Exam Mastering Physics (3NAB0)

Date: April 4, 2016 Time: 18:00 – 21.00

This exam contains ten problems (4 points each). All problems should be worked out on paper. It is mandatory to copy your final answers with units into the table below.

During the exam you are allowed to use (1) the printed formula pages from OASE; (2) (graphical) calculator; (3) dictionary.

Constants: g = 9.80 m/s2;

Name: ………………………………………………………

Student ID: …………………………… Department: ………………………………………………………

Problem Solution with units Problem Solution with units 1a

I1 =

1b

Q =

2

f =

3

Htot =

4

θb =

5

fL=

6

T1 =

7a

Θ= 7b

vf =

8a

Tw =

8b

Tair =

9a

T =

9b

f =

10

R=

1) Under steady-state conditions, in the multiloop circuit shown in Figure 1. Find the current I1 and the charge Q on the capacitor. Calculate: a) I1 b) Q

2) Sir Lancelot, who weighs 800N, is attacking a castle by climbing a uniform ladder that is 5.0m long and weighs 180N (Figure 2). The bottom ladder rests on a ledge and leans across the moat in equilibrium against a frictionless vertical castle wall. The ladder makes an angle of 53.1o with the horizontal. Lancelot pauses one-third of the way up the ladder. Find the friction force on the base of the ladder f. Calculate: f=

Figure 2.

3) A wall consists of 8 m2 brick and 1 m2 glass. The thickness of the brick is 20 cm and the glass is 5 mm thick. The thermal conductivity of both materials is 1 W/mK. Find the total heat current through the wall and the glass Htot, if the surface temperature at the inside is 20 oC and the surface temperature at the outside is -10 oC. Calculate: Htot =

Solution

H=Aglass*dT/ (dglass/kglass) + Abrick*dT/ (dbrick/kbrick) [W]

H= 1*30/(0.005/1) + 8*30/(0.2/1) = 7200 W

4) In Figure 3, material a is water and material b is glass with index of refraction 1.52. The incident ray makes an angle of 60.0° with the normal. Find the direction of the refracted ray θb. Calculate: θb =

Figure 3.

5) A police car’s siren emits a sinusoidal wave with frequency ƒS = 300 Hz. The speed of sound is 340 m/s and the air is still. The siren, see Figure 4, is moving away from the listener with a speed of 45 m/s relative to the air, and the listener is moving toward the siren with a speed of 15 m/s relative to the air. Find the frequency of the listener fL. Calculate

fL=

Figure 4.

6) Solve this exercise symbolically. A bag of cement weighing Fg N hangs in equilibrium from three wires as shown in Figure 5. Two of the wires make angles θ1 and θ2 . Find the tension T1 using θ1 , θ2 and Fg. Calculate:

T1 =

7) A collision. A 1500-kg car traveling east with a speed of 25.0 m/s collides at an intersection with a 2500-kg truck traveling north at a speed of 20.0 m/s as shown in Figure 6. Find the direction θ and magnitude of the velocity vf of the wreck. Calculate:

a) θ

b) vf

8) A solid gold statue. A 15.0-kg solid gold statue is raised from the sea bottom (Figure 7). Find the tension in the hoisting cable (assumed massless) when the statue is at rest and completely underwater (Tw) and at rest and completely out of the water Tair?

ρgold = 19300 kg/m3; ρwater = 1030 kg/m3; ρair = 1.2 kg/m3. Calculate:

a) Tw

b) Tair

9) In an attempt to get your name in Guinness World Records, you build a bass viol with strings of length 5.00 m between fixed points. One string, with linear mass density 40.0 g/m, is tuned to a 20.0-Hz fundamental frequency (the lowest frequency that the human ear can hear). Find the tension T of this string and the frequency f on the string of the second harmonic. Calculate: a) T b) f

10) Solve this exercise symbolically. Find the maximum horizontal range R (see Figure 8) of a projectile launched with speed v0 at an initial angle θ0 between 0° and 90°. Use g for acceleration due to gravity. Calculate

R =

Figure 8