Ano ang pagkain a ng Bugtong sa Palaisipan?

A 0.29 kg particle moves in an xy plane according to x(t) = - 19 + 1 t - 3 t3 and y(t) = 20 + 7 t - 9 t2, with x and y in meters

Artist 52 [7]

Answer:

Part a)

$F = 7.76 N$

Part b)

$\theta = -137.7 degree$

Part c)

$\theta = -127.7 degree$

Explanation:

As we know that acceleration is rate of change in velocity of the object

So here we know that

$x = -19 + t - 3t^3$

$y = 20 + 7t - 9t^2$

Part a)

differentiate x and y two times with respect to time to find the acceleration

$a_x = \frac{d^2}{dt^2}(-19 + t - 3t^3)$

$a_x = \frac{d}{dt}(0 +1 - 9t^2)$

$a_x = -18t$

$a_y = \frac{d^2}{dt^2}(20 + 7t - 9t^2)$

$a_y = \frac{d}{dt}(0 +7 - 18t)$

$a_y = -18$

Now the acceleration of the object is given as

$\vec a = (-18t)\hat i + (-18)\hat j$

at t= 1.1 s we have

$\vec a = -19.8 \hat i - 18 \hat j$

now the net force of the object is given as

$\vec F = m\vec a$

$\vec F = (0.29 kg)(-19.8 \hat i - 18 \hat j)$

$\vec F = -5.74 \hat i - 5.22 \hat j$

now magnitude of the force will be

$F = \sqrt{5.74^2 + 5.22^2} = 7.76 N$

Part b)

Direction of the force is given as

$tan\theta = \frac{F_y}{F_x}$

$tan\theta = \frac{-5.22}{-5.74}$

$\theta = -137.7 degree$

Part c)

For velocity of the particle we have

$v_x = \frac{dx}[dt}$

$v_x = (0 +1 - 9t^2)$

$v_y = \frac{dy}{dt}$

$v_y = (0 +7 - 18t)$

now at t = 1.1 s

$\vec v = -9.89\hat i - 12.8 \hat j$

now the direction of the velocity is given as

$\theta = tan^{-1}(\frac{v_y}{v_x})$

$\theta = tan^{-1}(\frac{-12.8}{-9.89})$

$\theta = -127.7 degree$

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Read 2 more answers

Discuss whether any work is being done by each of the following agents and, if so, whether the work is positive or negative: (a)

Aleks04 [339]

Answer:

a) As the chicken is still, the displacement is zero, which implies that the work is zero.

b) as the person is still there is no displacement therefore the work is zero

c) Lagraua applies a vertical force and the displacement is vertical, therefore the Work is positive

d) the force of gravity is directed downwards and the displacement is upwards, therefore the angle between it is 180º and the 180º fly is -1. Consequently the lock is negative

e) when the person meticulously feels the upward force and the displacement is downward, therefore the work is negative

Explanation:

Work is defined by the expression

W = F. r

bold letters indicate vectors, we can write this expression as a module

W= F r cos θ

where is at the angle between force and displacement.

Let's apply this expression to the different cases

a) As the chicken is still, the displacement is zero, which implies that the work is zero.

b) as the person is still there is no displacement therefore the work is zero

c) Lagraua applies a vertical force and the displacement is vertical, therefore the Work is positive

d) the force of gravity is directed downwards and the displacement is upwards, therefore the angle between it is 180º and the 180º fly is -1. Consequently the lock is negative

e) when the person meticulously feels the upward force and the displacement is downward, therefore the work is negative

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