II: 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 =
Section B: For problems, 5 – 11, 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 using 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 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 equation in Section A, the first equation in Section B 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 C: For problems 12, 13, and 14 use the two equations below. a =v2 r τ = rFsinθ Given 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 = 10N? Section D: For problems 15 – 23, use the equations below. 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? If 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 value of x as given in problem 20 and the k value you just found, use the last equation in Section B 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 E: For problems 24 – 26, use the equations below. p = mv J = FΔt = Δp Δp = mΔv If p is 12 kgm/s and m is 25 kg. Find v using the first equation? The symbol “∆” means “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 third equation together to find vi if vf = 0 m/s, m = 95 kg, F = 6000 N, and ∆t = 0.2 s?
Section F: 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 G: 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 first 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 H: 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 B, 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 equation, here)? Find v2 if v1 =300 m/s and A2 equals 2.5 A1?
Section I: For problems 39 – 43, use the equations below. 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 = 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 needs 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 J: For problems, 44 – 47, use the equations below. If v is constant, how does f change if λ quadruples? If 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 equal 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 K: 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?
Use the second and fourth equations together to find V if r = d, Q = 1.6 × 10-19 C and k is 9.0 × 109 Nm2/C2. Can you find the fifth equation in your algebraic steps? If I have a UE of 12 joules and I double Q and q then what is my new of UE? 58. If F is 0.2 N, d = 2.0 × 10-4 m, and q is 8.0 × 10-19 C, find V? Section M: For problems 59 – 64, use the equations below. QV = i If C is 12× 10-6 farads and V is 12 volts, find Q using the first equation?
The relationship between EOand k is described in problem number 35. Use that relationship to re-write the second equation listed in this section in terms of k instead of EO? EO is a constant and always equals 8.85× 10-12 C2/Nm2. If A = 0.3 m2 and d = 0.012 m, find C? 62. Given Q = 3.0 × 10-6 C, and C = 7× 10-6 F, find UC? 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 equation to find CS if C1 = 2× 10-6 F, C2 = 4× 10-6 F, and C3 = 6× 10-6 F? Section N: For problems 65 – 70 use the equations
µO is a constant and so is always equal to 4π × 10-7 (Tm)/A. If I = 0.2 A, r = 0.003 m, θ = 270° and ℓ = 0.15 m, then find FB? Find when B = 1.1 T, A = 2.0 m2, and θ = 53°? Remember how “∆” means “final state minus initial state”? Using that, assume B does not change from 0.3 T and θ = 0°, but A changes from 0.1 m2 to 0.4 m2. If ∆t = 1.1seconds, use the above information to find Eavg. ε is 0.12 V, B is 2.0× 10-3 T, and v is 12,000 m/s. Find ℓ using the last equation in the list. Section P: For problems 76 – 81, use the equations below. Find E if h = 6.63 x 10-34 J·s, λ = 450 nanometers, and c = 3 x 108 m/s. To solve this problem correctly, convert λ into meters before plugging in the number?