Two objects are connected by a massless string, as shown in the figure below. Th

Question

Two objects are connected by a massless string, as shown in the figure below. The pulley is massless and relates without friction. The object of smaller mass, m = 1.13 kg, slides without friction on an inclined plane that makes an angle of theta = 30 degree with the horizontal. The mass of the larger object is given as M = 2.1 kg and it hangs on the string. If the two objects are related from the rest with the string, what is their total kinetic energy (in J) when the object of Mass m has fallen 31 om?

Explanation / Answer

here,

m1 = 1.3 kg , m2 = 2.1 kg

theta = 30 degree

the accelration , a = (m2 * g - m1 * g * sin(theta)) /( m1 + m2)

a = ( 2.1 * 9.8 - 1.3 * 9.8 * sin(30)) /( 1.3 + 2.1) m/s^2

a = 4.18 m/s^2

s = 0.31 m

the final speed , v = sqrt(2 * a * s)

v = sqrt(2 * 4.18 * 0.31) = 1.61 m/s

the total kinetic energy , TE = 0.5 * v^2 *( m1 + m2)

TE = 0.5 * 1.61^2 * ( 1.3 + 2.1) J

TE = 4.41 J

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