A spring-loaded toy gun is used to shoot a ball straight up in the air. (Eigure 1)The ball reaches a maximum height H, measured from the equilibrium position of the spring. Figure H 1 of 1 ▾ Part A The same ball is shot straight up a second time from the same gun, but this time the spring is compressed only half as far before firing. How far up does the ball go this time? Neglect friction. Assume that the spring is ideal and that the distance by which the spring is compressed is negligible compared to H. ▸ View Available Hint(s) height= Submit Provide Feedback 15] ΑΣΦ ➜ ww ? Next >
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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<HW07: Work and Mechanical Energy
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A spring-loaded toy gun is used to shoot a ball straight up
in the air. (Figure 1) The ball reaches a maximum height
H, measured from the equilibrium position of the spring.
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The same ball is shot straight up a second time from the same gun, but this time
the spring is compressed only half as far before firing. How far up does the ball go
this time? Neglect friction. Assume that the spring is ideal and that the distance by
which the spring is compressed is negligible compared to H.
▸ View Available Hint(s)
P Pearson
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Item 18
<HW07: Work and Mechanical Energy
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Figure
M
P
Two children are trying to shoot a marble of mass m into
a small box using a spring-loaded gun that is fixed on a
table and shoots horizontally from the edge of the table. (
Figure 1) The edge of the table is a height H above the
top of the box (the height of which is negligibly small),
and the center of the box is a distance d from the edge of
the table. The spring has a spring constant k. The first
child compresses the spring a distance ₁ and finds that
the marble falls short of its target by a horizontal distance
d12.
H
JUL
22
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m
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By what distance, x2, should the second child compress the spring so that the
marble lands in the middle of the box? (Assume that height of the box is
negligible, so that there is no chance that the marble will hit the side of the box
before it lands in the bottom.)
Express the distance in terms of m, k, g, H, and d.
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