a ball of mass 10g is moving with a velocity of 50ms^-1, on applying a constant force on ball for 2.0s,it acquires a velocity of 70ms^-1.
calculate:
i) the initial momentum of ball
ii) the final momentum of ball
iii)the rate of change of momentum
iv) the acceleration of ball
v) the magnitude of force applied
Answers
Explanation:
As per the provided information in the given question, we have :
- Mass of the ball (m) = 10g = 0.01 g
- Initial velocity (u) = 50 m/s
- Time taken (t) = 2 seconds
- Final velocity (v) = 70 m/s
We've been asked to calculate :
- The initial momentum of ball
- The final momentum of ball
- The rate of change of momentum
- The acceleration of ball
- The magnitude of force applied
The initial momentum of ball :
↠⠀Initial momentum = mu
- m denotes mass
- u denotes initial velocity
↠⠀Initial momentum = 0.01 kg × 50 m/s
↠⠀Initial momentum = 0.5 kg.m/s
The final momentum of ball :
↠⠀Final momentum = mv
- m denotes mass
- v denotes final velocity
↠⠀Final momentum = 0.01 kg × 70 m/s
↠⠀Final momentum = 0.7 kg.m/s
The rate of change of momentum :
↠⠀Change in momentum = mv – mu
- mu denotes initial momentum
- mv denotes final momentum
↠⠀Change in momentum = (0.7 – 0.5) m/s
↠⠀Change in momentum = 0.2 m/s
The acceleration of ball :
By using the first equation of motion,
↠⠀v = u + at
- v denotes final velocity
- u denotes initial velocity
- a denotes acceleration
- t denotes time
↠⠀70 = 50 + 2a
↠⠀70 – 50 = 2a
↠⠀20 = 2a
↠⠀20 / 2 = a
↠⠀10 m/s² = a
The magnitude of force applied :
↠⠀F = ma
- F denotes force
- m denotes mass
- a denotes acceleration
↠⠀F = 0.01 × 10 N
↠⠀F = 0.1 N
⠀⠀⠀⠀_______________________________⠀⠀⠀⠀⠀
Answer:
Initial momentum = 0.5Kg.m/s.
final momentum = 0.7kg.m/s.
rate of change of momentum = 0.2m/s.
acceleration of ball = 10m/s².
magnitude of force = 0.1 N.