At the instant the displacement of a 2.00 kg object relative to the origin is d^

Question

At the instant the displacement of a 2.00 kg object relative to the origin is d^rightarrow = (2.00 m) i^hat + (4.00 m) j^hat - (3.00 m) k^hat, its velocity is V^rightarrow = (1.52 m/s)i^hat + (6.09 m/s) j^hat + (2.33 m/s) k^hat and it is subject to a force F^rightarrow = (868 N)i^hat - (8.74 N) j^hat + (6.73 N) k^hat. Find the acceleration of the object ((a), (b) and (c) for i^hat, j^hat and k^hat components respectively), the angular momentum of the object about origin ((d), (e) and (f) for i^hat, j^hat and k^hat components respectively), the torque about the origin acting on the object ((g), (h) and (i) for i^hat, j^hat and k^hat components respectively), and (j) the angle between the velocity of the object and force acting on the object. Number _________ units Number _________ units Number _________ units Number _________ units Number _________ units

Explanation / Answer

here,

d = 2 m i + 4 m j - 3 m k

v = ( 1.52 i + 6.09 j + 2.33 k ) m/s

F = ( 8.68 i - 8.74 j + 6.73 k) N

the accelration , a = F/m

a = (4.34 i - 4.37 j + 3.365 k) m/s^2

a )

the x component is 4.34 m/s^2

b)

y componennt is 4.37 m/s^2

c)

the z component is 3.365 m/s^2

d)

torque , T = d X F

T = ( 2 m i + 4 m j - 3 m k) X (8.68 i - 8.74 j + 6.73 k )

T = ( - 17.48 k - 13.46 j - 34.72 k + 26.92 i - 26.04 j - 26.22 i ) N.m

T = (0.7 i - 39.5 j - 52.2) N.m

the x component of torque is 0.7 N.m

e)

the y component of torque is - 39.5 N.m

f)

the z component of torque is - 52.2 N.m

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