Measuring Microscopic Objects

Transcription

1 Physics 100 In-Class Worksheet Name: Tutorial Section: Measuring Microscopic Objects An exercise in proportional reasoning St. No. (last 2 digits) Last 2 digits used for sorting. Video Camera Microscope TV R ruler Step 1: Find how big one millimeter appears on the tv screen. Distance between mm rulings on the TV screen: R = mm Video Camera Microscope TV hair Step 2: Find diameter of hair on the TV screen D = mm

2 Step 3: go figure Diameter of hair in real life Diameter of hair on TV or using abbreviations = Distance between mm rulings in real life Distance between mm rulings on TV d D = r R solve for d (in symbols) d = plug in numbers d = mm = mm Alternative ways of writing the answer express using power-of-ten notation d = x 10 mm change to meters change to micrometers d = x 10 m d = µm

3 Physics 100 in-class Worksheet Name Tutorial Section: St. No. last 2 digits): Measuring Long Distances by Triangulation Facts about Triangles: (which you should know before we start). 1. All the inside angles of a triangle add up to For two triangles, if each side of one triangle is equal to a side in the other triangle the triangles are equal. For example, AB = DF, BC = DE and AC = EF. 3. For two triangles, each angle of one triangle is equal to an angle in the other triangle, then one is a scale model of the other and we say the triangles are similar. For example α = δ, γ = φ and β = θ.therefore the following ratios are equal: GH/MK = GJ/LM, HJ/GJ = LK/LM and so forth. 4. For two triangles, if two angles of one are equal to two angles of the other then the triangles are similar, because, using fact 1, all angles must be equal. A G β H γ = α L δ J Similar Triangles D C B E Equal Triangles F M θ φ K Now down to business... A F D B right angle E C We want to measure distance AF. 1. Level the laser and move it up until it points at A. Call the laser position F. 2. Move the level laser down to C. 3. Tilt the laser up until it points at A, keeping the pivot at C. Measure the following distances: CE = m CF = m. We know that AF is parallel to BC (because we used a level on the laser in both cases. ) CF = AB AB = m DE = m

4 P 2 Identify the similar triangles using the three letters at its corners. Triangle is similar to triangle. Because AF = BC we want to find BC using the distances we know. BC AB = Solve for BC (in symbols): BC = Now plug in the numbers and solve for the distance in meters. BC = m = m

5 Physics 100 Name Tutorial Section: St. No. Displacements Instructions: Draw an arrow with its tail marking the beginning of the displacement and its head marking the end of the displacement. Label the beginning with x 1 and the end with x 2. Fill in the blanks and calculate the displacement. x x x 1 = 0 x 2 = 3.5 m x = x 2 x 1 = 3.5 m 0 = 3.5 m x 1 = x 2 = x = x 2 x 1 = = x 1 = x 2 = x = x 2 x 1 = = x 1 = x 2 = x = x 2 x 1 = = x 1 = x 2 = x = x 2 x 1 = =

6 x 1 = x 2 = x = x 2 x 1 = = x 1 = x 2 = x = x 2 x 1 = = x 1 = x 2 = x = x 2 x 1 = = x 1 = x 2 = x = x 2 x 1 = = P 2

7 Position-to-Velocity Worksheet Name Section St. No. (Last 2 digits) t x (t) x = x i x i v av = x/ t s m m m/s 0.0 x 0 = The current position is the position at time t. Get this from the position of the spots. The change in position during the time interval Calculate by subtracting the previous position from the current position. Average velocity during the interval. Divide the change in position by the time interval Plot at half seconds.

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9 Velocity-to-Position In-Class Worksheet Name Section St. No. (Last 2 digits): t v av ( t=1 s) x = v av t x (t) = x 0 + x 1 + x x t s m/s m m We get this by measuring Calculate by assuming the displacement between constant velocity between spots. Plot at half spots. Put at half seconds. seconds. 0.0 x 0 = Accumulate all displacements up to the current time and add on starting position to get current position. Plot at even seconds.

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11 Ol Man River Navigating across a flowing river using vectors. Problem 1: A boat heads directly across the river towards the opposite shore. The river carries it down stream. What is the speed and direction of the boat with respect to land? Know: v rg, direction and speed of river s flow with respect to the ground. v br, direction and speed of boat s travel with respect to the river. Want: v bg, direction and speed of boat s travel with respect to the ground Draw v rg with tail here. 1. Put arrow head on scale to mark speed. 0.1 m/s dock 2. Draw v br with arrow here m/s 2. Draw arrow s length on scale to mark speed. 0.1 m/s River flows to to Boat travels across river Measure speed of river flow: v rg speed dock *Plot a vector, to scale, showing speed and direction of river. direction 2. Measure speed of boat (tractor): v br *Plot a vector to scale showing speed and direction of boat (tractor). *Place tip of this vector on the tail of the river s vector. 3. Add the vectors tip to tail graphically. (Draw an arrow from the tail of v br to tip of v rg.) *Measure the speed and direction using the velocity scale and a protractor.. 4. Calculate: Your calculations go here v bg = 2 2 v br + vrg = θ bg = tan 1 v rg v br =

