Question

A train, with an initial velocity of 15 m s−1 along a straight track, accelerates at a constant 0.25 m s−2. Determine how far it travels before reaching a velocity of 20 m s−1.

A smooth slope makes an angle of 65o to the horizontal. Determine the acceleration due to gravity down the slope.

A 20-kg box sits on a flat surface. The coefficient of static friction is 0.73. Calculate the maximum static friction.

A wheel has a diameter of 60 cm. It rotates 4.5 times per second. Calculate the speed of a point on the rim.

A proton has a velocity of 6.3×104 m s−1. Determine its kinetic energy.

Answer 1

1)Guven,

u = 15 m/s ; v = 20 m/s ; a = 0.25 m/s^2

We know that

v^2 = u^2 + 2 a s

s = (v^2 - u^2)/2a

s = (20*20 - 15*15)/2 x 0.25 = 350 m

Hence, s = 350 m

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Given,

theta = 65 deg

a = g sin(theta)

a = 9.81 x sin65 = 8.89 m/s^2

Hence, a = 8.89 m/s^2

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Ff = us m g

Ff = 0.73 x 20 x 9.8 = 143.08 N

Hence, Ff = 143.08 N

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w = 4.5 rev/s = 6.3 rad/s

We know that

v = rw = 0.3 x 6.3 = 1.89 m/s

Hence, v = 1.89 m/s

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KE = 1/2 m v^2

KE = 0.5 x 1.67 x 10^-27 x (6.3 x 10^4)^2 = 3.31 x 10^-18 J

Hence, KE = 3.31 x 10^-18 J