Physics, 14.04.2020 17:52 briweaver9993

A 4.00 kg mass is moving at 4.00 m/s 45.0 degrees NORTH of WEST and a 6.00 kg mass is moving at 3.00 m/s 30.0 degrees SOUTH of EAST. Find the velocity of the center of mass, letting (a) = the east-west component, and (b) = the north-south component.

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Answer from: bommers144

(a) 0.428 m/s

(b) 0.232 m/s

Explanation:

mass, m = 4 kg

initial velocity, u = 4 m/s at 45° North of west = 4 ( - Cos 45 i + Sin 45 j)

$\overrightarrow{u}=- 2.83 \widehat{i} + 2.83 \widehat{j}$

mass, M = 6 kg

initial velocity, U = 3 m/s at 30° South of east = 3 (Cos 30 i - Sin 30 j)

$\overrightarrow{U}=2.6 \widehat{i} -1.5 \widehat{j}$

Let V is the velocity of centre of mass.

$\overrightarrow{V}=\frac{m\times \overrightarrow{u}+M\times \overrightarrow{U}}{m + M}$

$\overrightarrow{V}=\frac{4\times\left ( - 2.83 \widehat{i} +2.83 \widehat{j} \right )+ 6\times \left ( 2.6 \widehat{i} -1.5 \widehat{j} \right ) }{4 + 6}$

$\overrightarrow{V}= 0.428 \widehat{i}+0.232 \widehat{j}$

(a)

east west component of velocity of centre of mass is 0.428 m/s

(b)

north south component of velocity of centre of mass is 0.232 m/s.

Explanation:

Answer from: Quest

given data:

determine the horse power (h.p) = ?

force applied to move the box(f) = 10 pounds,

box lifted from a distance (d) = 3 feet

time taken to lift (t) = 10 sec,

the horse power is defined as amount of work required to move a load. the horse power is equal to 550 foot-pound per second

1 h.p = 550 foot-pound/second

it can also be defined as the the load that need to be move a body for certain distance in a certain amount of time.

mathematically,

h.p = (force × distance)/ time

= (10 × 3)/ 10

= 30/10

= 3 foot -pound/sec

hence, the horse power is needed to move the box is 3 foot-pound/second

important note: 1 h.p = 550 foot-pound/second = 746 watts

Answer from: Quest

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A 4.00 kg mass is moving at 4.00 m/s 45.0 degrees NORTH of WEST and a 6.00 kg mass is moving at 3.00...

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