Classical Mechanics Answers

Assume that the initial density of matter along the x axis is given p(x)= e^-x kg/m. If the mass with the constant velocity v= 10m/s in the direction of x axis
Find the total mass in the segment [1,2] at the time t=60.

A baloon rising with a uniform velocity of 1 m/s. A ball released from the baloon after 4 sec. Calculate time taken by the ball to reach ground

the force of capillary in plant is given by prgh/2, where r is the coefficient of the surface tension. is the equation correct or not? justify the answer

Ms. Tan is playing soccer.She weighs in at an intimidating 95kg. During the combine , she runs the 40m dash and shows that she is able to accelerate uniformly throughout the 40m distance traveled. She’s able to run the 40m in 4.09 seconds.

a). What’s Ms.Tian’s final velocity at the end of the 40m? (kinematic)

b). What’s her kinetic energy at this time ?

c). If she were to run at this speed and collide with a 120kg man running towards her (negative direction) with a velocity of 4m/s , and after the collision the other man continued to move at a rate of 1m/s in the negative direction. What would be her velocity after the collision? (elastic collision)

d). If she did a sick spin move so as to not fall down and continue moving forwards with the velocity from question c , how much work would she need to do in order to return to her original running speed? (work)

e). If she was able to do the work from question d in 23 seconds , how much power was she exerting ? (power)

A ball of mass 60kg is moving due south with a speed of 50m per second at latitude 30°N.Calculate the magnitude and direction of the coriolis force on the ball.Compare the magnitude of this force to the weight of the ball?

A track traveling towards the north colludes with a car traveling towards the east.after collision the car and truck stick together and move off at an angle of 30 degree east of north.if the speed of car before collision was 20 m per second and mass of the truck is twice of car ,calculate the speed of truck before and after collision?

A particle is projected vertically upwards from a point A on the ground. It takes T1 time to reach a point B but still continues to move up. If it takes T2 time to reach the ground from point B then height of point B from the ground is what?

A 85.0-kg daredevil exhibitionist hangs on to the end of a long bungee cord attached to the railing of the Brooklyn Bridge and oscillates vertically. (Do NOT try this!) The spring constant of the bungee cord is 131 N/m, and the system\'s damping constant is 0.128 kg/s. How long does it take for the oscillation amplitude to decrease to 94.9% of its initial value?

A block of mass m=0.1kg is released from a height of 4m on a curved smooth surface, path AB(1m) is smooth and path BC(2m) offers coefficient of friction 0.1. If the impact of block with vertical wall at C be perfectly elastic, the total distance covered by the block on the horizontal surface before coming to rest will be___…[g=10m/s^2]
Ans:59m
P.S Could you please show the path of motion of the block too?

Consider a classical linear oscillator with
E=(P^2/2M) + bX^2
where b is a constant. Assuming that the oscillator is in thermal equilibrium with a
heat reservoir at temperature T, calculate (i) the mean kinetic energy, (ii) the mean
potential energy for an assembly of N such oscillators