A 15 kg block is on a ramp which is inclined at 20o above the horizontal. It is connected by a string to a 19 kg mass which hangs over the top edge of the ramp. Assuming that frictional forces may be neglected, what is the magnitude of the acceleration of the 19 kg block

The magnitude of the acceleration of the 19 kg block is 1.414 m/s²

Explanation:

From Newton's second law of motion;

where;

m is the mass of the objects involved, kg

a is the acceleration of the object, m/s²

different forces on the block and string

⇒force due to 15 kg block

=mgcosθ = 15×9.8×cos20 = 15×9.8×0.9396

= 138.12 N

⇒Tensional Force on 19 kg mass:

T = mg = 19×9.8 = 186.2 N

186.2 - 138.12 = a(15+19)

48.08 =  a(34)

a = 48.08/34

a = 1.414 m/s²

Therefore, the magnitude of the acceleration of the 19 kg block is 1.414 m/s²

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