Problem 1: Consider the forces shown in the figure. Part (a) Find the magnitude ofthe force Fl shown in the figure in Newtons. Numeric : A numeric value is expected and not an expression. Part (b) Find the magnitude of the force F2 shown in the figure in Newtons. N umeric : A numeric value is expected and not an expression. Problem 2: A block with a mass of m = 11 kg rests on a frictionless surface and is subject to two forces acting on it. The first force is directed in the negative x-direction with a magnitude of Fl = 8.5 N. The second has a magnitude of = 18 N and acts on the body at an angle = 110 measured from horizontal, as shown. Part (a) Please select the correct free body diagram from the choices below. SchematicChoice 0 = 20 N 350 172 0 Free-body diagram Part (b) Write an expression for the component of net force, F netN in the x-direction, in terms of the variables given in the problem statement. Expression net,x Select from the variables below to write your expression. Note that all variables may not be required. cos(O), sinp), sin(O), tanp), tan(O), u, P, O, d, Fl, 172, g, m, t Part (c) Write an expression for the magnitude of the normal force, FN, acting on the block, in terms of 172, g, and the other variables of the problem. Assume that the surface it rests on is rigid. Expression Select from the variables below to write your expression. Note that all variables may not be required. cos(O), sinp), sin(O), tanp), tan(O), u, P, O, d, Fl, F2, g, m, t Part (d) Find the block's acceleration in the x-direction, ax, in meters per second squared. N umeric : A numeric value is expected and not an expression. Problem 3: A toy car rolls down a ramp at a constant velocity. The car's mass is m = 1.1 kg and the ramp makes an angle of = 11 degrees with respect to the horizontal. Assume the rolling resistance is negligible. Part (a) What is the magnitude of the car's acceleration, a in m/s2? N umeric : A numeric value is expected and not an expression. Part (b) What is the numeric value for the sum of the forces in the x-direction, EFx, in Newtons? Numeric : A numeric value is expected and not an expression. Part (c) Assuming the car experiences only air resistance in opposition to its motion, with magnitude F Write an expression for the sum of the forces in the x-direction using the acceleration due to gravity, g, and the variables provided. Expression Select from the variables below to write your expression. Note that all variables may not be required. cos(u), cos(O), sin(u), sinp), sin(O), u, p, O, d, Fr, g, h, m, t Part (d) What is the magnitude of the force caused by air resistance, Fr in Newtons? (Maintain the assumption that the car's velocity is constant.) N umeric : A numeric value is expected and not an expression. Fr Problem 4: Braces are used to apply forces to teeth to realign them. Shown in this figure are the tensions applied by the wire to the protruding tooth. Randomized Variables T=22.5N -I-go- What is the magnitude of the net force that is exerted on the tooth (in N) if the tension in the wire is 22.5 N? N umeric : A numeric value is expected and not an expression. F Problem 5: A crate of mass m =40.1 kg is on a horizontal surface. Assume there is no friction between the crate and the surface. Two forces with magnitude F =10.1 N are applied to the crate, as shown. One force is horizontal, and the other makes and angle of p 20.1 0 with horizontal, as shown. Part (a) Write an expression for the magnitude of the acceleration of the crate in terms of F, m, and p. Expression Select from the variables below to write your expression. Note that all variables may not be required. cos(u), cos(O), sin(u), sinp), sin(O), F, 7, O, d, F, g, h, m, n Part (b) What is the magnitude of the acceleration of the crate in m/s ? N umeric : A numeric value is expected and not an expression. m/s2 Problem 6: A chandelier hangs h = 0.52 m down from two chains of equal length. The chains are separated from one another by a length L = 0.25 m at the ceiling. The chandelier has a mass of m = 11 kg. Randomized Variables h = 0.52 m L = 0.25 m m = 11 kg Part (a) Choose the correct Free Body Diagram given the gravitational force, F the force exerted by the chains, FT, and the normal force, FN. SchematicChoice Part (b) What is the angle, 9 in degrees, between one of the chains and the vertical where it contacts the chandelier? N umeric : A numeric value is expected and not an expression. Part (c) Write an expression for Ftv the magnitude of the y-component of the tension in one chain, in terms of the given information and variables available in the palette. Expression Select from the variables below to write your expression. Note that all variables may not be required. cos(O), sinp), sin(O), u, B, O, a, b, d, g, i, j, m, t Part (d) Using your previous results, find the tension, FT in Newtons, in one chain. N umeric : A numeric value is expected and not an expression. Problem 7: A crate of mass m = O. 75 kg is on a frictionless incline that makes an angle of 9 = 20.1 degrees with horizontal. A force of magnitude P = 7.01 N is applied to the crate in a direction parallel and up the incline, as shown. Part (a) Write an expression for the acceleration ax of the crate, where positive x is up the incline. Your answer should be in terms of m, P, O, and g. Expression ax Select from the variables below to write your expression. Note that all variables may not be required. cos(u), cos(O), sin(u), sinp), sin(O), B, 7, O, d, g, h, m, n, P Part (b) What is the acceleration ofthe crate in m/s in the x direction defined in part (a)? N umeric : A numeric value is expected and not an expression. Part (c) What is the direction of the net force on the crate? MultipleChoice 1) 2) 3) 4) Down the incline Perpendicular to the incline Up the incline It is not possible to say based on the information known. Part (d) What is the direction of the velocity of the crate? MultipleChoice 1) Down the incline 2) It is not possible to say based on the information known. 3) Up the incline Problem 8: A horizontal force of magnitude F = 45 N pushes on a block of mass m 4.01 kg. The block is on a frictionless incline that makes and angle O = 30.1 degrees with horizontal. Part (a) Write an expression for the acceleration ax of the block, taking up the ramp to be the positive x direction. Express your answer in terms of F, m, O, and g (9.80 m/s2). Expression Select from the variables below to write your expression. Note that all variables may not be required. cos(u), cos(O), sin(u), sinp), sin(O), B, 7, O, d, F, g, h, m, n Part (b) What is the acceleration of the block in units of meters per seconds squared? N umeric : A numeric value is expected and not an expression. m/ s2 ax Problem 9: The diagram shows a crate of mass m 2 kg on a frictionless inclined plane that makes an angle, O 0 , with the horizontal. A coordinate system is provided. A force of magnitude F , parallel to and directed up the plane, is applied to the crate. The crate moves up the plane with constant velocity. In numeric responses, use 9.80 m/s2 for the acceleration due to gravity. Part (a) Write an expression for EFT, the net force in the a: direction. Your expression should be in terms of F , m, g, and O. Expression Select from the variables below to write your expression. Note that all variables may not be required. cos(u), cos(O), sin(u), sinp), sin(O), y, O, d, F, g, m, n, q, S Part (b) What is the numeric value, in newtons, of the applied force, F? N umeric : A numeric value is expected and not an expression. Problem 10: A contestant in a winter sporting event pushes an m kg block of ice across a frozen lake by applying a force F at an angle O below the horizontal as shown. Assume that the coefficient of static friction for ice on ice is 0.0300, and the coefficient of kinetic friction for the same is 0.0100. Let to the right be the positive x direction and up be the positive y direction for your equations. Part (a) Please use the interactive area below to draw a free body diagram to represent the situation when the contestant is pushing, but the force is not yet sufficient to start the block sliding. Use Fs for the force of static friction and Fk for the force of kinetic friction if they are needed for your free body diagram. FBI) Force Labels: Angle Labels: En, Fs, Fg, F, g, Fk, a, v 45, o, 90, 135, 180, 225, 270, 315, o Part (b) Enter an expression for the net force in the vertical direction, EF . Your expression may include the mass, m, the acceleration due to gravity, g, the normal force, FN, the applied force, F, and the angle of the applied force below the horizontal, 0. Expression Select from the variables below to write your expression. Note that all