Physics Energy And Forces

Question

A 2.0 kg brick is let go from the top of a curved incline in the shape of a quarter-circle that has a radius, r. The brick then slides across a flat surface before stopping 8.0 meters from the beginning of the horizontal plane. There is no friction on the curved incline but the horizontal surface results in a friction force of 4.0 newtons.

Calculate the acceleration of the brick while it slides over the flat surface.

Calculate much time elapses as the brick slides horizontally.

Calculate the radius of the quarter-circle incline in meters. 

Answer 1

(a) We know that

Given f = 4N

F = mv²/r

Using 1/2 mv² = mgr

mv²/r = 2 mg

mv²/r = 2 x 2 x 10

mv²/r = 40

⇒ F

Using F - f = ma

\({40-4}\over2\) = a

a = 18 m/s²

(b) v = u - at

o = 12√2 - 18t

12√2/18 = t

t = 12√2/18

t = 2/3 √2 sec

(c) Radius of the quarter circle incline in meter.

F = mv²/r

r = \({2\times288}\over40\)

r = 14.4 m