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 rotates without friction. The object of smaller mass,

m = 1.5 kg,

slides without friction on an inclined plane that makes an angle of

= 31°

with the horizontal. The mass of the larger object is given as

M = 3.2 kg

and it hangs on the string. If the two objects are released from rest with the string taut, what is their total kinetic energy (in J) when the object of mass M has fallen 33 cm?

( ) J

Explanation / Answer

for M

Fnet = Ma

Mg - T = M*a

for m

Fnet = ma

T - mg*sintheta = m*a

Mg - mgsintheta = a*(M+m)

a = g*(M - m*sintheta)/(M+m)

a = 9.8*(3.2 - (1.5*sin31))/(1.5+3.2)

acceleration a = 5.1 m/s^2

speed v = sqrt(2*a*h) = sqrt(2*5.1*0.33) = 1.83 m/s

KE = (1/2)*m*v^2 + (1/2)*M*v^2

KE = (1/2)*(1.5+3.2)*1.83^2 = 7.87 J

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