variables may not be required. cos(u), cos(O), sin(u), sinp), sin(O), y, 11K, PS, O, F, FN, g, m, n Part (c) Enter an expression for the magnitude of the the normal force, FN. Your expression may include the mass, m, the acceleration due to gravity, g, the applied force, F, and the angle of the applied force below the horizontal, 0. Expression Select from the variables below to write your expression. Note that all variables may not be required. cos(u), cos(O), sin(u), sinp), sin(O), y, 11K, PS, O, c, F, g, m, n Part (d) Enter an expression for the magnitude of the applied force, F, at the threshold where static friction is at its maximum value. Your expression may include the mass, m, the acceleration due to gravity, g, the angle of the applied force above the horizontal, 0, and appropriate coefficients of friction. The friction coefficients are and uS. Expression Select from the variables below to write your expression. Note that all variables may not be required. cos(u), cos(O), sin(u), sinp), sin(O), y, 11K, PS, O, F, g, m, n, v Part (e) Obtain a numeric value, in newtons, for the magnitude of the maximum applied force, F, consistent with static friction when the force makes an angle 150 below the horizontal and the mass of the block is 25 kg. N umeric : A numeric value is expected and not an expression. Part (f) Please use the interactive area below to draw a best free body diagram to represent the situation when the block has started to accelerate from rest due to the contestant pushing on it. Use Fs for the force of static friction and Fk for the force ofkinetic friction if they are needed for your free body diagram. FBI) Force Labels: En, Fk, Fg, F, g, Fs, a, v Angle Labels: 45, O, 90, 135, 180, 225, 270, 315, O Problem 1: Consider the forces shown in the figure. Part (a) Find the magnitude ofthe force Fl shown in the figure in Newtons. Numeric : A numeric value is expected and not an expression. Part (b) Find the magnitude of the force F2 shown in the figure in Newtons. N umeric : A numeric value is expected and not an expression. Problem 2: A block with a mass of m = 11 kg rests on a frictionless surface and is subject to two forces acting on it. The first force is directed in the negative x-direction with a magnitude of Fl = 8.5 N. The second has a magnitude of = 18 N and acts on the body at an angle = 110 measured from horizontal, as shown. Part (a) Please select the correct free body diagram from the choices below. SchematicChoice 0 = 20 N 350 172 0 Free-body diagram Part (b) Write an expression for the component of net force, F netN in the x-direction, in terms of the variables given in the problem statement. Expression net,x Select from the variables below to write your expression. Note that all variables may not be required. cos(O), sinp), sin(O), tanp), tan(O), u, P, O, d, Fl, 172, g, m, t Part (c) Write an expression for the magnitude of the normal force, FN, acting on the block, in terms of 172, g, and the other variables of the problem. Assume that the surface it rests on is rigid. Expression Select from the variables below to write your expression. Note that all variables may not be required. cos(O), sinp), sin(O), tanp), tan(O), u, P, O, d, Fl, F2, g, m, t Part (d) Find the block's acceleration in the x-direction, ax, in meters per second squared. N umeric : A numeric value is expected and not an expression. Problem 3: A toy car rolls down a ramp at a constant velocity. The car's mass is m = 1.1 kg and the ramp makes an angle of = 11 degrees with respect to the horizontal. Assume the rolling resistance is negligible. Part (a) What is the magnitude of the car's acceleration, a in m/s2? N umeric : A numeric value is expected and not an expression. Part (b) What is the numeric value for the sum of the forces in the x-direction, EFx, in Newtons? Numeric : A numeric value is expected and not an expression. Part (c) Assuming the car experiences only air resistance in opposition to its motion, with magnitude F Write an expression for the sum of the forces in the x-direction using the acceleration due to gravity, g, and the variables provided. Expression Select from the variables below to write your expression. Note that all variables may not be required. cos(u), cos(O), sin(u), sinp), sin(O), u, p, O, d, Fr, g, h, m, t Part (d) What is the magnitude of the force caused by air