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A toy is undergoing SHM on the end of a horizontal spring with force constant 310 N/m . When the toy is 0.120 m from its equilibrium position, it is observed to have a speed of 3 m/s and a total energy of 3.6 J . 1.) Find the mass of the toy.
2.) Find the amplitude of the motion.
3.) Find the maximum speed obtained by the object during its motion.

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Answer from: kratose

1) the mass of the toy is 0.304 kg

2) the amplitude of the motion is 0.1524 m

3) the maximum speed obtained by the object during its motion is 4.87 m/s

Explanation:

Given the data in the question;

force constant of spring k = 310 N/m

position of toy x = 0.120 m

speed v = 3 m/s

Total energy E = 3.6 J

let m represent mass of toy.

1.) Find the mass of the toy.

we know that; The total energy of the system equals the sum of kinetic energy of the toy and the potential energy of the spring;

E = $\frac{1}{2}$ kx² + $\frac{1}{2}$ mv²

we substitute

3.6 = ( $\frac{1}{2}$ × 310 × (0.120)² ) + ( $\frac{1}{2}$ × m × (3)² )

3.6 = 2.232 + 4.5m

3.6 - 2.232 = 4.5m

1.368 = 4.5m

m = 1.368 / 4.5

m = 0.304 kg

Therefore, the mass of the toy is 0.304 kg

2) Find the amplitude of the motion.

we know that;

E = $\frac{1}{2}$ kA²

where A is the amplitude of the motion,

we substitute

3.6 = $\frac{1}{2}$ × 310 × A²

3.6 = 155 × A²

A² = 3.6 / 155

A² = 0.0232258

A = √0.0232258

A = 0.1524 m

Therefore, the amplitude of the motion is 0.1524 m

3) Find the maximum speed obtained by the object during its motion;

we know that;

E = $\frac{1}{2}$ m $v_{max$ ²

where $v_{max$ is the maximum speed

so we substitute

3.6 = $\frac{1}{2}$ × 0.304 × $v_{max$ ²

3.6 = 0.152 × $v_{max$ ²

$v_{max$ ² = 3.6 / 0.152

$v_{max$ ² = 23.6842

$v_{max$ ² = √23.6842

$v_{max$ ² = 4.8664 ≈ 4.87 m/s

Therefore, the maximum speed obtained by the object during its motion is 4.87 m/s

Answer from: Quest

b.transmitters send radio waves, and receivers capture radio waves.

Answer from: Quest

You need to be more specific. i really don't know what a "motion map" is.you can draw a graph of an object's position, distance, displacement, speed,velocity, or acceleration versus time, or you can draw a graph of the object's x-position versus its y-position and not give any information about time at all.if the graph presents position or displacement against time, then constant velocity is a straight line . . i.e. a line that has constant slope.if the graph shows speed against time, then constant velocityis a horizontal piece of line.if the graph shows acceleration against time, then constant velocity is a piece of line that lies on the x-axis . . it's value is zero.

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A toy is undergoing SHM on the end of a horizontal spring with force constant 310 N/m . When the toy...

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