Three sleds are being pulled horizontally on frictionless horizontal ice using horizontal ropes (Fig. 5.48). The pull is horizontal and of magnitude 125 N. Find (a) the acceleration of the system and (b) the tension in ropes A and B.

acceleration=2.0833 m/s^2

Tension in rope A=104.167 N

Tension in rope B=62.5 N

Explanation

mass of sleds are 10,20 and 30 Kg respectively.

Total mass =60 kg

F=ma

a=f/m

f=125 N

a=125/60

a=2.0833 m/s^2

Now using equation of equilibrium

F-Ta=ma*a

Ta=F-ma*a

Ta=125-(10*2.0833)

Ta=104.167 N

Tb=mc*a

Tb=30*2.0833

Tb=62.5 N

initial speed when it is dropped is 150 ft/s

now at the same moment the acceleration due to gravity is perpendicular to its velocity

so as we know that

now we have centripetal acceleration a = 32 ft/s^2 as its perpendicular to velocity

while tangential acceleration at the same moment will be zero

so

now radius of curvature is given as

so the radius of curvature just after it is dropped is 703.125 ft