resistance, Fr in Newtons? (Maintain the assumption that the car's velocity is constant.) N umeric : A numeric value is expected and not an expression. Fr Problem 4: Braces are used to apply forces to teeth to realign them. Shown in this figure are the tensions applied by the wire to the protruding tooth. Randomized Variables T=22.5N -I-go- What is the magnitude of the net force that is exerted on the tooth (in N) if the tension in the wire is 22.5 N? N umeric : A numeric value is expected and not an expression. F Problem 5: A crate of mass m =40.1 kg is on a horizontal surface. Assume there is no friction between the crate and the surface. Two forces with magnitude F =10.1 N are applied to the crate, as shown. One force is horizontal, and the other makes and angle of p 20.1 0 with horizontal, as shown. Part (a) Write an expression for the magnitude of the acceleration of the crate in terms of F, m, and p. Expression Select from the variables below to write your expression. Note that all variables may not be required. cos(u), cos(O), sin(u), sinp), sin(O), F, 7, O, d, F, g, h, m, n Part (b) What is the magnitude of the acceleration of the crate in m/s ? N umeric : A numeric value is expected and not an expression. m/s2 Problem 6: A chandelier hangs h = 0.52 m down from two chains of equal length. The chains are separated from one another by a length L = 0.25 m at the ceiling. The chandelier has a mass of m = 11 kg. Randomized Variables h = 0.52 m L = 0.25 m m = 11 kg Part (a) Choose the correct Free Body Diagram given the gravitational force, F the force exerted by the chains, FT, and the normal force, FN. SchematicChoice Part (b) What is the angle, 9 in degrees, between one of the chains and the vertical where it contacts the chandelier? N umeric : A numeric value is expected and not an expression. Part (c) Write an expression for Ftv the magnitude of the y-component of the tension in one chain, in terms of the given information and variables available in the palette. Expression Select from the variables below to write your expression. Note that all variables may not be required. cos(O), sinp), sin(O), u, B, O, a, b, d, g, i, j, m, t Part (d) Using your previous results, find the tension, FT in Newtons, in one chain. N umeric : A numeric value is expected and not an expression. Problem 7: A crate of mass m = O. 75 kg is on a frictionless incline that makes an angle of 9 = 20.1 degrees with horizontal. A force of magnitude P = 7.01 N is applied to the crate in a direction parallel and up the incline, as shown. Part (a) Write an expression for the acceleration ax of the crate, where positive x is up the incline. Your answer should be in terms of m, P, O, and g. Expression ax Select from the variables below to write your expression. Note that all variables may not be required. cos(u), cos(O), sin(u), sinp), sin(O), B, 7, O, d, g, h, m, n, P Part (b) What is the acceleration ofthe crate in m/s in the x direction defined in part (a)? N umeric : A numeric value is expected and not an expression. Part (c) What is the direction of the net force on the crate? MultipleChoice 1) 2) 3) 4) Down the incline Perpendicular to the incline Up the incline It is not possible to say based on the information known. Part (d) What is the direction of the velocity of the crate? MultipleChoice 1) Down the incline 2) It is not possible to say based on the information known. 3) Up the incline Problem 8: A horizontal force of magnitude F = 45 N pushes on a block of mass m 4.01 kg. The block is on a frictionless incline that makes and angle O = 30.1 degrees with horizontal. Part (a) Write an expression for the acceleration ax of the block, taking up the ramp to be the positive x direction. Express your answer in terms of F, m, O, and g (9.80 m/s2). Expression Select from the variables below to write your expression. Note that all variables may not be required. cos(u), cos(O), sin(u), sinp), sin(O), B, 7, O, d, F, g, h, m, n Part (b) What is the acceleration of the block in units of meters per seconds squared? N umeric : A numeric value is expected and not an expression. m/ s2 ax Problem 9: The diagram shows a crate of mass m 2 kg on a frictionless inclined plane that makes an angle, O 0 , with the horizontal. A coordinate system is provided. A force of magnitude F , parallel to and directed up the plane, is applied to the