physics

- You CANNOT use kinematics or Newton’s 2nd Law to solve any problems (although you may use them to check your answers)

1. A 60kg skydiver steps out of an airplane 7000m above the ground. As she

descends, the average air drag force is 550N. She opens her parachute 1000m above the ground. What is her speed when she opens her parachute? (Use energy conservation)

2. A child is pulling a 10kg wagon behind him. The handle of the wagon is 30o

above the horizontal, and the wagon starts at rest. After being pulled for 3m the wagon reaches a speed of 2m/s. What was the force with which the child pulled on the handle? Ignore friction and use energy conservation.

3. An electron (mass 9.1 x 10-31kg) is fired horizontally at a speed of 1000m/s toward a sheet of gold foil. The electron bounces backward off the gold foil with a speed of 700m/s at an angle of 20o above the horizontal.

a. What was the impulse experienced by the electron?

b. If the collision lasted for 1.0 x 10-6 s, what was the average force experienced by the electron?

4. a. A 110 kg football player running at 8 m/s slams into a 90 kg person moving in the opposite direction at 9 m/s. If the collision is perfectly inelastic (i.e., they ‘stick’ together), what is their final velocity? Include the before and after pictures in your solution.

b. Do a special-case analysis of your solution, using the standard IF… AND… THEN… AND/BUT… THEREFORE… procedure.

5. A 1000 kg car moving East at 30 m/s collides with a 5000 kg truck moving South at 8 m/s. If the car and truck stick together after the collision, what is the magnitude v and direction θ of their final velocity? Remember that v =

( ) ( )22 yx vv + and θ = tan-1 (vy / vx).

6. A 80 kg person is riding a rollercoaster at Cedar Point. When the coaster passes

through a dip of radius 10 m at point A (shown below), the normal force of the seat on the person is 1000 N.

a. What is the speed of the rollercoaster at point A?

b. What is the magnitude centripetal acceleration of the rollercoaster at point A? What direction is the centripetal acceleration in?

7. A neutron star is an extremely dense type of star, with a typical mass of 4.2 x

1030kg and radius of 10,000m. a. If a neutron star completes one rotation every 0.02s, what is its angular

velocity?

R=10 m

Point A

b. The moment of inertia for a solid sphere (such as a neutron star) is I = (2/5)MR2. What is the moment of inertia for the neutron star?

c. Neutron stars gradually stop spinning due to drag forces from their environment. If a neutron star stops spinning after 1000 years ( = 3.2 x 1010 seconds), what was the net torque acting on the neutron star?

8. In this totally everyday scenario, a 50kg woman stands 1m from the left end of a 3m plank. The plank is supported by two ropes (one at each end). If the mass of the plank is 10kg, what is the tension in each rope?

9. A uniform beam of length 2m and mass 40kg is supported by a cable as shown below. The cable is at an angle of 300 from the beam. In addition, a rope is attached to the end of the beam at a 450angle, and is being pulled with a tension of 100N.

Rope 1 Rope 2

a. What is the tension in the cable? b. What is the strength of the horizontal reaction force (Rx) acting on the

beam?

300

hinge 100N

450

10. a. Define each of the following terms: Systematic Error: Random Error:

b. You’re home, and you’re bored, so you and your buddy Scooter decide to do a physics experiment to liven things up. Your goal is to determine the acceleration of gravity at your location, which you will do by measuring the time it takes rocks to fall a known height. You are outside, standing on grass. The plan is for Scooter to drop a rock when you say “GO!” You will start a stopwatch when you say “GO!”, and then stop the stopwatch when the rock hits the ground. You’ll then use energy conservation (ignoring air drag) to determine g. Using a meter stick, you find that the height from which the rock will be released is 1.6m.

Describe one systematic error, including how it will skew your results. Also, include two random errors, and what you would need to do to reduce the random errors.

Equation Sheet – Exam 2 Physics 220

______________________________________________________________________________ Work-Energy: units for work/energy are Joules (J = kg∙m 2/s2) K = (1/2)mv2 v is the speed of the object Ug = mgy Must choose reference point for y = 0 m. And g is +9.8 m/s2 Us = (1/2)kx2 x is how much spring is compressed/stretched, k is spring constant WF = F d cos(θ) θ is the angle between line of motion and the direction of force F Only friction, pushing, and pulling forces do work. For Friction, Ff = μk FN Energy Conservation: Always draw initial/final pictures Ki + Ug i + Us i + Wext = Kf + Ug f + Us f ______________________________________________________________________________ Momentum-Impulse: units for momentum/impulse are (kg m/s) p = mv v is the velocity of object (can be + or -, depending on direction) J = Favg Δt is the momentum given/taken by the force F Momentum Conservation: Always draw initial/final pictures 1-object: pi + J = pf Use if we only know the mass for one object in collision 2-objects: p1i + p2i = p1f + p2f If collision is 2-dimensional, then need x and y components separately. If collision is inelastic: Objects stick together, so v1f = v2f ≡ vf If collision is perfectly elastic, then can also use energy conservation. ______________________________________________________________________________ Circular Motion: Centripetal acceleration: a = v2/R points to middle of circle Net force: Fnet = ma = mv2/R points to middle of circle Period & Frequency: T = 1/f = 2π/ω When solving circular motion problems, choose + direction to be towards the middle of the circle. That way, Fnet is always positive. ______________________________________________________________________________ Rotational Motion & Static Equilibrium: torque has units of N∙m Kinematics: ω = angular velocity (rad/s) α = angular acceleration (rad/s2) Velocity: v = ω·R Converts between angular and linear velocities Torque: τ = ± F r sin(θ) where + if F tries to make object rotate counterclockwise - if F tries to make object rotate clockwise r is the distance from hinge to where force F is applied θ is the angle between F and the lever arm Torque & Acceleration: τnet = I α where I is the moment of inertia (in kg∙m 2) and α is the angular acceleration (in radians / s2) Static Equilibrium: τnet = 0 N∙m Fnetx = 0 N Fnety = 0 N