A mass of 100g falls freely under the action of gravity. Find the force acing on it, its momentum and kinetic energy after 10 seconds.
Please answer correctly, i have to submit it in the school.
Answers
(i) Force acting on the mass falling freely = 0.981 N
(ii) Momentum of the mass falling freely (after 10 sec) = 9.81 kg-m/s
(iii) Kinetic Energy of the mass falling freely (after 10 sec) = 481.1805 Joules
Explanation:
Given :
Mass of freely falling body under action of gravity (M) = 100g = 0.1 kg
Instance of Time (t) for calculating momentum (p) and kinetic energy (KE) = 10 seconds.
Value of acceleration due to gravity (g) = 9.81 m/sq.sec [assumed as universal constant]
To find :
(i) Force (F) acting on the freely falling body
(ii) Momentum (p) of the body after 10 sec
(iii) Kinetic energy (KE) of the body after 10 seconds.
Formulae :
(i) F = M.g [force = mass x acceleration]
(ii) p = M.v [momentum = mass x velocity]
(iii) KE = (1/2).M.v^2
(iv) v = u + gt
where v = velocity of freely falling body after 10 seconds.
u = initial velocity of freely falling body starting from rest
Solution:
Step-1 : u = 0 (freely falling body starts from rest)
Step-2 : Apply formula (iv) : v = u + gt = 0 + (9.81).(10) = 98.1 m/s
Step-3 : Apply formula (i) : F = M.g = 0.1 x 9.81 = 0.981 N
Step-4 : Apply formula (ii) : p = M.v = 0.1 x 98.1 = 9.81 kg-m/s
Step-5 : Apply formula (iii) : KE = (1/2).M.v^2 = (1/2).(0.1).(98.1)x(98.1) = 481.1805 Joules