Maria sets up a simple track for her toy block ( m = 0.36 kg) as shown in the fi

Question

Maria sets up a simple track for her toy block (m = 0.36 kg) as shown in the figure below. She holds the block at the top of the track, 0.54 m above the bottom, and releases it from rest.

(a) Neglecting friction, what is the speed of the block when it reaches the bottom of the curve (the beginning of the horizontal section of track)?

(b) If friction is present on the horizontal section of track and the block comes to a stop after traveling 0.86 m along the bottom, what is the magnitude of the friction force acting on the block?

Explanation / Answer

here,

mass of the block , m = 0.36 kg

height of track . h =0.54 m

(a)

let the speed of block when it reaches the bottom curve be v

using conservation of energy

kinetic energy gained = change in potential energy

0.5 * m * v^2 = m*g*h

0.5 * v^2 = 9.8 * 0.54

v = 3.25 m/s

the speed of block at the bottom of the block is 3.25 m/s

(b)

let the magnitude of the friction force acting on the block is ff

work done by the friction force = change in kinetic energy

ff*0.86 = 0.5 * m*v^2

ff *0.86 = 0.5 * 0.36 * 3.25^2

ff = 2.22 N

the magnitude of the friction force acting on the block is 2.2 N

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