Week 2/3 Problems

1. What thickness of rubber tread is worn off of the tire of a typical automobile as it travels one mile?

2. How long would it take for you to walk from Los Angeles to Philadelphia?

3. Ten pounds of flour correspond to how many kilograms of flour? (1 pound = 454 g)

4. A car driving at 65 miles/hour is travelling at what speed in cm/minute? (1 mile =5280 ft)

5. A football field is 57,600 , how much is this in ? (1 in = 2.54f t2 m2 cm)

6. What are the dimensions of A? SI units? See board

7. If I double A, how does B change? If I half A? Hold everything else

constant. See board

Week 4 Monday Problems Note: For kinematics, you’ll use T to your advantage since sometimes you’re working with two separate things happening at the same time so that’s how you can relate them.

1. Eq practice, pick the equation you’d use for each set of givens/unknowns:

a. Find t given a, , V0xΔ b. Find a given t, V0 , Vf c. Find V0 given Vf , a, xΔ d. Find given V0 , Vf , txΔ

2. (t) (m/s )t 6 (m/s) v = 7 2 + x=5 at t=0. What are the functions of x(t) and a(t)?

3. Ratio: (remember, hold everything constant except for the 2 variables you’re changing)

a. A ball is dropped from rest from a height H and takes time T to hit the ground. If I want it to take 3T, what height should I drop it from? If I drop it from 3H how long will it take to hit the ground?

b. A car is driving at a speed U, the driver sees a brick wall a distance D away from him, he’s able to avoid collision by decelerating at constant acceleration A. If he notices the wall at D/2, what must his acceleration be to avoid a collision?

4. Two friends are running towards each other. Friend A starts at x=0 and runs at constant speed U, Friend B starts from rest at x=D and runs with constant acceleration A.

a. If they meet at x=1/4 D, what was Friend B’s acceleration? b. What is Friend B’s final velocity when they meet? Just set up

eq. and list givens. c. When do they have the same velocity? Just set up.

1. A student throws a ball off a building of height H at V0. He throws it at 4 different angles below the horizontal: 0 °, 30°, 60°, and 90°.

a. Rank the angles from longest to shortest air time. Explain. b. Rank the angles from longest to shortest range. Explain. c. Conceptually, what is V0y when theta = 0 ° and 90°?

2. (t) (m/s )t (x) 6 (m/s)(y) v = 7 2 + The particle starts at (0,1) at t=0.

What are the functions of r(t) and a(t)? Give x and y components for both.

3. A projectile’s launch speed is five times its speed at maximum height. Call the speed at maximum height v (parts b and c will be in terms of v).

a. What is the launch angle with respect to the horizontal? (not in terms of v) b. How much time is the projectile in the air (from launch to when it lands again on the

ground)? c. What is the maximum height that the projectile reaches?

4. I can throw a paper airplane at 4 m/s. There is a wind is blowing at 2 m/s east. At what angle

(relative to north) should I throw my paper airplane if I want it to hit my friend who is 12 m directly north of me?

5. Concept: Say you’re in an open trolley going 15 mi/h down a street. You throw a ball up in the air. Draw its motion (x vs. y) in your frame of reference. Now draw its motion in the frame of reference of a person standing on the street.

Week 6 1. Draw a FBD for each of these scenarios

a. A block moving in the +x direction at 6 m/s on a frictionless surface b. Blocks A and B, one on top of the other, are at rest on a surface. c. A block moving at constant velocity with a Normal force of 40 N and

frictional force of 30 N. 2. Give the N3L “reaction” force to each of these forces:

a. I push on a wall with 20 N b. The earth pulls on me with Mmeg c. I pull a rope attached to a car with 100 N

3. A person with mass M rides an elevator while standing on a scale that reads N. For any given acceleration A, set up how you would solve for each M, N, and A in those terms.

4. A box of mass M with acceleration A has an applied force F that points 30 degrees below the horizontal. It is moving along a surface with friction.

a. Draw a FBD for the box b. What is the Normal force? (y direction) c. What is the frictional force? (x direction)

Week 7 Problems 1. See #1 on the board

a. Draw FBD for each block. b. Rank N a, N b, and N c c. If each block were moving alone, draw and rank fa, fb, and fc

(assume same )μ d. Explain relationship between part b and part c

2. See #2 on the board. Fill in the missing forces so the block has no net acceleration.

3. See #3 on the board. a. FBD b. When released from rest, block 2 accelerates at A downward,

what is f on block 1? 4. Forces and kinematics: You’re driving a car of mass M at V0 when

you suddenly a brick wall a distance D away. What does the force f between the car and the road have to be to survive?

5. (Review) A person with mass M rides an elevator while standing on a scale that reads N. For any given acceleration A, set up how you would solve for each M, N, and A in those terms.

Week 8 Problems

1. On your papers, draw a Force vs. distance graph that represents +30 J of work 2. You pull a box a distance D in the +x direction with force F (these do not

change). You pull it at = 0, 40, and 80 degrees above the horizontal. At whichθ angle do you do the most work on the box and why?

