A toy rocket engine is securely fastened to a large puck that can glide with neg

Question

A toy rocket engine is securely fastened to a large puck that can glide with negligible friction over a horizontal surface, taken as the xy plane. The 4.70-kg puck has a velocity of 1.10 m/s at one instant. Eight seconds later, its velocity is (7.00 + 9.0) m/s.

(a) Assuming the rocket engine exerts a constant horizontal force, find the components of the force.

(b) Find its magnitude.

Step 1.

The apparatus described is good for demonstrating how a rocket works. The puck is gaining velocity directed into the first quadrant, so that both components of the net force on it are positive and at least one newton in size, as is the magnitude of the force.

We solve a motion problem to find the acceleration of the puck. The only horizontal force is the force exerted by the rocket engine, which we find from Newton's second law. Then the Pythagorean theorem gives the magnitude of the force. We will use two models: the object under constant acceleration and the object under net force.

m/s2

= t

= 1 + 2 m/s 3 m/s 8.00 s

= 4 + 5 m/s 8.00 s

= 6 + 7

m/s2

Explanation / Answer

data given -

initial velocity, u = 1.10 i

final velocity, v = 7 i + 9 j

time taken, t = 8 sec

suppose acceleration in horizontal direction is a1 and in vertical is a2-

v = u + at

7 i + 9 j = 1.10 i + (a1 + a2) 8

7 i + 9 j + 1.10 i + 8 a1 + 8 a2

a1 + a2 = (5.9 i + 9 j)/8

a1 + a2 = 0.74 i + 1.125 j

so a1 = 0.74 m/sec2

a2 = 1.125 m/sec2

so net force, F = m[a12 + a22]

F = 4.70[0.742 + 1.1252]

F = 4.70*1.265

F = 5.95 N

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