A 0.60 kg block rests on a frictionless horizontal surface, where it is attached to a massless spring whose k-value equals 18.5 N/m. Let x be the displacement, where x = 0 is the equilibrium position and x > 0 when the spring is stretched. The block is pushed, and the spring compressed, until x, = -4.00 cm. It then is released from rest and undergoes simple harmonic motion. (a) What is the block's maximum speed (in m/s) after it is released? 1.23 x Mechanical energy is conserved in this system, and the gravitational term remains unchanged (since all motion is horizontal). Write an expression for mechanical energy that includes the kinetic energy and the potential energy of the spring. Which term(s) can be ignored when the spring is compressed and the block at rest? Which term(s) can be ignored when the block is moving at its greatest speed? Use the remaining terms, and the given quantities, to solve for the maximum speed. m/s (b) How fast is the block moving (in m/s) when the spring is momentarily compressed by 2.20 cm (that is, when x = -2.20 cm)? 1.03 x Mechanical energy is conserved in this system, and the gravitational term remains unchanged (since all motion is horizontal), Write an expression for mechanical energy that includes the kinetic energy and the potential energy of the spring. Which term(s) can be ignored when the spring is compressed and the block at rest? Use the remaining terms, and the given quantities, to solve for the maximum speed. m/s (c) How fast is the block moving (in m/s) whenever the spring is extended by 2.20 cm (that is, when passing through x = +2.20 cm)? 1.03 x You are computing the speed of the block when it has the same distance from the midpoint as it had in part (b)-but on the other side. Does any term in the energy-conservation equation depend on the sign of the displacement, x? Could this insight help you answer this question once you have correctly solved part (b)? m/s (d) Find the magnitude of the displacement (in cm) at which the block moves with one-half of the maximum speed. [x] 3.46 cm
A 0.60 kg block rests on a frictionless horizontal surface, where it is attached to a massless spring whose k-value equals 18.5 N/m. Let x be the displacement, where x = 0 is the equilibrium position and x > 0 when the spring is stretched. The block is pushed, and the spring compressed, until x, = -4.00 cm. It then is released from rest and undergoes simple harmonic motion. (a) What is the block's maximum speed (in m/s) after it is released? 1.23 x Mechanical energy is conserved in this system, and the gravitational term remains unchanged (since all motion is horizontal). Write an expression for mechanical energy that includes the kinetic energy and the potential energy of the spring. Which term(s) can be ignored when the spring is compressed and the block at rest? Which term(s) can be ignored when the block is moving at its greatest speed? Use the remaining terms, and the given quantities, to solve for the maximum speed. m/s (b) How fast is the block moving (in m/s) when the spring is momentarily compressed by 2.20 cm (that is, when x = -2.20 cm)? 1.03 x Mechanical energy is conserved in this system, and the gravitational term remains unchanged (since all motion is horizontal), Write an expression for mechanical energy that includes the kinetic energy and the potential energy of the spring. Which term(s) can be ignored when the spring is compressed and the block at rest? Use the remaining terms, and the given quantities, to solve for the maximum speed. m/s (c) How fast is the block moving (in m/s) whenever the spring is extended by 2.20 cm (that is, when passing through x = +2.20 cm)? 1.03 x You are computing the speed of the block when it has the same distance from the midpoint as it had in part (b)-but on the other side. Does any term in the energy-conservation equation depend on the sign of the displacement, x? Could this insight help you answer this question once you have correctly solved part (b)? m/s (d) Find the magnitude of the displacement (in cm) at which the block moves with one-half of the maximum speed. [x] 3.46 cm
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Simple harmonic motion
Simple harmonic motion is a type of periodic motion in which an object undergoes oscillatory motion. The restoring force exerted by the object exhibiting SHM is proportional to the displacement from the equilibrium position. The force is directed towards the mean position. We see many examples of SHM around us, common ones are the motion of a pendulum, spring and vibration of strings in musical instruments, and so on.
Simple Pendulum
A simple pendulum comprises a heavy mass (called bob) attached to one end of the weightless and flexible string.
Oscillation
In Physics, oscillation means a repetitive motion that happens in a variation with respect to time. There is usually a central value, where the object would be at rest. Additionally, there are two or more positions between which the repetitive motion takes place. In mathematics, oscillations can also be described as vibrations. The most common examples of oscillation that is seen in daily lives include the alternating current (AC) or the motion of a moving pendulum.
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Transcribed Image Text:A 0.60 kg block rests on a frictionless horizontal surface, where it is attached to a massless spring whose k-value equals 18.5 N/m.
Let x be the displacement, where x = 0 is the equilibrium position and x > 0 when the spring is stretched. The block is pushed, and
the spring compressed, until x, = -4.00 cm. It then is released from rest and undergoes simple harmonic motion.
(a) What is the block's maximum speed (in m/s) after it is released?
1.23
X
Mechanical energy is conserved in this system, and the gravitational term remains unchanged (since all motion is horizontal).
Write an expression for mechanical energy that includes the kinetic energy and the potential energy of the spring. Which
term(s) can be ignored when the spring is compressed and the block at rest? Which term(s) can be ignored when the block is
moving at its greatest speed? Use the remaining terms, and the given quantities, to solve for the maximum speed. m/s
(b) How fast is the block moving (in m/s) when the spring is momentarily compressed by 2.20 cm (that is, when x = -2.20 cm)?
1.03
Mechanical energy is conserved in this system, and the gravitational term remains unchanged (since all motion is horizontal).
Write an expression for mechanical energy that includes the kinetic energy and the potential energy of the spring. Which
term(s) can be ignored when the spring is compressed and the block at rest? Use the remaining terms, and the given
quantities, to solve for the maximum speed. m/s
(c) How fast is the block moving (in m/s) whenever the spring is extended by 2.20 cm (that is, when passing through
x= +2.20 cm)?
1.03
You are computing the speed of the block when it has the same distance from the midpoint as it had in part (b)-but on the
other side. Does any term in the energy-conservation equation depend on the sign of the displacement, x? Could this insight
help you answer this question once you have correctly solved part (b)? m/s
(d) Find the magnitude of the displacement (in cm) at which the block moves with one-half of the maximum speed.
1x1 = 3.46
cm
in i
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