3. A 100-kg (M) skydiver has a speed of 10 m/s (V0) at an altitude of 900 m (H) above the ground. Assume no air resistance.

a. What is the kinetic energy of the skydiver? (5000 J) b. What is the work done by gravity after he has fallen 300 m? (294 kJ) c. What is his new velocity? (77.3 m/s)

4. A new conveyor system at the local packaging plan will utilize a motor-powered mechanical arm to exert an average force of 890 N to push large crates a distance of 12 meters in 22 seconds. Determine the power output required of such a motor. ( 485 W)

5. A 6.8-kg toboggan is kicked on a frozen pond, such that it acquires a speed of 1.9 m/s. The coefficient of friction between the pond and the toboggan is 0.13. Determine the distance which the toboggan slides before coming to rest. Don’t use kinematics! (1.4 m)

Week 9 Problems 1. Briefly define/explain the following:

a. Conservative forces b. Conservation of energy c. Relationship between PE and F (graph helps)

2. See #2 on board. If the mass of the object it 2kg, what is KE at these points? Is the force positive or negative from A to B, B to C, and C to D?

3. A 1 kg mass is dropped from rest from a height of 4 meters above the ground. When it has free-fallen 1 meter its total mechanical energy with respect to the ground is ____. Don’t use kinematics. [39.2 J]

4. If there had been air resistance in the fall from #3 would the object's kinetic energy be greater than, the same, or less than KE for #3?

5. A ball of mass 2.00-kg is dropped from a height of 1.5 m (from the ground) onto a massless spring (the spring has an equilibrium length of 0.50 m from the ground). The ball compresses the spring by an amount of 0.20 m by the time it comes to a stop. Calculate the spring constant of the spring. [1,175 N/m]

Week 10 Problems 1. See Board. We drop the ball from a height H. Where is the energy and in what

state (potential or kinetic) is it in at different points along the fall and the resulting bounce back from the spring?

2. See Board. Write out what P0 and Pf are, symbolically. 3. What is V2 in terms of V1? 4. Different Scenarios: Fill out diagram I drew on the board with info about different

types of interactions. Bullet points are for examples. 5. A 92-kg fullback moving south with a speed of 5.8 m/s is tackled by a 110-kg

lineman running west with a speed of 3.6 m/s. Assuming momentum conservation and a “sticky” collision, determine the speed and direction of the two players immediately after the tackle. [3.3 m/s, 53° S of W]

Week 11 Problems

1. (t) (rad/s )t 6 (rad/s) ω = 7 2 + =0 at t=0. What are the functions of and θ (t) θ (t) α 2. Eq. practice, pick the equation you’d use for each set of givens/unknowns:

a. Find t given , , 0α θ Δ ω b. Find given t, 0 , fα ω ω c. Find 0 given f , , ω ω α θ Δ d. Find given 0 , f , tθ Δ ω ω

3. A hoop of mass M and radius R, starting from rest, is accelerated at a rate of = 5 rad/ s2.α After 15 seconds... I= MR^2

a. What is the angular velocity of the hoop? [75 rad/s] b. What is the total angular displacement over this period of time? [562.5 rad] c. How much work is done? [2812.5MR2 J]

4. A roll of toilet paper is held initially at rest by the first piece and allowed to unfurl. The roll has an outer radius R = .06 m, an inner radius r = .018 m, a mass m = .2 kg, and falls a distance s = 3.0 m. Assuming the diameter and mass of the roll do not change significantly during the fall, find… Note: moment of inertia for hollow cylinder = Not on quiz.m(R )2

1 2 + r2 a. The final angular speed of the roll b. The final translational speed of roll c. The angular acceleration of the roll d. The translational acceleration of the roll

5. The moment of inertia for a rod of mass M and length L, rotating about one end, is initially .I After I change the axis of rotation, the moment of inertia is .25I.

a. In terms of L, how far did I move the axis of rotation by? b. What if, for the same rod, the new moment of inertia was , in terms of L, how far75I .

did I move the axis of rotation by?

Week 12 Problems 1. Draw FBD for a, b, and, c on the board 2. What are the linear velocities at points 1 and 2. (See board) 3. Why do some objects take less time to roll down a ramp then others? Think conservation of energy. 4.

5.

Week 13 Problems https://youtu.be/9cbF9A6eQNA?t=1m3s (until 3:55)

1. Follow along and do the ladder problem with the video. 2. What is equilibrium? Write the two equations necessary for

equilibrium.(check your notes) 3. What is static equilibrium? Do the two equations above always mean

static equilibrium? 4. (See board) Add a force to make the beams be in equilibrium. 5. Don’t worry about the limit part. Draw FBD.

Week 14 Problems 1. A hydraulic press can lift a 700 N car when 250 N of force is applied

to its smaller end. a. What is the ratio r/R where r is the radius of the smaller end and

R is the radius of the wider end. b. If water were to flow through a tube with ends of the same ratio

as part a, what would the speed of water going out be if the speed of water going in was 20 m/s? Water goes in through the wider end.

2. What is the max pressure difference a square airplane window can withstand if the maximum net force on it can be 250N? Sides = .5 m

3. A block of wood floats in fresh water with two-thirds of its volume V submerged and in oil with 0.90V submerged. Find the density of (a) the wood and (b) the oil.