crate. The crate moves up the plane with constant velocity. In numeric responses, use 9.80 m/s2 for the acceleration due to gravity. Part (a) Write an expression for EFT, the net force in the a: direction. Your expression should be in terms of F , m, g, and O. Expression Select from the variables below to write your expression. Note that all variables may not be required. cos(u), cos(O), sin(u), sinp), sin(O), y, O, d, F, g, m, n, q, S Part (b) What is the numeric value, in newtons, of the applied force, F? N umeric : A numeric value is expected and not an expression. Problem 10: A contestant in a winter sporting event pushes an m kg block of ice across a frozen lake by applying a force F at an angle O below the horizontal as shown. Assume that the coefficient of static friction for ice on ice is 0.0300, and the coefficient of kinetic friction for the same is 0.0100. Let to the right be the positive x direction and up be the positive y direction for your equations. Part (a) Please use the interactive area below to draw a free body diagram to represent the situation when the contestant is pushing, but the force is not yet sufficient to start the block sliding. Use Fs for the force of static friction and Fk for the force of kinetic friction if they are needed for your free body diagram. FBI) Force Labels: Angle Labels: En, Fs, Fg, F, g, Fk, a, v 45, o, 90, 135, 180, 225, 270, 315, o Part (b) Enter an expression for the net force in the vertical direction, EF . Your expression may include the mass, m, the acceleration due to gravity, g, the normal force, FN, the applied force, F, and the angle of the applied force below the horizontal, 0. Expression Select from the variables below to write your expression. Note that all variables may not be required. cos(u), cos(O), sin(u), sinp), sin(O), y, 11K, PS, O, F, FN, g, m, n Part (c) Enter an expression for the magnitude of the the normal force, FN. Your expression may include the mass, m, the acceleration due to gravity, g, the applied force, F, and the angle of the applied force below the horizontal, 0. Expression Select from the variables below to write your expression. Note that all variables may not be required. cos(u), cos(O), sin(u), sinp), sin(O), y, 11K, PS, O, c, F, g, m, n Part (d) Enter an expression for the magnitude of the applied force, F, at the threshold where static friction is at its maximum value. Your expression may include the mass, m, the acceleration due to gravity, g, the angle of the applied force above the horizontal, 0, and appropriate coefficients of friction. The friction coefficients are and uS. Expression Select from the variables below to write your expression. Note that all variables may not be required. cos(u), cos(O), sin(u), sinp), sin(O), y, 11K, PS, O, F, g, m, n, v Part (e) Obtain a numeric value, in newtons, for the magnitude of the maximum applied force, F, consistent with static friction when the force makes an angle 150 below the horizontal and the mass of the block is 25 kg. N umeric : A numeric value is expected and not an expression. Part (f) Please use the interactive area below to draw a best free body diagram to represent the situation when the block has started to accelerate from rest due to the contestant pushing on it. Use Fs for the force of static friction and Fk for the force ofkinetic friction if they are needed for your free body diagram. FBI) Force Labels: En, Fk, Fg, F, g, Fs, a, v Angle Labels: 45, O, 90, 135, 180, 225, 270, 315, O Part (g) Obtain an expression for the acceleration of the block corresponding to the free body diagram from part (O. Your expression may include the mass, m, the acceleration due to gravity, g, the applied force, F, the angle of the applied force below the horizontal, 0, and appropriate coefficients of friction. The friction coefficients are and gs. Expression Select from the variables below to write your expression. Note that all variables may not be required. cos(u), cos(O), sin(u), sinp), sin(O), y, 11K, PS, O, c, F, g, m, n Part (h) Obtain a numeric value for the acceleration, a, in meters per squared seconds, when the mass of the block is 25 kg and the angle ofthe rope is 150 below the horizontal. For the magnitude of the applied force, use the threshold value obtained in part (e). N umeric : A numeric value is expected and not an expression. 2 m/s All 2023 TN LLC