In the figure below, 5.2 kg block A and 6.2 kg block B are connected by a string of negligible mass. Force A = (16 N) acts on block A; force B = (27 N) acts on block B. What is the tension in the string? (Express your answer in vector form.)
To see the figure copy and paste the link part by part
part1://d2vlcm61l7u1fs.cloudfront.
part2: net/media%2Fb47%2Fb47609cf-37a7-48c4-9f83-59d72599bd89%2FphpKQ2twf.png
27 - T = 6.2 a
16 + T = 5.2 a
----------------add
43 = 11.4 a
a = 3.77 m/s^2
T = 5.2 (3.77) - 16 Newtons
To determine the tension in the string, we need to consider the forces acting on each block and the fact that they are connected by a string.
First, let's analyze the forces acting on block A:
1. The force applied on block A, denoted as F_A, is given as 16 N.
2. The weight of block A, W_A, is equal to the mass of block A multiplied by the acceleration due to gravity. Since the mass of block A is 5.2 kg and the acceleration due to gravity is approximately 9.8 m/s^2, the weight of block A is W_A = 5.2 kg * 9.8 m/s^2.
Next, let's analyze the forces acting on block B:
1. The force applied on block B, denoted as F_B, is given as 27 N.
2. The weight of block B, W_B, is equal to the mass of block B multiplied by the acceleration due to gravity. Since the mass of block B is 6.2 kg and the acceleration due to gravity is approximately 9.8 m/s^2, the weight of block B is W_B = 6.2 kg * 9.8 m/s^2.
Now, considering that both blocks are connected by a string, the tension in the string is the same for both blocks. We can denote the tension as T.
To find the tension, we need to apply Newton's Second Law of Motion to each block:
For block A:
F_net_A = T - W_A = m_A * a_A
For block B:
F_net_B = F_B - T - W_B = m_B * a_B
Since both blocks are connected, they experience the same acceleration, denoted as a. Therefore, a_A = a_B = a.
Now, let's solve for the tension in the string:
From the equation for block A:
T - W_A = m_A * a_A
T - (m_A * g) = m_A * a
From the equation for block B:
F_B - T - W_B = m_B * a_B
F_B - T - (m_B * g) = m_B * a
We can substitute a in both equations with a_A or a_B since they are the same.
Rearranging the equations, we have:
T = m_A * a + W_A
T = F_B - m_B * a - W_B
Plugging in the values, we can calculate the tension.