Part 2: Geometry Calculate the area of the following shapes. It may be necessary to break up the figure into common shapes. 1. 7 m 2. 12 m 6 m 22 m 16 m 15 m 18 m Area = Area = Calculate the unknown angle values for questions 3-6. 3. 4. A B m C D E F n G H Lines m and n are parallel. A = 75° B = C = D = E = F = G = H = 5. 6. θ1 =____ θ2 =_________ θ3 =_________ θ4 = A = B = θ5 = C = D =
Find an expression for h in terms of l and θ. What is the value of h if l = 6 m and θ = 40°? Part 5: Algebra Solve the following (almost all of these are extremely easy – it is important for you to work independently). Units on the numbers are included because they are essential to the concepts, however they do not have any effect on the actual numbers you are putting into the equations. In other words, the units do not change how you do the algebra. Show every step for every problem, including writing the original equation, all algebraic manipulations, and substitution! You should practice doing all algebra before substituting numbers in for variables. Section I: For problems 1-5, use the three equations below: vf = vO + at x = xo+vot+1/2at2 vf 2 = vo2 + 2a(xf - xo) Using equation (1) solve for t given that v0 = 5 m/s, vf = 25 m/s, and a = 10 m/s2. v0 = 0 m/s, x0 = 0 m and t = 10 s, use the second and third equations together to find xf . a = 10 m/s2, x0 = 0 m, xf = 120 m, and v0 = 20 m/s. Use the second equation to find t. vf = - v0 and a = 2 m/s2. Use the first equation to find t / 2. How does each equation simplify when a = 0 m/s2 and x0 = 0 m? Section II: For problems, 6 – 9, use the four equations below. ΣF = ma fk = µk N fs ≤ µs N Fs = −kx If ΣF = 10 N and a = 1 m/s2, find m the first equation?
Given ΣF = fk , m = 250 kg, µk = 0.2, and N = 10m, find a? ΣF = T – 10m, but a = 0 m/s2. Use the first equation to find m in terms of T? Given the following values, determine if the third equation is valid? (Given: ΣF = fs , m = 90 kg, and a = 2 m/s2. Also, µs= 0.1, and N = 5 N). Use the first equation in Section I, the first equation in Section II and the following givens and find ΣF? (given: m = 12 kg, v0 = 15 m/s, vf = 5 m/s, and t = 12 s) Use the first equation in Section I, the first equation in Section II and the following givens to find ΣF? (given: m = 12 kg, v0 = 15 m/s, vf = 5 m/s, and t = 12 s) Use the last equation to solve for Fs if k = 900 N/m and x = 0.15 m?
Section III: For problems 12, 13, and 14 use the two equations below. a =v2 r τ = rFsinθ that v is 5 m/s and r is 2 meters, find a? Originally, a = 12 m/s2, then r is doubled. Find the new value for a? Use the second equation to find θ when τ = 4 Nm, r = 2 m, and F = 10 N? Section IV: For problems 15 – 23, use the equations K = 1/2mv2 ΔUg = mgh W = F(Δx)cosθ Us = 1/2kx2 P = W/t P=Fvavgcosθ Use the first equation to solve for K if m = 12 kg and v = 2 m/s. If ∆Ug = 10 J, m = 10 kg, and g = 9.8 m/s2, find h using the second equation. K = ∆Ug, g = 9.8 m/s2, and h = 10 m. Find v. The third equation can be used to find W if you know that F is 10 N, ∆x is 12 m, and θ is 180°.
Use the value for W you found in the previous question to find P if t = 2 s. Which equation do you need? Given Us = 12 joules, and x = 0.5 m, find k using the fourth equation. For the same of x as given in problem 20 and the k value you just found, use the last equation in Section II to find Fs. Assuming θ = 0° and F = Fs, use the third equation listed above along with the numbers found and given in the previous two questions to find W. For P = 2100 W, F = 30 N, and θ = 0°, find vavg using the last equation in this section. Section V: For problems 24 – 26, use the equations below. p = mv J = FΔt = Δp Δp = mΔv p is 12 kgm/s and m is 25 kg. Find v using the first equation. “∆” “final state minus initial state”. So, ∆v means vf – vi and ∆p means pf – pi. Find vf using the third equation if pf = 50 kgm/s, m = 12 kg, and vi and pi are both zero. Use the second and equation together to find vi if vf = 0 m/s, m = 95 kg, F = 6000 N, and ∆t = 0.2 s.
