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Problem 10: A block of mass m is located on an inclined plane that makes an angle with he horizontal. The coefficient of kinetic friction between the block and the inclined plane is ₁. The lock presses against, but is not attached to, a spring with constant k₁. When the spring is at its quilibrium position, the block is at a height h above the ground, as shown. The initial position of the lock, from which it is released, is a bit further up the inclined plane such that the spring is initially ompressed by Az. At the bottom of the inclined plane is a horizontal plane with a different oefficient of friction, μ2, for the first distance, d, after which the surface is frictionless, and the quilibrium position of a spring with constant k₂ is encountered. 0 μ₁ ₂www

Problem 10: A block of mass m is located on an inclined plane that makes an angle with he horizontal. The coefficient of kinetic friction between the block and the inclined plane is ₁. The lock presses against, but is not attached to, a spring with constant k₁. When the spring is at its quilibrium position, the block is at a height h above the ground, as shown. The initial position of the lock, from which it is released, is a bit further up the inclined plane such that the spring is initially ompressed by Az. At the bottom of the inclined plane is a horizontal plane with a different oefficient of friction, μ2, for the first distance, d, after which the surface is frictionless, and the quilibrium position of a spring with constant k₂ is encountered. 0 μ₁ ₂www

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Problem 10: A block of mass m is located on an inclined plane that makes an angle with the horizontal. The coefficient of kinetic friction between the block and the inclined plane is 1. The block presses against, but is not attached to, a spring with constant k₁. When the spring is at its equilibrium position, the block is at a height h above the ground, as shown. The initial position of the block, from which it is released, is a bit further up the inclined plane such that the spring is initially compressed by Az. At the bottom of the inclined plane is a horizontal plane with a different coefficient of friction, µ2, for the first distance, d, after which the surface is frictionless, and the equilibrium position of a spring with constant ką is encountered. V= .CK: U 0 .5% Part (a) Suppose that numeric values are chosen such that the block comes to rest before reaching the bottom of the ramp. Let z be the distance uaveled from the equilibrium position of the block towards the bottom of the ramp. Enter an expression for 2. P art (b) Suppose that the block has mass m = 2.1 kg, the angle of the plane with the horizontal is 0 = 36°, the coefficient of friction between the block and the inclined plane is p₁ = 0.35, the height of the block when the spring is at its equilibrium length is h = 0.49 m, the spring constant is k₁ = 37 N/m, and the initial compression of the spring is Az = 0.21 m. With these values, the block will reach the bottom of the ramp.. Find the speed, in meters per second, of the block when it reaches the end of the ramp. Treat the block as a point. m/s ack. μ₁ μ₂ Grade Summary Part (c) Once the block reaches the bottom, it encounters a new coefficient of friction, 2 = 0.11. What distance, x, in meters, could the block travel on this surface before stopping if no obstacles were in the way? Assume the size of the block is negligible and that it transitions smoothly from the ramp to the horizontal plane. Part (d) The block travels a distance d = 0.11 m along the surface with friction coefficient 2 = 0.11. The horizontal surface then becomes frictionless, at the equilibrium position of a spring with constant k2= 6.5 N/m. Calculate the distance, As, in meters, by which the spring is compressed as the block comes to rest.
Transcribed Image Text:Problem 10: A block of mass m is located on an inclined plane that makes an angle with the horizontal. The coefficient of kinetic friction between the block and the inclined plane is 1. The block presses against, but is not attached to, a spring with constant k₁. When the spring is at its equilibrium position, the block is at a height h above the ground, as shown. The initial position of the block, from which it is released, is a bit further up the inclined plane such that the spring is initially compressed by Az. At the bottom of the inclined plane is a horizontal plane with a different coefficient of friction, µ2, for the first distance, d, after which the surface is frictionless, and the equilibrium position of a spring with constant ką is encountered. V= .CK: U 0 .5% Part (a) Suppose that numeric values are chosen such that the block comes to rest before reaching the bottom of the ramp. Let z be the distance uaveled from the equilibrium position of the block towards the bottom of the ramp. Enter an expression for 2. P art (b) Suppose that the block has mass m = 2.1 kg, the angle of the plane with the horizontal is 0 = 36°, the coefficient of friction between the block and the inclined plane is p₁ = 0.35, the height of the block when the spring is at its equilibrium length is h = 0.49 m, the spring constant is k₁ = 37 N/m, and the initial compression of the spring is Az = 0.21 m. With these values, the block will reach the bottom of the ramp.. Find the speed, in meters per second, of the block when it reaches the end of the ramp. Treat the block as a point. m/s ack. μ₁ μ₂ Grade Summary Part (c) Once the block reaches the bottom, it encounters a new coefficient of friction, 2 = 0.11. What distance, x, in meters, could the block travel on this surface before stopping if no obstacles were in the way? Assume the size of the block is negligible and that it transitions smoothly from the ramp to the horizontal plane. Part (d) The block travels a distance d = 0.11 m along the surface with friction coefficient 2 = 0.11. The horizontal surface then becomes frictionless, at the equilibrium position of a spring with constant k2= 6.5 N/m. Calculate the distance, As, in meters, by which the spring is compressed as the block comes to rest.
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