(10%) Problem 9: Consider the 61 kg ice skater being pushed by two others shown in the figure. The coefficient of static friction is My=0.4 and kinetic is uk=0.02. Randomized Variables m = 61 kg F 1 = 246 N Free-body diagram F2 = 173 N F. (a) (b) 25% Part (a) Find the magnitude of Ftot, the total force exerted on her by the others, given that the magnitudes F1 and F2 are 246 N and 173 N, respectively in Newtons. F tot = sin() cos() tan() 7 8 9 HOME cotan() asin acos() 4 5 6 atan() acotan() sinh() 2 3 cosh( tanh() cotanh() + 0 END Degrees O Radians VO BACKSPACE DEL CLEAR Submit Hint Feedback I give up! Hints: 5% deduction per hint. Hints remaining: 2 Feedback: 5% deduction per feedback. 4 25% Part (b) Find the direction of Ftot (in degrees relative to the horizontal), the total force exerted on her by the others, given that the magnitudes F1 and F2 are 246 N and 173 N, respectively. 4 25% Part (c) What is the maximum value of the static friction force, in Newtons, that can act on the skater before she moves? 4 25% Part (d) What is her acceleration assuming she is already moving in the direction of Ftot in m/s?(10%) Problem 3: A block with a mass of m = 1.5 kg rests on a wooden plank. The coefcient of static friction between the block and the plank is [LS = 0.42. One end of the board is attached to a hinge so that the other end can be lifted forming an angle, 0, with respect to the ground. Assume the x-axis is along the plank as shown in the gure. A 17 % Part (a) Please use the interactive area below to draw the Free Body Diagram for this block, assuming it is in static equilibrium. If necessary, use F s for the force of static friction, and Fk for the force of kinetic friction. 5 17 % Part (b) Assuming the x-direction is along the plank as shown, nd an expression for the magnitude of the force of gravity in the y-direction F 5 gy perpendicular to the plank in terms of given quantities and variables available in the palette. A 17 % Part (c) Write an expression for the magnitude of the maximum friction force along the surface, F s, in terms of given quantities and variables available in the palette. E 3 17% Part ((1) Assuming the static friction is maximized, write an expression, using only the given parameters and variables available in the palette, for the sum of the forces along the plank, ZFx. 6 17 % Part (e) Write an expression for the maximum angle, 0m, that the board can make with respect to the horizontal before the block starts moving: (Write in terms of the given parameters and variables available in the palette .)_ D & 17% Part (f) Solve numeric\" " \" maximum angle, 0m, in degrees. 59559.95\" 0\(10%) Problem 6: A spring with a spring constant of k = 157 N/m is initially compressed by a block a distance d = 031 In. The block is on a horizontal surface with coefcient of kinetic friction . ,uk, static friction ,us, and has a mass of m = 6 kg. 'U"$"'hd length *" i A 25 % Part (a) Assuming the block is released from the initial position and begins to move to the right, please use the interactive area below to draw the Free Body Diagram for the block. Use F sp as the spring force. If necessary, use F s for the force of static friction and F k as the force of kinetic friction. i A 25 % Part (b) Assuming the block is released from the initial position and begins to move to the right, input an expression for the sum of the forces in the xdirection in the conguration shown above, using the variables provided. 2 A 25 % Part (c) How large would the coefcient of static friction us need to be to keep the block from moving? 9 A 25 % Part ((1) Assuming the block has just begun to move and the coefcient of kinetic friction is [4k = 0.2, what is the block's acceler: tion in meters per square second? a=| sin() cosO tan() n ( 7 8 9 cotan() asin() acos() E 4 5 6 atanO acotanO sinh() 1 2 3 cosh() tanh() cotanh() + - 0 ODegrees 0 Radians J0 (10%) Problem 8: Consider a spherical bacterium, with radius 0.95 um , falling in water at 20 C. Find the terminal speed of the spherical bacterium in meters per second, ignoring the buoyant force on the bacterium and assuming Stokes' 1 ww for the viscous force. You will first need to note that the drag force is equal to the weight at terminal velocity. Take the density of the bacterium to be 1.5 x 10' kg/m3. The viscosity of water at 20 C is 1.002 x 10-3 kg/m's and the density is 998 kg/m3. V = sin() cos() tan() 7 8 9 HOME cotan() asin() acos() E A 4 5 6 atan() acotan() sinh() 2 3 cosh() tanh() cotanh() + 0 END Degrees O Radians VO BACKSPACE DEL CLEAR