Worksheet 4: Energy. 1 Mechanical Energy

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1 Name: 3DigitCoe: Worksheet 4: Energy 1 Mechanical Energy ##$%$ A) B) C) D) ##$)$ ##$($ ##$'$ ##$&$ (left) Threeballsarefiresimultaneouslywithequal spees from the same height above the groun. Ball 1 is fire straight up, Ball 2 is fire horizontally, an Ball 3 is fire straight own. Ball 4 an Ball 5 are release from same height as the others but are roppe from rest. All the balls have the same mass except Ball 5 which is much heavier than the others. Rank in orer, from largest to smallest, their spees v 1, v 2, v 3, v 4,anv 5 as they hit the groun. Next rank the time that they are in the air, T 1, T 2, T 3, T 4,anT 5. Use Kinematics an Energy conservation to make your argument. (right) ourballsofequalmassarereleasefromrestatthetopoffourfrictionlessramps,each with ifferent curvature but the same starting an ening heights. Ramp A is the most irect, Ramp B is a loop-the-loop, Ramp C goes own an then comes up, an Ramp D levels off a bit before coming own. Rank in orer, from largest to smallest, their spees v A, v B, v C an v D as they come out of each track. Next rank the time that they are on the track, T A, T C,anT D (on t worry about T B ). Use Kinematics an Energy conservation to make your argument.

2 2 Work An object experiences a force while unergoing the isplacement shown. Is the work one positive (+), negative (-), or zero (0)? A) B) C) D) E) ) G) H) A) B) C) D) E) ) G) H) Draw a free boy iagram along with a vector for the isplacement. List all the forces in the table provie along with the sign of the work one by that force on the object. 1) 2) 3) 4) 1) A rope pulls a box up. 2) You pull a box with a rope at a 45 o angle with the horizontal across a floor with friction. 3) You push a box up a frictionless ramp. 4) You throw a ball in the air an it s on its way own.

3 3 Energy Account Book A) #" B) $" %" A) A heavy object is release from rest at position 1 above a spring. It falls an contacts the spring at position 2. The spring achieves maximum compression at position 3. ill in the table below to inicate whether each of the quantities are +,, or 0. Pay careful attention to signs. change in kinetic energy (of mass + spring), KE change in gravitational potential energy (of mass + spring), PE g change in spring potential energy (of mass + spring), PE s work one by gravity on mass, W g work one by spring on mass, W s B) A weightlifter lifts a 100 kg umbbell to a height of 2 m in 3 secons. Then he hols it in place for 10 secons. This time plug in actual values in the units esire. change in umbbell kinetic energy KE [J] change in umbbell potential energy, PE g [J] work one by gravity on umbbell, W g [J] work one by man on umbbell, W s [J] Power exerte by man, P [W] from groun to 2 m holing in place

4 4 Manipulating equations or each of these situations you are either comparing between two scenarios of the same measurements (i.e. m A vs. m B )orlookingatchangesovertimeforthesamescenario(i.e. x = x f x i ). Solve for the algebraic expression that is aske. It might also help to think about the physical situation that is being consiere. Example) s = k x If k A = k B an x A =2 x B,whatis sa / sb? When the same spring is extene twice as much, the force require is ouble. sa / sb =2 A) KE = 1 2 mv2 If m A = m B /2anKE A =8 KE B,whatisv A /v B? B) PE s = 1 2 kx2 If k A =2 k B an x A = x B /2, what is PE sa / PE sb? C) PE g = mgh If h A = h B an PE ga =10 PE gb,whatism A /m B? D) E tot = KE + PE g If E tot =0,m i = m f,an h = h f h i, What is KE? E) W = x If x A =5 x B,anW A = W B, What is A / B? ) P = E t If E ia = E ib, t A = t B, E fa =2E ia,ane fb =4E ib,whatisp A /P B?

5 5 Solving Problems with Conservation of Energy or each problem follow the following steps: 1. Pick a coorinate system with an origin (this is up to you to ecie). 2. Draw separate pictures for the initial an final conition. 3. List the Knowns an Unknowns. Work out any important geometry in the problem 4. Write out the total energy at the initial an final position. 5. Solve algebra. #" $" %" R θ (left) A) You rop a mass of 2 kg from rest that is 5 m above a spring (position 1 2). The spring compresses 2 m (position 2 3). What is the spring constant of the spring? (right) B)Aboxofmassm slies aroun on a frictionless, hemispherical bowl with raius R. Suppose the cube is release at an angle θ. What is the box s spee at the bottom of the bowl?

6 [Try solving C) an D) by using the Work/Energy theorem. You might want to check that you can also solve them using Newton s secon Law an Kinematics equations.] C) D) C) A 10 kg box with an initial velocity of 5 m/s slies across a table with coefficient of kinetic friction 0.3. How much istance will it travel before it comes to a rest? D) A 100 kg box is at a height of 5 m. It slies own a ramp that is at an incline of 50 o. The coefficient of kinetic friction is What is the final velocity of the box when it reaches the bottom of the ramp?