GROUP Assignment. A block of mass m = 680 grams is attached to a spring whose...

GROUP Assignment. A block of mass m = 680 grams is attached to a spring whose spring constant k is 65 N/m. The block is pulled a distance x = 11 cm from its equilibrium position at x = 0 on a frictionless surface and released from rest at t = 0 s. (a) What are the angular frequency ω, frequency f, and period T of the resulting motion? (b) What is the amplitude A, the maximum speed v_max, and the maximum acceleration a_max of the block?

Solutions

Expert Solution

Given : mss of block = 680 g = 0.68 Kg force constant = 65 N / m

The displacement , x = 11 cm = 0.11 m

( a ) According to Hooke's Law F = -kx

ma = -Kx since F = ma according to newton's second law

a = - K /m . x

Angular velocity , = K /m = 65 / 0.68 = 9.8 rad / s

the frequency , f = / 2 = 9.8 / ( 2 x 3.14 ) = 1.6 H_z

The time period , T = 1 /f = 1 / 1.6 = 0.64 s

( b ) As the displacement 11 cm is the maximum displacement the maximum amplitude is 11 cm.

i.e A = 11 cm.

The maximum speed , V_max = x_max

= 9.8 rad /s x 11 cm = 107.8 cm /s =1.1 m/s

The maximum acceleration = ² x_max

= 9.8 x9.8 x 11 = 1056.44 cm /s = 10.5644 m/ s = 11 m/s

genius_generous answered 5 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 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...

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 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 μk = 0.11. In the initial position, where the spring is compressed by a distance of d = 0.19 m, the mass is at...

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.

1. A block of mass m attached to a spring with spring constant k oscillates horizontally...

1. A block of mass m attached to a spring with spring constant k oscillates horizontally on a frictionless table. Its velocity is 20 cm/s when x = -5 cm. Taking m = 100 gm, and spring constant = 2.5 N/m, a) Find out the equations of position, velocity, and acceleration of the ball. Find also the total energy of the block when its velocity was 20 cm/s. b) Oscillating particles generate waves. What will be the equation of a...

A block of 0.42 kg attached to a horizontal spring whose spring constant is 130.00 N/m...

A block of 0.42 kg attached to a horizontal spring whose spring constant is 130.00 N/m has a simple harmonic motion (SHM) with an amplitude of 0.11 m. The figure above shows one complete cycle of the SHM, and the vertical green dashed line indicates the equilibrium position of the block. (d) Calculate the block 's velocity at 0.045 s. The velocity can be positive, zero or negative. Notice that the unit of angular frequency ω is rad/s, the unit...

A block of mass m= 10.0kg is attached to the end of an ideal spring. Due...

A block of mass m= 10.0kg is attached to the end of an ideal spring. Due to the weight of the block, the block remains at rest when the spring is stretched a distance h= 8.00cm from its equilibrium length. (Figure 1) The spring has an unknown spring constant k. Take the acceleration due to gravity to be g = 9.81m/s2 . What is the spring constant k? Express your answer in newtons per meter. k...

A block with a mass m = 2.12 kg is pushed into an ideal spring whose...

A block with a mass m = 2.12 kg is pushed into an ideal spring whose spring constant is k = 3580 N/m. The spring is compressed x = 0.073 m and released. After losing contact with the spring, the block slides a distance of d = 1.71 m across the floor before coming to rest. A.) Write an expression for the coefficient of kinetic friction between the block and the floor using the symbols given in the problem statement...

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...

Subjects