A rope attached to a 20 kg wood sled pulls the sled up a 20 degree snow-covered

Question

A rope attached to a 20 kg wood sled pulls the sled up a 20 degree snow-covered hill. A 10 kg wood box rides on top of the sled. If the tension in the rope steadily increases, at what value of the tension does the box slip? The 100 kg block in FIGURE P7.38 takes 6.0 s to reach the floor after being released from rest. What is the mass of the block on the left? The pulley is mass less and frictionless. The 10.2 kg block in FIGURE P7.39 is held in place by a force applied to a rope passing over two mass less, frictionless pulleys. Find the tensions T_1, to T_5 and the magnitude of force F vector.

Explanation / Answer

As given in the question,

Height of 100 kg block from ground: s = 1 m

Time for this to reach the ground: t = 6 s

Initial velocity of 100 kg block: u = 0 m/s

Equation of motion on 100 kg block to get it's acceleration (a),

s  = u*t + (1/2)*a*(t)^2

=> 1 = 0*6 + (1/2)*a*(6)^2 =>   a = 0.0556 m/s^2

Force balance on 100 kg block to get Tension in th rope,

100*g - T  = 100*a

=> 100*(9.8) - T = 100*(0.0556) =>   T = 974.4 N

Now force balance on mass(m kg) block to get the value of m,

  T - m*g  = m*a

=>    974.4 - m*(9.8) = m*(0.0556) => m = 98.87 kg

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