12 Problem 2: A boat heads across the river going upstream so that it can reach the opposite dock. The river carries it down stream. What direction should the boat head in order to reach the dock? Know: v rg, direction and speed of river s flow with respect to the ground. v br, speed of boat s travel with respect to the river. Want: θ br, direction of boat s travel with respect to the river so that it reaches the dock. v bg, speed of boat s travel with respect to the ground 0.2 m/s 1. Draw v rg with head here. 1. Draw arrow s length to scale. 0.1 m/s dock 0.1 m/s 0.2 m/s 2. Draw v br with its tip on the tail of v rg and its tail on the dock-to-dock line. River flows to the Boat travels across river m/s 1. Write speed of river flow: v rg dock speed direction *Plot a vector, to scale, showing speed and direction of river. 2. Write speed of boat (tractor): v br? *Plot a vector to scale representing the speed of the boat (tractor) on a piece of scrap paper. *Place tip of this vector on the tail of the river s vector. *Place the tail of this vector on the dock-to-dock line Draw this vector on the worksheet. 3. Add the vectors tip to tail graphically. (Draw an arrow from the tail of v br to tip of v rg.) *Measure the angle of v br, θ br, using a protractor *Measure the speed v bg using the velocity scale. 4. Calculate: Your calculations go here v bg = 2 2 v br vrg = θ br = sin 1 v rg v br =

13 Name: Physics 100 In-Class Worksheet Circular Motion r St. No. (last 2 digits): F m Object: Measure the mass of a tennis ball by slinging it around and around. Method: Adjust radius r string passes through hollow tube clip to mark string length F = m 4π 2 r T 2 Measure period T Plot T 2 vs r. W 2-newton weight F = W =2 N 1 Go figure. Data Table 2 Data Graph Label the axes yourself. r 10T T T 2 (m) (s) (s) (s 2 ) r (m) 4 Calculations (fill in the boxes): 2. write equation for the slope F = m 1. solve for T2 4π 2 r T 2 slope = 3. solve it for m 3 Slope of graph = Don t forget the units! T 2 = r m = slope of graph 4. plug in numbers m =

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15 Spring Fling Objective: We want to launch a spring 2 m straight up into the air by hooking it over a ruler, pulling it down and letting it fly. How far should we pull it down? Step 1 Measure the spring constant. Apply a force and measure the stretch. Physics 100 In-Class Worksheet Name Section 2 m St. No.: (last 2 digits): Step 2 mgh = Figure out the gravitational potential energy gained by the spring when it has jumped up 2 m. (Mass of spring is 40 g.) (symbols) 1m s k = F (numbers) k = = s Measure height from the unstretched spring s centre of mass. Step 3 Figure out how far to stretch the spring to give it enough energy to reach the 2 m height. Call this stretch s Step 4 Try it! Use conservation of energy to derive an equation. Spring s elastic potential energy when stretched at the bottom. = Gravitational potential energy at 2 m height. Write in symbols and solve for s. = s =

16 Spring Fling, the sequel Objective: We want to launch a spring at 45 from the horizontal. Can we predict how far it will go from how much it is stretched before launch? Step 2 Initial velocity can be got from conservatioin of energy: 1/2 mv i 2 = 1/2k s2 v i 2 = k s2/m Assume v ix is constant. v ix Analyse the initial velocity into components. v i 2 = v ix 2+ v iy 2 Because the angle of launch is 45 v i 2 = 2v ix 2 = 2 v iy 2 = 2 v iy v ix v i v iy Step 1 Range: R = v ix t v ix Step 3 We also need to calculate the time of flight which is the time it takes to go up and back down to y =0. y = v iy t 1/2gt2 = 0 (v iy 1/2gt) t = 0 (by factoring) This has two solutions: t = 0 (At the start) Step 4 Putting it all together Range: R = v ix t R = v ix (2 v iy /g) R = 2v ix v iy /g = v i 2/g R = (k/mg) s 2 45 The spring is stretched s. Its spring constant is k. and t = 2 v iy /g (At the end..the one we want!)

17 Physics 100 In-class Worksheet Name: St. No. (last 2 digits) Suicide Pendulum height y 1.25 m Potential Energy PE = mgy Total Mechanical Energy Etotal Kinetic Energy KE = Etotal PE Speed v = 2KE / m h 0.50 y Calculate gravitational potential energies: PE = mgy. (Bottom of swing is zero.) Mass of ball: m = kg, g = 9.8 m/s 2 2. Identify maximum height h. Set Kinetic Energy = 0 at h. At h, Total Mechanical Energy = Potential energy 3. Total Mechanical Energy, E total, at lower heights is the same as it is at h. 4. Kinetic Energy below h is KE = E total PE. 5. Speed at any height lower than h is v = 2KE m (Because KE = 1 2 mv2 ) 6. Problem : Show that v = 2g(h y )