15-kg block is on a ramp which is inclined at 20° 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 downward acceleration of the 19-kg block?
Given m1 = 15 kg, m2
= 19 kg, θ
Find the acceleration a.
system moves with a constant acceleration a, that is the net force
acting on the first mass is
and the net force acting on the second mass if F2
The forces acting on the first mass are the weight W1
the reaction N, and the tension force T1.
Note that the force N is compensated by the normal component of the
θ and the net force is
directed along the inclined plane and equals F1
= T1 –
where the latter is the second component of the weight W1.
the second mass we have F2
= m2g– T2.
Note that the string has no mass and therefore, the forces T1
have the same
magnitude. By adding the two above equations, we get