Two masses M1 = 6.30 kg and M2 = 3.30 kg are on a frictionless surface, attached by a thin string. A force of 40.3 N pulls on M2 at an angle of 28.5° from the horizontal as shown in the figure. Calculate the tension T in the string.
To calculate the tension T in the string, we can break down the force into horizontal and vertical components.
First, let's find the horizontal component of the force applied to M2. To do this, we need to multiply the magnitude of the force (40.3 N) by the cosine of the angle (28.5°), using the formula:
Horizontal component = Magnitude of the force * cos(angle)
Horizontal component = 40.3 N * cos(28.5°) ≈ 34.92 N
Next, let's find the vertical component of the force applied to M2. To do this, we need to multiply the magnitude of the force (40.3 N) by the sine of the angle (28.5°), using the formula:
Vertical component = Magnitude of the force * sin(angle)
Vertical component = 40.3 N * sin(28.5°) ≈ 19.01 N
Since the system is in equilibrium (no acceleration), the tension T in the string will be equal in magnitude but opposite in direction to the total force applied to M2.
To find the tension T, we need to sum up the forces acting on M2 in the vertical direction (upward is positive). In this case, M1 exerts a downward force due to gravity, and the vertical component of the applied force adds to it. So the equation becomes:
T - M1 * g + Vertical component = 0
where g is the acceleration due to gravity (approximately 9.8 m/s²).
Simplifying the equation, we get:
T = M1 * g - Vertical component
T = 6.30 kg * 9.8 m/s² - 19.01 N
T ≈ 61.74 N
Therefore, the tension T in the string is approximately 61.74 N.