The movement of a material point is described by the equation x = 10-16t + 18t ^ {2} Taking its mass equal to 4kg,
| April 8, 2021 | education
The movement of a material point is described by the equation x = 10-16t + 18t ^ {2} Taking its mass equal to 4kg, find the impulse in 4s and 8s after the start of the time count, as well as the force that caused this change in impulse.
x = 10 -16 * t + 18 * t ^ 2.
m = 4 kg.
t1 = 4 s.
t2 = 8 s.
p1 -?
p2 -?
F -?
V (t) = x (t) “.
V (t) = (0 – 16 * t + 18 * t ^ 2) “= – 16 +18 * 2 * t = 36 * t – 16.
V1 = 36 * 4 – 16 = 128 m / s.
V2 = 36 * 8 – 16 = 272 m / s.
p1 = m * V1.
p1 = 4 kg * 128 m / s = 512 kg * m / s.
p2 = m * V2.
p2 = 4 kg * 272 m / s = 1088 kg * m / s.
F = (p2 – p1) / (t2 – t1).
F = (1088 kg * m / s – 512 kg * m / s) / (8 s – 4 s) = 144 N.
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