Q1.if v is the speed of trolley and sand bag if the mass is 200 kg and a sand bag of mass 10kg if its leaking sand 0.05kg/seconds find the speed of trolley when total sand empty
Answers
Step-by-step explanation:
Correct Question :
A trolley of mass 200 kg carrying a sandbag of 10 kg is moving uniformly with a speed of 27 km/hr on a frictionless track. After a while, sand starts leaking out of a hole on the floor of the trolley at the rate of 0.05 kg/second. What is the speed of the trolley after the entire sandbag is empty?
Given :
Mass of the trolley = 200 kg
Mass of the sand bag = 10 kg
Initial velocity = 27 km/hr
To Find :
Final velocity of trolley when total the entire sand bag is empty..
Solution :
❖ Since no external horizontal force acts on the whole system, linear momentum is conserved throughout the motion.
We know that it is measured as the product of mass and velocity.
Initial momentum (p) = (M + m) u
Final momentum (p') = M v [∵ m = 0]
- » M denotes mass of trolley
- » m denotes mass of sand bag
Initial velocity = 27 km/hr = 7.5 m/s
By substituting the given values;
➙ (M + m) u = M v
➙ (200 + 10) × 7.5 = 200 v
➙ 210 × 7.5 = 200 v
➙ v = 1575/200
➙ v = 7.88 m/s