1.) In the figure provided, a 283 kg crate is released from rest and hits the gr
ID: 1783401 • Letter: 1
Question
1.) In the figure provided, a 283 kg crate is released from rest and hits the ground 2.36 m below after 6.09 s. What is the mass of the crate to the left of the pulley? Assume the rope and pulley are massless. ( please use as many numbers as possible during calculations then in the end 3 sig figs). I appreciate it a lot !
2.)
In the figure provided, two crates are sliding down a ramp. If the crate at the top has a mass of 37.7 kg and the other has a mass of 75.4 kg, what is the tension in the string? Assume the string is massless.
Explanation / Answer
(1) First find out the value of the acceleration of the system by using the expression -
s = ut + (1/2)*a*t^2
=> 2.36 = 0 + 0.5*a*6.09^2
=> a = 2.36 / (0.5*6.09^2) = 0.127 m/s^2
Write the force - mass acceleration and suppose T is the tension in the cord and a is the accleration of the mass -
T - mg = ma
=> T = mg + ma
for bigger mass -
283g - T = 283a
put the value of T -
283g - mg - ma = 283a
=> 283(g-a) = m(g+a)
put the value of a -
=> 283(9.81-0.127) = m(9.81+0.127)
=> m = (283*9.683) / 9.937 = 275.8 kg.
Answer in three significant figures = 276 kg.
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