Physics 203 Final

Dr. M. Xu

July 22, 2003
LAST NAME: ___________________________________________________________________________________________________ FIRST NAME: __________________________________________________________________________________________________ SS#: ________________________________________________________________________________________________________________

General Instruction

You have 2 hours to answer 8 questions on this exam. Please answer each question only on the sheet provided for this problem, using the back if necessary. Please write the name and the last 4 digits of your SS# on each sheet at the top of the page.

You must indicate the reasoning and show all the steps.

If you are unable to obtain the answer to part of a problem and you need the answer to solve the subsequent parts, use an appropriate symbol for the answer to the previous part and solve in terms of that symbol.

The following may be useful:

g = 10m/s2
v2 = v 02 + 2as
x = x0 + v0t + at2/2
ac = v2/R
PV = nRT
R = 8.31J/mol . K
NA = 6.022 × 1023mol-1
t = Ia
P2 = P1 + rgh
P2 + r2v22/2 + r 2gh = P1 + r1v12/2 + r 1gh

1. (5 points) The free body diagram in the drawing shows the forces acting on a thin rod. The three forces are drawn to scale and lie in the plane of the paper. Are these forces sufficient to keep the rod in equilibrium, or are additional forces necessary? Explain. PIC

2. (5 points) A glass beaker, filled to the brim with water, is resting on a scale. A block of wood is placed in the water, causing some of it to spill over. The water that spills is wiped away, and the beaker is still filled to the brim. How do the initial and final readings on the scale compare? Explain your answer.

3. (10 points) Three jumper leaves the ground at angle of 30o, 45o, 60o, and each with a takeoff speed 8m/s. For each,


(a) (3 points) What is the x and y components of the initial velocity?
(b) (3 points) How long would the jumper stay in the air?
(c) (3 points) What is the horizontal distance the jumper would travel?
(d) (1 point) Who jumps furthest?

4. (20 points) An external force is applied on a block with an angle 37o as shown in the figure. The magnitude of the force is 50N. The mass of the block is 10kg. There is friction between the ground and the block.


(a) (4 points) Draw a diagram of all the forces acting on the block.
(b) (4 points) What is the normal force between the block and the ground?
(c) (4 points) How big would the friction force be to make the block move with no acceleration?
(d) (4 points) What is the friction coefficient between the block and the ground?
(e) (4 points) If the block travels on the ground for 5m, what is the work done by the external force?

PIC

5. (15 points) The ropes and the pulley are massless. A person is pulling two blocks together with a force 80N.


(a) (5 points) How big is the acceleration of the two blocks?
(b) (5 points) What is the tension on the rope which pulls 1kg (T1)?
(c) (5 points) What is the tension on the rope between two blocks (T2)?

PIC

6. (10 points) The drawing shows a person whose weight is W=585N doing pushups. Find the normal forces exerted by the floor on each hand and each foot, assuming that the person holds this position. “cg” denotes the center of gravity of the person.

PIC

7. (15 points) An object of mass m=0.200kg attached to a spring is vibrating on a horizontal frictionless surface. The spring has a spring constant k=500N/m. It is stretched initially for x0 = 4.5cm and then released from rest.


(a) (5 points) Find the angular velocity w and period T of this SHM.
(b) (5 points) Find the maximum speed of the object. At which positions x does the object obtain its maximum speed?
(c) (5 points) Find the speed of the object when it is at position x = x0/2.

8. (20 points) A mercury barometer is shown in the following figure. The atmospheric pressure can be determined from the height h of the mercury in the tube. The mass density of mercury is r = 13.6 × 103kg/m3. The standard atmospheric pressure is Patm = 1.013 × 105Pa. No air is enclosed inside the tube except for a negligible amount of mercury vapor hence the pressure (P1) inside the tube can be regarded as zero.


(a) (5 points) What is the height of the mercury under the standard atmospheric pressure?
(b) (5 points) Since some air is accidentally enclosed inside the tube, the height of mercury is found to be 700mm under the standard atmospheric pressure and room temperature (27oC). What is the pressure (P 1) now of the air enclosed inside the tube?
(c) (10 points) Find the mass of the air enclosed inside for (b) if the volume of the air is 10cm3. The molar mass of air is 28.8g/mol. What is the number of air molecules enclosed inside?

PIC