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Numerical Problem from Laws of Motion

An 8000 kg engine pulls 40000 kg train alonged a level track and gives an acceleration of 1.2m/s2. Find the accelaration produced by same engine on a train of mass 16000kg?

Answer:

Force exerted by the engine = mass of train x acceleration =  40000 x 1.2=48000N

When the same engine pulls a 16000 kg train, the acceleration = 48000/16000=3m/s2

An interesting numerical problem from kinematics

George’s favorite food was bananas. One day he was walking with his friend, the man in the yellow hat, as he was eating a banana. They were in New York City and they were walking up the Empire State Building. Finally they made it to the top! George spied a nice young woman walking down 5th avenue balancing this hat on her head.  She was very noticeable for she was six feet tall! George, being the troublemaker he was, wanted to see if he could drop his banana peel in her hat. He noticed that she was jogging at a constant pace of 6 miles per hour. George was on the 102nd floor observatory, which is 1,224 feet from the ground.*
Assuming that George lands the banana peel in the hat……..
A)      How long will the banana peel be in the air? (Assuming there is no wind and the banana will drop straight down from the empire state building)
B)      What will the velocity of the banana peel be right before it lands in the woman’s hat?
C)      How far away must the woman’s hat be from the landing point of the banana peel (horizontally) when George makes his scandalous move and drops the peel.
D)      If George decides to throw another peel one second later to land it on the ground and trip the jogger, at what velocity must he throw it at so that it hits the ground at the same the original peel lands in the hat.

Motion of a charge particle in an electric field – Numerical Problem

At t=0 a very small object with mass 0.400mg and charge +9.00μC is travelling at 125 m/s in the -x-direction. The charge is moving in a uniform electric field that is in the +y-direction and that has magnitude E= 895 N/C. The gravitational force on the particle can be neglected. How far is the particle from the origin at t= 7.99 ms.

Hint for solving the above problem:

displacement along X direction; x=-uxt=125 x 7.99/1000

Displacement along Y direction, y=0.5 ay t2

ay=qE/m

s=√(x2+y2)

Just substitute the values and get the answer

Numerical Problem from Friction

“The friction coefficient between a road and the tyre of a vehicle is 4/3.find the maximum incline the road may have so that once hard brakes are applied and the wheel starts skidding,the vehicle going down at a speed of 10m/s is stopped within 5m” Raju Rabha asked

Numerical Problem from Motion of Connected systems

Two blocks A and B of mass m1 and m2 respectively are kept in contact on a frictionless table.The experimenter pushes the block A from behind so that the blocks accelerate. If  the block A exerts a force F on the block B,what is the force exerted by the experimenter on A.

A numerical Problem from optics

AK asks:

When an object is kept at a distance of 60cm from a concave mirror, the magnification is 1/2. Where should the object be placed to get magnification of 1/3??

please answer this question….

Ans:

In the first part, u=-60, m=(-)1/2 implies v=-30 cm (Since the image must be real as concave lens form virtual image of bigger size only)

Substituting in eqn mirror_formula

or  mirrorformula

we get f = –20 cm

In II case

m=-1/3

v=u/3

f=-20cm

substituting in mirrorformula

we get u=4f=4 x (-20)=-80 cm

(If this is not the expected answer please respond)

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