PHY2020 Test II Formula Sheet, Exams of Physics

Download PHY2020 Test II Formula Sheet and more Exams Physics in PDF only on Docsity! TestII PHY2020 Formula sheet All problems worth 4 points total except #1; parts are worth the stated points. Do problems 1, 2a, 2b (you must do these) AND any 6 of the remaining 8 problems for full credit. Perfect score = 25 (1 pt for #1, plus 6 x 4 pts.) Do more than 6 of the last 8 for extra credit (but no one can get more than a perfect score of 25 pts.). g=9.8 m/s2 100 cm=1 m 39.37 inches=1 m 1 km=1000 m 12 inches=1 foot 5280 feet=1 mile 1 kg = 1000 g 1 hour = 3600 s G=6.7 10-11 Nm2/kg2 1 J = 1N*m 1 W=1 J/s Comparison between metric and English units of Force: 1 lb (pound) = 4.45 N Useful formulas: Linear: Espring = ½ kx2 Egrav. potential = mgh (h is the height) EKinetic Energy = ½ mv2 p(the momentum) = mv (remember, p and v are vectors, so p has both size and – if it’s important – direction) If there are no external forces (→ momentum is conserved) and the collision is elastic (→ energy is conserved) if mass m1 hits a stationary mass m2 then v1final = v1initial (m1-m2)/( m1+m2) and v2final = v1initial (2m1)/( m1+m2) Rotational: s=rθ vlinear=r alinear=r Remember, use radians for θ, , and  in these and all formulas below. 1 rotation = 360 o (<- don’t use!) = 2 radians Erot. Kin. Energy = ½ I2 L(angular momentum)=I I(moment of Inertia) is for a point mass a distance ‘r’ from the axis of rotation=mr2 (If you need a moment of inertia for a special problem – as long as that’s not the question – you will be given it.) torque = I also, torque = F times ‘lever arm’, where ‘lever arm’ is the distance of closest approach to the axis of rotation of the Force vector extended forwards and backwards. Density is represented by the Greek letter ρ. ρ=M/V, where M is the mass of the object and V is the volume the object takes up. circumference of a circle: 2r, where r is the radius 7. If some rotating object free from external torques and moving at angular speed =100 rad/s suddenly changes its moment of inertia I from Iinitial to 1/3 of the initial moment of inertia (i. e. Inew = 1/3 Iinitial), what is the new , in units of rad/s? Free from external torques means angular momentum (L=I) is conserved. Thus the new  = 3 * 100 rad/s = 300 rad/s, since new * Inew has to equal the given (initial)  of 100 rad/s times Iinitial. This is just like the spinning person in the chair who decreases their moment of inertial by pulling weights in closer to the axis of rotation – they speed up when their moment of inertial is smaller so L is conserved. _________________________rad/s 8. A rotating object initially has 50 J of rotational kinetic energy. A torque is applied to increase the velocity of the rotating object until it now has 300 J of rotational kinetic energy. The moment of inertia remains constant. What is the new angular velocity in terms of the old one? Erot KE = ½ I 2. If the rotational KE is increased by a factor of 6, then new 2 = 6 * old2, so new = (6)0.5 old , and the squareroot of 6 = 2.45 to three sig figs new = _______________old (where the blank line is some 3 sig. fig. number) 9. Consider the picture below. If the block weighs 500 N and is in equilibrium, what is the magnitude of F1 (magnitude of a vector F1 = (F1x2 + F1y2)1/2) in newtons, 3 sig figs? In equilibrium means no net forces in either x or y direction. sum of Fy = 0 =F1y – 500 N= F1*sin20o – 500 N=0 → F1 = 1462 N since F2 has no y- component __________________ N 10. How many kilograms (1 kg=1000 g) of air are in our lecture hall, which has approximate dimensions 12 m wide x 20 m long x 3 m high(the density of air is about 0.0013 g/cm3)? (1 m = 100 cm) (3 sig figs) Volume of lecture hall = 12 * 20 * 3 m3 = 720 m3, Mass of air = density of air * Vol = 720 m3 * 0.0013 10-3 kg/ (10-2 m)3 since 1 g = 10-3 kg and 1 cm=10-2 m thus Mass of air in lecture hall is 936 kg – a large number. _______________________kg