Section VI: For problems 27 – 29 use the equations below. Tp is 1 second and g is 9.8 m/s2. Find l using the second equation. m = 8 kg and Ts = 0.75 s. Solve for k. Given that Tp = T, g = 9.8 m/s2, and that l = 2 m, find f (the units for f are Hertz). Section VII: For problems 30 – 33, use the equations below. 30. Find Fg if G = 6.67 × 10-11 m3 kg-1 s-2, M = 2.6 × 1023 kg, m = 1200 kg, and r = 2000 m? 31. What is r if Ug = -7200 J, G = 6.67 × 10-11 m3 kg-1 s-2, M = 2.6 × 1023 kg, and m = 1200 kg? Use the equation in Section IV for this problem. K = Ug, G = 6.67 × 10-11 m3 kg-1 s-2, and M = 3.2 × 1023 kg. Find v?
Using the first equation above, describe how Fg changes if r doubles? Section VIII: For problems 34 – 38, use the equations below. If P0 = 100,000 Pa, ρ = 1.2 kg/m3, g =9.8 m/s2, and h = 75 m, calculate the value of P? If m doubles but V is halved, how does Fb change if g is constant? Using the first equation, third equation, and the first equation from Section II, determine the value of a if ρ = 1000 kg/m3, V = 2 m3, and g = 9.8 m/s2. Assume Fb = ΣF? If y is constant, how does P change if v is tripled (use the fifth equation, here)?
Find v2 if v1 =300 m/s and A2 equals 2.5 A1? Section IX: For problems 39 – 43, use the equations PV = nRT Q = mc∆T W = −P∆V ∆U = Q + W What is T if V = 2x10-3 m3, n = 1 mol, R = 8.31 J/kg·K, and P = 7x106 Pa? Assuming n and R are both held constant, what happens to T if P is doubled and V is tripled? Calculate m if c = 4000 J/kg°C, Q = 6.2 kJ, and T = 12 °C. To do this correctly kJ to be converted into units of J? If U doubles and kB, R, and M remain the same values, how does vrms change?
If ΔV is positive and ΔU is zero, what is the sign of Q? Justify your answer using the last two equations? Section X: For problems, 44 – 47, use the equations If v is constant, how does f change if λ quadruples? c is to 3x108 m/s. What is the value of n if v equals 2.25 x 108 m/s? If n2 is greater than n1, is θ1 greater than, less than, or to θ2? Justify your answer using the third equation?
Assuming θ2 is 90°, write an expression for θ1 in terms of n1 and n2. Section XI: For problems 48-52, use the equations below. = If si = -5 cm and s0 = 2 cm, calculate the value of f (units are cm for f)? R is known to be -3.2 cm. Find si if s0 = 4 cm? What is the numerical value of M if s0 = 2f (M has no units)?
51. What is θ if d = 8.5x10-4 m, m = 2, and λ = 6.3x10-7 m? Using the last two equations, calculate xm if θ is 1.2°, m is 1, λ is 400 nm, and L is 1.4 m. To solve this correctly, λ should be converted from units of nm to m? Section XII: For problems 53– 58, use the equations = qV k is a constant and is always equal to 9.0 × 109 Nm2/C2. If q = 1.2 × 10-13 coulombs, Q = -q, and F = -10 Newton’s then find r using the first equation? Another way of writing k is . Using k = 9.0 × 109 Nm2/C2, solve for Eo? Find E using the fourth equation if V = 120 volts and d = 0.2 meters?
Use the fourth equation to find CP if C1 = 2× 10-6 F, C2 = 4× 10-6 F, and C3 = 6× 10-6 F? Use the fifth equation to find CS if C1 = 2× 10-6 F, C2 = 4× 10-6 F, and C3 = 6× 10-6 F? Section XIV: For problems 65 – 70 use the equations V = IR
Given V = 220 volts, and I = 0.2 amps, find R (the units are ohms, Ω)? If ∆Q = 0.2 C, t = 1s, and R = 100 Ω, find V using the first two equations? R = 60 Ω and I = 0.1 A. Use these values to find P using the first and third equations? Let RS = R. If R1 = 50 Ω and R2 = 25 Ω and I = 0.15 A, find V? Let RP = R. If R1 = 50 Ω and R2 = 25 Ω and I = 0.15 A, find V? 70. Given R = 110 Ω, l = 1.0 m, and A = 22× 10-6 m2, find ρ? Section XV: For problems 71 – 75 use the equations BAcosθ E = Bℓv 71. Find v if q = -4.8 × 10-19 C, B = 3.0 Teslas, θ = 90°, and FB = -1.0 × 10-9 N?