Answer:
The answer is below
Step-by-step explanation:
A 140 kg load is attached to a crane, which moves the load vertically. Calculate the tension in the
cable for the following cases:
a. The load moves downward at a constant velocity
b. The load accelerates downward at a rate 0.4 m/s??
C. The load accelerates upward at a rate 0.4 m/s??
Solution:
Acceleration due to gravity (g) = 10 m/s²
a) Given that the mass of the crane (m) is 140 kg. If the load moves downward, the tension (T) is given by:
mg - T = ma
Since the load has a constant velocity, hence acceleration (a) = 0. Therefore:
mg - T = m(0)
mg - T = 0
T = mg
T = 140(10) = 1400 N
T = 1400 N
b) If the load moves downward, the tension (T) is given by:
mg - T = ma
T = mg - ma = m(g - a)
T = 140(10 - 0.4) = 140(9.96) = 134.4
T = 134.4 N
c) If the load moves upward, the tension (T) is given by:
T - mg = ma
T = ma + mg = m(a + g)
T = 140(0.4 + 10) = 140(10.4)
T = 145.6 N
2) To find the distance (s) if the load move from rest (u= 0) and accelerates for 20 seconds (t = 20). We use:
s = ut + (1/2)gt²
s = 0(20) + (1/2)(10)(20)²
s = 2000 m