Question

In: Physics

3. An 8 kg stone rests on a vertical spring of force constant 785 N /...

3. An 8 kg stone rests on a vertical spring of force constant 785 N / m. The stone is pushed down about 30 cm and released. (a) Obtain the elastic potential energy of the compressed spring just before releasing it (b) Obtain the maximum height reached by the stone (c) Obtain the velocity just after it leaves the spring.

Solutions

Expert Solution

The elastic potential energy of the spring is given as

U = ½kx² , k is spring constant and x is spring compression.

Maximum hight the stone can reach is

h =U/mg


Related Solutions

A 0.59 kg object connected to a light spring with a force constant of 19.2 N/m...
A 0.59 kg object connected to a light spring with a force constant of 19.2 N/m oscillates on a frictionless horizontal surface. If the spring is compressed 4.0 cm and released from rest. (a) Determine the maximum speed of the object. cm/s (b) Determine the speed of the object when the spring is compressed 1.5 cm. cm/s (c) Determine the speed of the object when the spring is stretched 1.5 cm. cm/s (d) For what value of x does the...
The spring (force) constant of HF is 970 N/m (1 N = 1 kg m s2...
The spring (force) constant of HF is 970 N/m (1 N = 1 kg m s2 ). (A) Calculate the fundamental frequency (expressed in units of cm-1 ) and the zero point energy (in energy units, J). (B) Earlier in the term we discussed the relationship between the energy and the position and momentum uncertainties. For the harmonic oscillator case, it would be E ≥ ((Δp) 2 / 2µ) + (1 / 2) µω2 (Δx) 2 (Equation 1) The ground...
A 11.9-kg object oscillates at the end of a vertical spring that has a spring constant...
A 11.9-kg object oscillates at the end of a vertical spring that has a spring constant of 1.80 ✕ 104 N/m. The effect of air resistance is represented by the damping coefficient b = 3.00 N · s/m. (a) Calculate the frequency of the damped oscillation. Hz (b) By what percentage does the amplitude of the oscillation decrease in each cycle? % (c) Find the time interval that elapses while the energy of the system drops to 3.00% of its...
A 2.20 kg frictionless block is attached to an ideal spring with force constant 314 n/m...
A 2.20 kg frictionless block is attached to an ideal spring with force constant 314 n/m . Initially the block has velocity -3.70 m/s and displacement 0.270 m.Find the amplitude of the motion in mFind the maximum acceleration of the block in m/s^2Find the maximum force the spring exerts on the block in n
A 0.59-kg object connected to a light spring with a force constant of 22.2 N/m oscillates...
A 0.59-kg object connected to a light spring with a force constant of 22.2 N/m oscillates on a frictionless horizontal surface. The spring is compressed 4.0 cm and released from rest. (a) Determine the maximum speed of the object. m/s (b) Determine the speed of the object when the spring is compressed 1.5 cm. m/s (c) Determine the speed of the object as it passes the point 1.5 cm from the equilibrium position. m/s (d) For what value of x...
A 0.900-kg block attached to a spring with force constant k = 1.20 N/m oscillates with...
A 0.900-kg block attached to a spring with force constant k = 1.20 N/m oscillates with an amplitude equal to half its natural length. The natural (un-stretched) length of the spring is 18.0 cm. (a) When submitting your work, sketch the figure below illustrating the position, and directly underneath that, the velocity of the mass as a function of time. Assume that x = 9.00 cm and v =0 m/s when t = 0.00 s. Label the amplitude A and...
2)A 0.520-kg object attached to a spring with a force constant of 8.00 N/m vibrates in...
2)A 0.520-kg object attached to a spring with a force constant of 8.00 N/m vibrates in simple harmonic motion with an amplitude of 10.2 cm. (Assume the position of the object is at the origin at t = 0.) (a) Calculate the maximum value of its speed. Answer must be in cm/s (b) Calculate the maximum value of its acceleration. Answer must be in cm/s2 (c) Calculate the value of its speed when the object is 8.20 cm from the...
A spring-mass system has a spring constant of 3 N/m. A mass of 2 kg is...
A spring-mass system has a spring constant of 3 N/m. A mass of 2 kg is attached to the spring, and the motion takes place in a viscous fluid that offers a resis- tance numerically equal to the magnitude of the instanta- neous velocity. If the system is driven by an external force of (12 cos 3t − 8 sin 3t) N, determine the steady-state response. (a) Find the gain function if the external force is f(t) = cos(ωt). (b)...
A particle of mass 2.00 kg is attached to a spring with a force constant of...
A particle of mass 2.00 kg is attached to a spring with a force constant of 300 N/m. It is oscillating on a horizontal frictionless surface with an amplitude of 4.00 m. A 7.00 kg object is dropped vertically on top of the 2.00 kg object as it passes through its equilibrium point. The two objects stick together. (a) Does the amplitude of the vibrating system increase or decrease as a result of the collision? decreases increases no change (b)By...
A particle of mass 4.00 kg is attached to a spring with a force constant of...
A particle of mass 4.00 kg is attached to a spring with a force constant of 300 N/m. It is oscillating on a horizontal frictionless surface with an amplitude of 5.00 m. A 9.00 kg object is dropped vertically on top of the 4.00 kg object as it passes through its equilibrium point. The two objects stick together. a) By how much does the amplitude of the vibrating system change as a result of collision? b) By how much does...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT