A block of mass m = 2.5 kg is attached to a spring with spring constant...

A block of mass m = 2.5 kg is attached to a spring with spring constant k = 640 N/m. It is initially at rest on an inclined plane that is at an angle of θ = 27° with respect to the horizontal, and the coefficient of kinetic friction between the block and the plane is μ_k = 0.11. In the initial position, where the spring is compressed by a distance of d = 0.19 m, the mass is at its lowest position and the spring is compressed the maximum amount. Take the initial gravitational energy of the block as zero.

Question:

If the spring pushes the block up the incline, what distance, L in meters, will the block travel before coming to rest? The spring remains attached to both the block and the fixed wall throughout its motion?

Solutions

Expert Solution

genius_generous answered 9 months ago

Next > < Previous

Related Solutions

a block of mass m=0.10 kg attached to a spring whose spring constant is k=2.5 N/m...

a block of mass m=0.10 kg attached to a spring whose spring constant is k=2.5 N/m . At t=0.2s, the displacement x=-0.3m, and the velocity v=-2.0m/s a) find the equation of displacement as a function of time b) sketch the displacement as a function of time for the first cycle starting t=0s

A 0.5-kg mass is attached to a spring with spring constant 2.5 N/m. The spring experiences...

A 0.5-kg mass is attached to a spring with spring constant 2.5 N/m. The spring experiences friction, which acts as a force opposite and proportional to the velocity, with magnitude 2 N for every m/s of velocity. The spring is stretched 1 meter and then released. (a) Find a formula for the position of the mass as a function of time. (b) How much time does it take the mass to complete one oscillation (to pass the equilibrium point, bounce...

A block with a mass of 0.488 kg is attached to a spring of spring constant...

A block with a mass of 0.488 kg is attached to a spring of spring constant 428 N/m. It is sitting at equilibrium. You then pull the block down 5.10 cm from equilibrium and let go. What is the amplitude of the oscillation? A block with a mass of 0.976 kg is attached to a spring of spring constant 428 N/m. It is sitting at equilibrium. You then pull the block down 5.10 cm from equilibrium and let go. What...

A block with a mass M is attached to a horizontal spring with a spring constant...

A block with a mass M is attached to a horizontal spring with a spring constant k. Then attached to this block is a pendulum with a very light string holding a mass m attached to it. What are the two equations of motion? (b) What would these equations be if we assumed small x and φ? (Do note that these equations will turn out a little messy, and in fact, the two equations involve both variables (i.e. they are...

A block of mass m = 2.6kg is attached to a single spring of spring constant...

A block of mass m = 2.6kg is attached to a single spring of spring constant k = 4.4Nmand allowed to oscillate on a horizontal, frictionless surface while restricted to move in the x-direction. The equilibrium position of the block is x=0m. At time t=0s the mass is at position x=2.7m and moving with x-component of velocity vx=−6.8ms. What is the x-component of velocity at time t=1.3s? Answer in meters per second.

The displacement of a block of mass 1.280 kg attached to a spring whose spring constant...

The displacement of a block of mass 1.280 kg attached to a spring whose spring constant is 50 N/m is given by x = A cos ωt, where A = 12 cm. In the first complete cycle, find the values of x and t at which the kinetic energy is equal to one half the potential energy.

a. Consider a 1.5-kg mass of a block attached to a spring of spring constant 16.0...

a. Consider a 1.5-kg mass of a block attached to a spring of spring constant 16.0 N/m on a frictionless table. (i) At rest/At Equilibrium: The spring-mass system is at rest, the mass is at the equilibrium position. Calculate the potential energy (PEs), kinetic energy (KE) and total mechanical energy (Etot) of the spring-mass system. (ii) At rest/Displaced from Equilibrium: The mass is displaced 6 cm to the left (negative X-direction) by compressing the spring, the spring-mass system is at...

A mass-spring oscillator consists of a 3.40-kg block attached to a spring of spring constant 103...

A mass-spring oscillator consists of a 3.40-kg block attached to a spring of spring constant 103 N/m. At time t = 1.40 s, the position and the velocity of the block are x = 0.150 m and v = 3.18 m/s respectively. What is the amplitude of oscillation? What was the position of the block at t = 0? What was the speed of the block at t = 0?

A 1.40 kg block is attached to a spring with spring constant 16.5 N/m . While...

A 1.40 kg block is attached to a spring with spring constant 16.5 N/m . While the block is sitting at rest, a student hits it with a hammer and almost instantaneously gives it a speed of 43.0 cm/s . What are The block's speed at the point where x= 0.350 A?

A 1.25 kg block is attached to a spring with spring constant 18 N/m . While...

A 1.25 kg block is attached to a spring with spring constant 18 N/m . While the block is sitting at rest, a student hits it with a hammer and almost instantaneously gives it a speed of 42 cm/s What is the amplitude of the subsequent oscillations? What is the block's speed at the point where x=0.25A?

Subjects