A force F applied to an object of mass produces an acceleration of 3.30 m/s2. Th

Question

A force F applied to an object of mass produces an acceleration of 3.30 m/s2. The same force applied to a second object of mass m2 produces an acceleration of 2.00 m/s^2. What is the value of the ratio m_1/m_2? If m_1 and m_2 are combined, find their acceleration under the action of the force F. To model a spacecraft, a toy rocket engine is securely fastened to a large puck, which can glide with negligible friction over a horizontal surface, taken as the xy plane. The 2.00 kg puck has a velocity of 3.00 i m/s at one instant. Eight seconds later, its velocity is to be (7.00 i + 14.0 j) m/s. Assuming the rocket engine exerts a constant total horizontal force, find the components of the force. Find its magnitude.

Explanation / Answer

(1)

Given

a1 = 3.30 m/s^2

a2 = 2.0 m/s^2

Since F = m1a1 = m2 a2

a) m1/m2 = a2/a1

= 2.0 m/s^2/(3.30 m/s^2)

m1/m2 = 0.6

b) F = ( m1 + m2) a

a = F/(m1 +m2) m/s^2

____________&&&&&______&&&&&_______

Given thatthe mass of the puck is m = 2.00 Kg
The initial velocity is U=3.00i m/s
The final velocityis V = (7.00i + 14.0j) m/s
------------------------------------------------------------------------------------
Then the force F =m(V-U)/t
= (2.00Kg)((7.00i + 14.0j) m/s- 3.00i m/s) / (8s-1s)
= (2.00/ 7s) (4.00i + 14.0j) N
= (4.28i+ 12.0j) N
then the magnitue of the force is F =(4.282+12.02)1/2
= --------- N
=--------- N

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