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Tags: Class 11 , Physics , Laws of Motion Asked by Vagmita Pandya
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y = ut + ½ gt2
Differentiate y with respect to t which gives velocity as dy/dt = v
dy/dt = u + ½ g (2t)
v=u + gt -------------------Eqn (1)
Differentiate v with respect to t which gives velocity as d2y/dt2 = dv/dt = a
dv/dt = 0 + g
a = g ----------------------Eqn (2)
We know that force acting on a mass m is given by F = ma
Now from Eqn (2), substitute a =g, Hence, F = mg
Answered on: 2018/02/02 by ExamFear Education
The motion of a particle of mass m is described by y = ut +1 / 2 g ∧∧ 2 . Find the force acting on the particle
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Text Solution
Solution : To find the force, we need to find the acceleration experienced by the particle. <br> The acceleration is given by `a = (d^2 y)/(dt^2) " or " a = (dv)/(dt)` <br> Here v= velocity of the particle in y direction ` v = (dy)/(dt) = u - "gt"` <br> The momentum of the particle ` = mv = m ( u - "gt" )` <br> `a = (dv)/(dt) = - g` <br> The force acting on the object is given by F = ma = -mg <br> The negative sign implies that the force is acting on the negative y direction. This is exactly the force that acts on the object in projectile motion.
Text Solution
Solution : Here, ` y = ut + (1)/(2) g t^(2) ` <br> ` velocity , upsilon = (dy)/(dt)=u+ (1)/(2) g (2t)= u + g t , ` <br> acceleration `a = (du)/(dt) = 0 + g = g ` <br> ` As F= ma :. F = mg ` <br> Thus the given equation describes the motion of a partical under acceleration due to gravity , and y is the position co- ordinate in the direction of g .