HCI SPECIMEN PAPER B Higher Paper Answers

1 Name: _________________________________________ ( ) Class: ______________ HWA CHONG INSTITUTION SPECIMEN PAPER B HIGHER PHYSICS Level : Secondary Three Duration : 1 hour INSTRUCTIONS TO CANDIDATES Do not open this booklet until you are told to do so. Write your name, index number and class on the top of this page. Answer the questions in Section A and B in the spaces provided. All workings must be shown. In Section B, answer only 2 questions out of the 3 questions. Staple any graph paper used at the back of the answer script. INFORMATION FOR CANDIDATES In Sections A and B the intended marks for each question or part of a question a re given in brackets [ ]. Any working should be done in the space provided. When necessary, take acceleration due to gravity, g to be exactly 10 m s-2. ______________________________________________________________________________ This question paper consists of 14 printed pages, including this page.

2 Section A [20 marks] 1. This question is about a spider web. An experiment was carried out to measure the extension x of a thread of a spider’s web when a load F is applied to it. The results of the experiment are plotted as shown below. Uncertainties in the measurements are not shown. (a) Draw a best-fit line for the data points. [1] [1]: correct best fit line, based on line passing through the majority of the points. Continue next page

3 (b) When a load is applied to a material, it is said to be under “stress”. The magnitude P of the stress is given by FP A= where, A is the area of cross-section of the sample of the material. Use the graph and the data below to deduce that the thread used in the experiment has a greater breaking stress than steel. . . − − = = 92 6 Breaking stress of steel 1 0 10 N m Radius of spider web thread 4 5 10 m [1]: from the graph breaking load = ( ).. − 28 5 0 1 10 N [1]: ( ) . . .. − − − = =   2 92 2 12 8 5 10breaking stress 1 3 10 Pa or N m 3 14 4 5 10 [1]: some statement of conclusion, can e.c.f if calculation is wrong. [3] Continue next page

4 (c) In a particular web, one thread has the same original length as the thread used in the experiment. While making the web, the original length of the thread is extended by . − 22 4 10 m . (i) Use the graph to deduce the amount of work required to further extend the thread to the length at which it just breaks is about . − 31 6 10 J . Explain your working. [3] [1]: =work area under graph [1]: between ( ) ( ). , . . , .− − − −   2 2 2 22 4 10 1 6 10 and 5 6 10 8 5 10 [1]: ( ) ( ). . . . . − − −=   +   = 4 4 3 11 6 3 2 10 3 2 6 9 10 1 6 10 J2 OR [1]: =work average force distance / displacement / extension [1]: . −= 2average force 5 1 10 N , [1]: . −= 2extension 3 2 10 m to give . − 31 6 10 (ii) If the thread is not to break due to the impact of a flying insect, then the thread must be capable of absorbing all the kinetic energy of the insect as it is brought to rest by the impact. Determine the impact speed that an insect of mass 0.15 g must have in order that it just breaks the thread. [1]: . −= =  3K.E. of insect work needed to break web 1 6 10 J [1]: v m= 2K.E. [1]: . .. − − − ==  3 1 4 3 2 10 4 6 m s1 5 10 Allow e.c.f. if value . − 31 6 10 J is not used. =Impact speed ………………………………. [3]

5 2. This question is about the physics of falling objects. (Ignore air resistance for calculation.) (a) A 1.80 m tall geologist was walking in a cave. He saw a drop of water fall past his face and splash on the ground. Struck by inspiration, he waited and timed the next drop; it took 0.10 s to fall from the top of his head to the ground. Calculate the height of the ceiling above his head. [1]: ( ) ( )( ).. s ut at u =+ =+ 2 2 1 2 11.80 0 1 10 0 102 [1]: .u −= 117 5 m s [1]: ( )( ). v u ah h =+ =+ 22 2 2 17 5 0 2 10 [1]: .h=15 3 m Height above his head = …………………………. m [4] Continue next page

6 (b) In a particular fountain, two drops of water fall over the edge of the bowl into a pool h m below. The drop from the left falls directly into the pool. The drop from the right falls 1 m, hits a projection from a nearby Christmas tree and instantaneously loses all its speed and then begins to fall again. After it has fallen another metre, it hits another projection, …, and so on in equal stages until it hits the pool. How much longer does it take for the drop on the righ t to reach the pool? Express your answer in terms of the distance fallen on the left h , the number of stages on the right n , and the acceleration due to gravity g. [4] [1]: for the drop on the left: left left hh gt t g== 212 or 2 [1]: for the drop on the right: right right gt nt n n g = = 211 for 1 stage or 2 2 for stages [1]: right leftt nt t = − [1]: ( ) hn n hg g g= − = −2 2 2 or Continue next page Water drops Water drops hitting a projection at every metre of fall. Pool h Picture for illustration only. The number of stages on the right is n not 5.

7 (c) The distance an object falls is directly proportional to the square of its time of flight . If it falls 16 feet in 1 s, how long will it take to fall 144 feet? Recognize that there is no need to convert to S.I. unit for length [1]: t= 2 144 16 1 [1]: t = 3 s Time= …………………………. [2] End of Section A

8 Section B [20 marks] Answer two out of the three questions in this section. 3. This question is about body armor. When a high-speed projectile such as a bullet or bomb fragment strikes a modern body armor, the fabric of the armor stops the projectile and prevents penetration by quickly spreading the projectile’s energy over a large area. This spreading is done by long itudinal and transverse pulses that move radially from the point of impact, where the projectile pushes a cone-shaped dent into the fabric. The longitudinal pulse, racing along of the fibers of the fabric at speed lv ahead of the denting, causes the fibers to thin and stretch, with the material flowing radially inward into the dent. One such radial fiber show in the figure below. Part of the projectile’s energy goes into this motion and stretching. The transverse pulse, moving at a slower speed tv , is due to the denting. As the projectile increases the dent’s depth, the dent increases in radius, causing the material in the fibers to move in the same direction as the projectile (perpendicular to the transverse pulse’s direction of travel). The rest of the projectile’s energy goes into this motion. All the energy that does not eventually go into permanently deforming the fibers ends up as thermal energy. The graph below shows the speed v versus the time t for a bullet of mass . − 21 02 10 kg fired from a .38 Special revolver directly into the body armor. The scales of the vertical and horizontal axes are set by sv −= 1300 m s and .st −= 640 0 10 s . Take .lv −= 312 00 10 m s and the half-angle  of the conical dent to be . o60 0 . Side view of the bullet impact. The transverse radius (dent) is smaller than the longitudinal radius (thinned region). Speed – time graph of the bullet. Continue next page

9 (a) Calculate the radius of the thinned region at the end of the collision. Recognize that radius of thinned