Question

During a stage production of Peter Pan, the 50kg actress playing Peter has to fly in vertically (descend). To be in time with the music, she must, starting from rest, be lowered distance of 3.2m in 2.2s at a constant acceleration. Backstage, a smooth surface sloped at 50 degrees supports a counterweight of mass m. Show the calculations that the stage manager must perform to find(a) the mass of the counterweight that must be used and(b) the tension in the wire.

Answer 1

Answer:

a) mc=38.34kg

b) T=434N

Explanation:

With kinematics equation:

$Yf = Vo*t-a/2*t^2$

$-3.2 = 0-a/2*2.2^2$

$a=1.32m/s^2$

The sum of forces on the counterweight is:

$T - m_c*g=m_c*a$   Solving for T

$T =m_c*(a + g)$

The sum of forces on the actress is:

$T - m*g=-m*a$   Replacing the tension:

$m_c*(a + g) - m*g=-m*a$

$m_c=m*(g - a)/(a + g) = 38.34kg$

Now we use this value to calculate the tension:

T = 434N