill? (13.4m/s)
   
   

7. A 20 kg block of marble slides down a 20 m tall ramp. It turns out the velocity is only        16 m/s at the bottom of the ramp. How much energy was ‘lost’ as heat? (1440 J)
   
   
   

8. If a 4 kg object is moving at 45 m/s, and then comes to a stop over a distance of 200 m, how much thermal energy did it ‘create’ in the process? (4050 J)
   
   

9. What is the force of friction between the object and the surface in problem 8? (20.25 Newtons)
   
   
   

10. A 20 kg object sits at the top of a 30 m high hill. If there is no friction until it reaches the bottom of the hill, after which it is on flat ground with a coefficient of friction of 0.6, how far past the bottom of the hill will it slide before it stops? (50 meters)