A 2.0 kg block is released from rest at the top of a curved incline in the shape of a quarter of a circle of radius R = 3.0 m. The block then slides onto a horizontal plane where it finally comes to rest a distance D from the beginning of the plane. The curved incline is frictionless, but there is a coefficient of friction, μ = 0.5, on the horizontal plane. Determine the velocity of the box at maximum kinetic energy

The velocity of the block at maximum kinetic energy is 7.668 m/s.

From  potential energy formula,

PE = m g h

Where,

m = mass = 2 kg

g -gravitational acceleration = 9.8 m/s²

h - height = 3 m

Put the values in the formula,

PE = (2.0 kg) (9.8 m/s²) (3.0 m)  

PE = 58.8 J

Since,  

PE = KE

Thus,

58.8 J = 1/2 m v ²  

117.6 J = (2.0 kg) v ²  

v = √((117.6 J) / (2.0 kg))  

v = 7.668 m/s

Therefore, the velocity of the block at maximum kinetic energy is 7.668 m/s.

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The block has maximum kinetic energy at the bottom of the curved incline. Since its radius is 3.0 m, this is also the block's starting height. Find the block's potential energy PE :

PE = m g h

PE = (2.0 kg) (9.8 m/s²) (3.0 m)

PE = 58.8 J

Energy is conserved throughout the block's descent, so that PE at the top of the curve is equal to kinetic energy KE at the bottom. Solve for the velocity v :

PE = KE

58.8 J = 1/2 m v ²

117.6 J = (2.0 kg) v ²

v = √((117.6 J) / (2.0 kg))

v ≈ 7.668 m/s ≈ 7.7 m/s

this is an example of "committed" time.

committed time, as contracted time, takes need over essential and available time since it is seen as profitable work. it alludes to the time allotted to keep up a home and family. at the point when a man is commuting using committed time this individual may feel that the drive is an obligation to family, for example, strolling youngsters to class or driving a mate to work. contracted and committed time clients may feel that their commute could really compare to the commute of important or leisure time clients on the grounds that their commute is profitable work. in this manner, they might be more disposed to pick a mechanized method of movement.