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 4.60-kg puck has a velocity of 5.00 I m/s at one instant. Eight seconds later, its velocity is (6i + 18j) m/s Assuming the rocket engine exerts a constant horizontal force, find the components of the force. Find its magnitude. A force F applied to an object of mass m_1 produces an acceleration of 3.30 m/s^2. The same force applied to a second object of mass m_2 produces an acceleration of 1.50 m/s^2. What is the value of the ratio m_1/m_2? If m_1 and m_2 are combined into one object, find its acceleration under the action of the force F.

Explanation / Answer

(Question 1) As given in the question,

Mass of rocket: m = 4.6 kg

Initial velocity: u = 5 i^ m/s

Final velocity: v = 6 i^ + 18 j^ m/s

Time taken: t = 8 s

x-directional motion,

v(x) = u(x) + a(x)*t

=> 6 = 5 + a(x)*8 => a(x)  = 0.125 m/s^2

y-directional motion,

v(y) = u(y) + a(y)*t

=> 18 = 0 + a(y)*8 => a(y)  = 2.25 m/s^2

(a) The component of force:

F(x)  = m*a(x)  = 4.6*0.125 = 0.575 N

F(y)  = m*a(y)  = 4.6*2.25 = 10.35 N

(b)   The magnitude of the force,

  F  = sqrt{ F(x)^2 + F(y)^2 }  = sqrt{ 0.575^2 + 10.35^2 } = 10.37 N

(Question 2) As given in the question,

a1 = 3.3 m/s^2 and a2 = 1.5 m/s^2

(a) As we know that,

  F  = m*a   => a  = F / m

a1 / a2 = 3.3 / 1.5

   => (F / m1) / (F / m2) = 3.3 / 1.5

=>   m1 / m2 = 1.5 / 3.3 = 5 / 11

(b) Now m1 and m2 are combined together to get one mass "m",

m  = m1 + m2

Suppose the acceleration = "a"

  => a / a1  = m1 / (m1 + m2)

  => a  = a1*m1 / (m1 + m2) = 3.3*5 / (5 + 11) = 1.013 m/s^2

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