Problem 6: A block of mass m rests against a spring with a spring constant of...
A block of mass m = 3.5 kg is attached to a spring with spring constant k = 520 N/m. It is initially at rest on an inclined plane that is at an angle of θ = 21° with respect to the horizontal, and the coefficient of kinetic friction between the block and the plane is μk = 0.16. In the initial position, where the spring is compressed by a distance of d = 0.14 m, the mass is at...
A block of mass m = 3.5 kg is on an inclined plane with a coefficient of friction μ1 = 0.31, at an initial height h = 0.53 m above the ground. The plane is inclined at an angle θ = 54°. The block is then compressed against a spring a distance Δx = 0.11 m from its equilibrium point (the spring has a spring constant of k1 = 39 N/m) and released. At the bottom of the inclined plane...
A block of mass m = 4.5 kg is attached to a spring with spring constant k = 710 N/m. It is initially at rest on an inclined plane that is at an angle of θ = 25° with respect to the horizontal, and the coefficient of kinetic friction between the block and the plane is μk=0.18. In the initial position, where the spring is compressed by a distance of d = 0.12 m, the mass is at its lowest...
A block of mass m = 3.5 kg is attached to a spring with spring constant k = 780 N/m. It is initially at rest on an inclined plane that is at an angle of θ = 28° with respect to the horizontal, and the coefficient of kinetic friction between the block and the plane is μk = 0.19. In the initial position, where the spring is compressed by a distance of d = 0.19 m, the mass is at...
A mass m is tied to an ideal spring with force constant k and rests on a frictionless surface. The mass moves along the x axis. Assume that x=0 corresponds to the relaxed position of the spring. The mass is pulled out to a position xm and released. Derive an expression for the positions at which the kinetic energy of the mass is equal to the elastic potential energy of the spring. Express your answer in terms of Xm.
d = the distance the spring compresses A block of mass M is placed on an inclined plane that makes an angle theta relative to the horizontal. The block and plane interact with friction coefficients. The angle of inclination is greater then that required for the block to slip and so once it is released, the mass begins to move. It slides a distance L until it makes contact with a spring with stiffness k. The spring compresses a distance...
A 195 g block is pressed against a spring of force constant 1.60 kN/m until the block compresses the spring 10.0 cm. The spring rests at the bottom of a ramp inclined at 60.0° to the horizontal. Using energy considerations, determine how far up the incline in m) the block moves from its initial position before it stops under the following conditions. (a) if the ramp exerts no friction force on the block (b) if the coefficient of kinetic friction is 0.360...
A block of mass m = 6.14 kg is attached to a spring with spring constant k = 1682 N/m and rests on a frictionless surface. The block is pulled, stretching the spring a distance of 0.135 m, and is held still. The block is then released and moves in simple harmonic motion about the equilibrium position. (Assume that the block is stretched in the positive direction.) (b) Where is the block located 3.24 s after it is released? (Give...
A block of mass m sits at rest against a spring, which has spring constant k and is compressed an amount of deltax from its equilibrium length. The spring is released, and the block slides along the smooth ground before reaching a ramp that makes an angle theta with respect to the ground. a) What is the maximum distance along the length of the ramp that the block will slide? GIve your answer in terms of the variables given. b)...
A 195 g block is pressed against a spring of force constant 1.50 kN/m until the block compresses the spring 10.0 cm. The spring rests at the bottom of a ramp inclined at 60.0° to the horizontal. Using energy considerations, determine how far up the incline (in m) the block moves from its initial position before it stops under the following conditions. (a) if the ramp exerts no friction force on the block m (b) if the coefficient of kinetic...