1) A block of mass m is initially held in place on a surface a distance...

 

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1) A block of mass m₁ is initially held in place on a surface a distance L. away from the edge and is attached with a rope over a frictionless pulley to a second block of mass m2. The coefficient of kinetic friction between the block with mass m₁ and the surface is μ, and the pulley has a radius R, see figure 1. If at time t = 0 the block m₁ is allowed to move and begins sliding towards the edge of the table, compute the following in terms of m₁, m₂, L, Hk, R and g: a) Draw the free-body diagram for mass m₁. b) Draw the free-body diagram for mass m₂. c) Write Newton's equation in the x and y directions for mass m₁. d) Write Newton's equation in the x and y directions for mass m2. e) Determine the acceleration of the boxes and the Tension in the rope. f) Determine the time it takes for block m₁ to reach the edge of the table. g) Determine the angular acceleration of the pulley. h) Determine the angular velocity of the pulley. i) Determine the number of revolutions the pulley makes when mass m₁reaches the edge of the table. j) Using the work energy theorem and placing the origin for the gravitational potential energy at the initial location of mass m₂, write an equation relating the work done by the friction force to the total change in the energy of the system from the moment mass m₁ is allowed to move until mass m, reaches the edge of the table. x 0 m2 m₁ Mk 2) Consider the situation depicted in Figure 2: A box of mass m = .250 kg slides down a frictionless rollercoaster. If at the beginning of the slide the box has an energy of E₁ = 100 J and a velocity of V₁ = 0, determine a) the initial height, h, of the box. Also, determine the velocities b) v and c) vc of the box. (Note: The initial energy of the system is taken with respect to a co-ordinate system with origin placed at ground level.) If at the end of the boxes journey it comes to a complete STOP by slamming into a spring with spring-constant k = 100 Nm, d) determine the amount the spring was compressed from it's equilibrium value, Ax. (Note: The height of the box when it comes to a stop against the spring is h.) Figure 2 E A=0 E h .... m: VB m VC m 3 35 2 Ax 0 m 1) A block of mass m₁ is initially held in place on a surface a distance L. away from the edge and is attached with a rope over a frictionless pulley to a second block of mass m2. The coefficient of kinetic friction between the block with mass m₁ and the surface is μ, and the pulley has a radius R, see figure 1. If at time t = 0 the block m₁ is allowed to move and begins sliding towards the edge of the table, compute the following in terms of m₁, m₂, L, Hk, R and g: a) Draw the free-body diagram for mass m₁. b) Draw the free-body diagram for mass m₂. c) Write Newton's equation in the x and y directions for mass m₁. d) Write Newton's equation in the x and y directions for mass m2. e) Determine the acceleration of the boxes and the Tension in the rope. f) Determine the time it takes for block m₁ to reach the edge of the table. g) Determine the angular acceleration of the pulley. h) Determine the angular velocity of the pulley. i) Determine the number of revolutions the pulley makes when mass m₁reaches the edge of the table. j) Using the work energy theorem and placing the origin for the gravitational potential energy at the initial location of mass m₂, write an equation relating the work done by the friction force to the total change in the energy of the system from the moment mass m₁ is allowed to move until mass m, reaches the edge of the table. x 0 m2 m₁ Mk 2) Consider the situation depicted in Figure 2: A box of mass m = .250 kg slides down a frictionless rollercoaster. If at the beginning of the slide the box has an energy of E₁ = 100 J and a velocity of V₁ = 0, determine a) the initial height, h, of the box. Also, determine the velocities b) v and c) vc of the box. (Note: The initial energy of the system is taken with respect to a co-ordinate system with origin placed at ground level.) If at the end of the boxes journey it comes to a complete STOP by slamming into a spring with spring-constant k = 100 Nm, d) determine the amount the spring was compressed from it's equilibrium value, Ax. (Note: The height of the box when it comes to a stop against the spring is h.) Figure 2 E A=0 E h .... m: VB m VC m 3 35 2 Ax 0 m

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Solutions Step 1 The schematic diagram of the system is given as The freebody diagram is given by In this diagram the weight m1g of the mass m1 is act ... View the full answer