A spring with constant #2# #kgs^-2# is lying on the ground with one end attached to a wall. An object with a mass of #1/2# #kg# and speed of #3/5# #ms^-1# collides with and compresses the spring until it stops moving. How much will the spring compress?
The kinetic energy of the moving mass,
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Use the conservation of mechanical energy:
[ \frac{1}{2}m v^2 = \frac{1}{2}k x^2 ]
Solve for compression (x):
[ x = \sqrt{\frac{m v^2}{k}} ]
Substitute given values:
[ x = \sqrt{\frac{\frac{1}{2} \times \left(\frac{3}{5}\right)^2}{2}} ]
[ x \approx 0.346 , \text{m} ]
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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
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