A $ 4.0 $ $ \text{kg} $ block is held in place against a spring with spring constant $ 1100 $ $ \text{N/m} $. The spring is compressed $ 25 $ $ \text{cm} $ from its equilibrium position. After release, the block slides without friction along a track that first contains a vertical circular loop of radius $ 20 $ $ \text{cm} $ and then continues up a straight incline that makes an angle of $ 20^{\circ} $ with the horizontal, as shown in Figure $ 1 $. Assume friction between the block and the track is negligible throughout the motion.
Figure 1. Spring launches block through loop then up a $ 20^{\circ} $ incline.

Question

A $ 4.0 $ $ \text{kg} $ block is held in place against a spring with spring constant $ 1100 $ $ \text{N/m} $. The spring is compressed $ 25 $ $ \text{cm} $ from its equilibrium position. After release, the block slides without friction along a track that first contains a vertical circular loop of radius $ 20 $ $ \text{cm} $ and then continues up a straight incline that makes an angle of $ 20^{\circ} $ with the horizontal, as shown in Figure $ 1 $. Assume friction between the block and the track is negligible throughout the motion.
Figure 1. Spring launches block through loop then up a $ 20^{\circ} $ incline.(a) Calculate the speed of the block at the top of the loop.
, (b) Calculate the normal force exerted on the block by the track when the block is at the top of the loop.
, (c) Calculate the distance, $ D $, that the block slides up the incline before coming to rest.
:

Jason · Accepted Answer

$3.06\,\text{m/s}$
$1.48\times10^{2}\,\text{N}$
$2.56\,\text{m}$

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