a mass of 1200 kg hung by a massless cable supported by a counterweight of mass 900 kg. You may assume the gravitational acceleration to be 10 m/s2. Determine the magnitude of the acceleration (in m/s2) of the 1200 kg mass and also the magnitude of the tension (in N) in the cable. Show your workings clearly.
Answers
Answer:
10,300 N.
Explanation:
The 1200 kg mass has two forces acting on it, the tension pulling up and the weight pulling down. Similarly, the 900 kg mass has two forces acting on it, tension pulling up and weight pulling down.
According to Newton's second law, to the first mass - 1200 kg.
∑F = ma
T - W = M(-a)
T - Mg = -Ma -- (1)
Now we apply Newton's second law to the second mass - 900 kg
∑F = ma
T - W = ma
T - mg = ma--- (2)
Subtracting the two equations,
-mg − (-Mg) = ma − (-Ma)
-mg + Mg = ma + Ma
g (M - m) = a (M + m)
a = g (M - m) / (M + m)
M = 1200 kg, m = 900 kg, and g = 10 m/s² (Given)
a = 10 m/s² (1200 kg - 900 kg) / (1200 kg + 900 kg)
a = 10/7 m/s²
a = 1.43 m/s²
Tension by substituting into either of the two equations.
T - mg = ma
T - (900 kg) (10 m/s²) = (900 kg) (10/7 m/s²)
T = 72000/7 N
T = 10,300 N.
Answer:
Explanation:
Since an image is not provided in the question I am making some assumptions here. That there is a table and on one side a mass of 1200 kg is hung through a cable that runs horizontally on table and through other side a mass of 900 kg is hung. Now we calculate acceleration.
Let acceleration be a.
For 1200 kg, equations of force that are balanced comes out to be:
1200*10 + 1200/a=T (1)
where T is the tension in the cable
Other equation for 900 kg is T + 900*a = 900*10 (2)
Solving these two equations one gets the value of a.
You solve these equations as a practice work.