Collisions & Motion (Momentum & Energy) Video Lessons

Concept

Problem: A baseball of mass m1 = 0.37 kg is thrown at another ball hanging from the ceiling by a length of string L = 1.45 m. The second ball m2 = 0.72 kg is initially at rest while the baseball has an initial horizontal velocity of V1 = 4.5 m/s. After the collision the first baseball falls straight down (no horizontal velocity.) m1 = 0.37 kgm2 = 0.72 kgL = 1.45 mV1 = 4.5 m/sPart (a) Select an expression for the magnitude of the closest distance from the ceiling the second ball will reach d. Schematic Choice:a) d=(m1V1)22m22gb) d=L-V122gc) d=L-m1V12m2gd) d=L-(m1V1)22m22gPart (b) What is the angle that the string makes with the vertical at the highest point of travel in degrees? Numeric: A numeric value is expected and not an expression.θ = _____________

FREE Expert Solution

In this problem, we have collisions, kinetic, and gravitational potential energy.

Conservation of momentum:

$\overline{){{\mathbf{m}}}_{{\mathbf{1}}}{{\mathbf{v}}}_{{\mathbf{01}}}{\mathbf{+}}{{\mathbf{m}}}_{{\mathbf{2}}}{{\mathbf{v}}}_{{\mathbf{02}}}{\mathbf{=}}{{\mathbf{m}}}_{{\mathbf{1}}}{{\mathbf{v}}}_{\mathbf{f}\mathbf{1}}{\mathbf{+}}{{\mathbf{m}}}_{{\mathbf{2}}}{{\mathbf{v}}}_{\mathbf{f}\mathbf{2}}}$

Conservation of energy:

$\overline{){{\mathbf{K}}}_{{\mathbf{0}}}{\mathbf{+}}{{\mathbf{U}}}_{{\mathbf{0}}}{\mathbf{+}}{{\mathbf{W}}}_{{\mathbf{nc}}}{\mathbf{=}}{{\mathbf{K}}}_{{\mathbf{f}}}{\mathbf{+}}{{\mathbf{U}}}_{{\mathbf{f}}}}$ where Wnc is the work done by non-conservative forces such as friction.

Height of pendulum:

$\overline{){\mathbf{h}}{\mathbf{=}}{\mathbf{L}}{\mathbf{-}}{\mathbf{L}}{\mathbf{c}}{\mathbf{o}}{\mathbf{s}}{\mathbf{\theta }}}$

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Problem Details

A baseball of mass m1 = 0.37 kg is thrown at another ball hanging from the ceiling by a length of string L = 1.45 m. The second ball m2 = 0.72 kg is initially at rest while the baseball has an initial horizontal velocity of V1 = 4.5 m/s. After the collision the first baseball falls straight down (no horizontal velocity.)

m1 = 0.37 kg
m2 = 0.72 kg
L = 1.45 m
V1 = 4.5 m/s

Part (a) Select an expression for the magnitude of the closest distance from the ceiling the second ball will reach d

Schematic Choice:

Part (b) What is the angle that the string makes with the vertical at the highest point of travel in degrees? Numeric: A numeric value is expected and not an expression.

θ = _____________