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Proposed Exercise: Conservation of the Linear Moment

Consider a block of M grease originally kept at rest on an inclined plane, without friction, by a block A. If a mass bullet m is fired with a velocity v against the block, getting stuck in it, find an expression for the distance d that the "block+bullet" system will move up to the position where it stops momentarily. Tip: here it is necessary to decompose the speed for the calculations

Proposed Exercise Conservation of the Linear Moment Consider a block of M grease originally kept at rest on an inclined plane without friction by a block A If a class=

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Explanation:

Momentum is conserved when there is no net external force.  So momentum is conserved in the direction parallel to the incline.

p₀ = p

m v cos θ = (m + M) vₓ

vₓ = m v cos θ / (m + M)

After the collision, energy is conserved.

PE = KE

(m+M) gh = ½ (m+M) vₓ²

gh = ½ vₓ²

h = vₓ² / (2g)

d sin θ = [m v cos θ / (m + M)]² / (2g)

d = [m v cos θ / (m + M)]² / (2g sin θ)