(b) A block weighing 20 kg rest on a rough surface with the coefficient of kineticfriction, p=0.3. A force F=(22+ s²) N, where s is in meter, acts in the directiondepicted in Figure Q.4(b) on the block. The spring is originally unstretched andmove the block from a position s=s1 and a speed v=vy to a position s=s; and aspeed v=v2. Given that at position s/=0 the block is at rest and s2=0.5m.(i) Using the principle of work and energy, calculate speed v2(ii) Calculate the power generated to move the block to szIT k=5 N/mwwwwwwFigure Q.4(b)20°F

Given that :Block weight (mass) Coefficient of friction Force Initial position (the block is…

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2 (a) Write down the equation of motion for the point particle of mass m moving in the Kepler potential U(x) = -A/x+B/x² where x is the particle displacement in m. (b) Introduce a dissipative term in the equation of motion assuming that the dissipative force acting on a particle is proportional to the partical velocity with the coefficient of proportionality v. Write down the modified equation of motion. (c) Determine the dimensions of parameters A, B, vin SI system of units.
TIL A point-like mass is constrained to move along the z-axis only. It is attached to two springs, each of spring constant k, and each of rest length 0. One spring has one of its ends fixed at x = 0 and y = h; the other spring is fixed at one end to x = 0 and y = -h as shown in the figure below. Gravity does not act on the system. The springs do not bend but contract and extend along straight lines between their end points. y h (b) Write down the Lagrangian of the system. h (a) How many degrees of freedom does the system have? wwww (c) Write down the corresponding Euler-Lagrange equation(s). m X
A block of mass m is attached to a spring (constant k), sliding on a frictionless incline (angle theta), with respect to the horizontal. The spring begins compressed at a distance x and is released from rest. The block travels past an equilibrium point (point B) and has speed v, traveling up the plane. What equation is used to calculate the speed, v, up the plane?
A point-like mass m is constrained to move along the z-axis only. It is attached to two springs, each of spring constant k, and each of rest length 0. One spring has one of its ends fixed at x = 0 and y = h; the other spring is fixed at one end to z = 0 and y=-h as shown in the figure below. Gravity does not act on the system. The springs do not bend but contract and extend along straight lines between their end points. y m (d) Determine the equilibrium position of the system and the frequencies of small oscillations about this equilibrium position. Hint: use approximations (i.e. Taylor expansion) to simplify the equation of motion near the equilibrium position to that of a harmonic oscillator. (e) Repeat part (d) for the case where the two springs have different spring constants k₁ and k₂ and are placed at different distances on the y-axis h₁ and h₂.
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Let's say we have a spring with a constant of K= 300 N/m and this spring is attached to the incline at the top making an angle of θ=44.0° with the horizontal. Now, after we have this problem, there is a projectile that has a mass of 1 kg that is pointing up the plane. The initial position of this projectile is d = 1.3 m and it is from the end 0f a uncompressed spring. Answer the following questions: Let’s say the incline has no friction at all and given the kinetic energy for the projectile is 15 J. How much c0mpression will the spring receive? Let's say we have a coefficient of friction = 0.300 and the spring will have to c0mpress 1.10 the instant the projectile stops..in order for this to happen, what should be the initial speed of the projectile?
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A crate of mass m1 slides down a well-lubricated hill of height h, with negligible friction. At the bottom, where it is moving horizontally, it collides with another crate, of mass m2, that initially was sitting at rest and that is attached to a wall by a spring of spring constant k that initially is at its equilibrium length. Assume that the spring itself has negligible mass. a)Given that the distance d that the crates compress the spring is d=0.35 m, calculate the speed v2 of the crates immediately after the collision, in units of meters per second. Use the following values:k=950 N/mm1=2.4 kgm2=2.6 kgμ=0.49g=9.8 m/s2 b) What was the speed of the crate of mass m1 just before the collision with the second block, in meters per second? c)What is the height h of the hill, in meters?
A 4.00 kg mass on a frictionless incline plane of angle 1 degrees is released and begins sliding down the incline. At the bottom of the incline is a spring (k=20 N/m) If the mass slides 0.10 m along the incline plane before it contacts the spring, how far is the spring compressed by the mass? (round to the nearest hundredth) How would the length of the spring compression change if there was friction between the incline plane and the mass? - The spring would be compressed the same length? -The spring would be compressed more? -The spring would be compressed less?
You are working with a movie director and investigating a scene with a cowboy sliding off a tree limb and falling onto the saddle of a moving horse. The distance of the fall is several meters, and the calculation shows a high probability of injury to the cowboy from the stunt. Let's look at a simpler situation. Suppose the director asks you to have the cowboy step off a platform 2.55 m off the ground and land on his feet on the ground. The cowboy keeps his legs straight as he falls, but then bends at the knees as soon as he touches the ground. This allows the center of mass of his body to move through a distance of 0.670 m before his body comes to rest. (Center of mass will be formally defined in Linear Momentum and Collisions.) You assume this motion to be under constant acceleration of the center of mass of his body. To assess the degree of danger to the cowboy in this stunt, you wish to calculate the average force upward on his body from the ground, as a multiple of the cowboy's…
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