Unit 7 Exam Energy, and Power work, Lab Practicum A dart of mass m is accelerate

Question

Unit 7 Exam Energy, and Power work, Lab Practicum A dart of mass m is accelerated horizontally through a tube of length L situated a height h above the ground by a constant force F.Upon exiting the tube, the dart travels a horizontal distance Ax before striking the ground, as depicted in the diagram below. a. Develop an expression for the velocity of the dart, as it leaves the tube in terms of 4 h, and any fundamental constants. V b. Derive an expression for the kinetic energy ofthe dart as it leaves the tube in terms of m, h, and any fundamental constants. KE c. Derive an expression for the work done on the dart in the tube in terms ofFand L. d. Derive an expression for the height of the tube above the ground in terms of m, 4x, F and any fundamental constants.

Explanation / Answer

Here ,

a) for the velocity of dart v

Using work energy theorum

0.5 * m * v^2 = F *L

v = sqrt(2 * F *L/m)

the velocity of the dart is sqrt(2 * F *L/m)

b)

for the kinetic energy of dart leaving the tube

kinetic energy = F *L

c)

for the work done on dart inside the tube

work done on dart inside the tube = F *L

d)

time of flight ,t = sqrt(2 * h/g)

also , t = del x/v

sqrt(2 * h/g) = del x /(sqrt(2 * F *L/m))

2 h/g = x^2 * m/(2 * F *L)

h = x^2 * m*g/(4 * F *L)

the height h is x^2 * m*g/(4 * F *L)

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