A plank ab 3.0cm long weighing 20kg with its center of gravity 2m from the end a carries a load of mass 10kg of the end a . It rest on two support c and d
Compute the values of the reaction force r1 ,r2 at c and d
To compute the values of the reaction forces r1 and r2 at supports c and d, we can use the principle of moments.
Since the mass of the plank is 20kg and its length is 3.0m, the weight of the plank can be calculated using the formula: weight = mass * gravity
Weight of the plank = 20kg * 9.8m/s^2 = 196N
Similarly, the weight of the load is: Weight of the load = 10kg * 9.8m/s^2 = 98N
Since the center of gravity of the plank is 2m from the end, the distance from support c to the center of gravity is 2m, and the distance from support d to the center of gravity is 1m.
To calculate the reaction forces at supports c and d, we can take moments about point c.
Summing the moments about c should be equal to zero to find the value of the reaction force r1:
196N * 1m - 98N * 3m - r2 * 2m = 0
Simplifying the equation:
196N - 294N - 2r2 = 0
-2r2 = -98N
r2 = -98N / -2
r2 = 49N
The reaction force at support d, r2, is 49N.
To find the value of the reaction force r1, we can sum the vertical forces and set it to zero:
r1 + r2 - 196N - 98N = 0
r1 + 49N - 196N - 98N = 0
r1 - 245N = 0
r1 = 245N
The reaction force at support c, r1, is 245N.
Therefore, the values of the reaction forces r1 and r2 at supports c and d are 245N and 49N, respectively.