To find the tension in the string, we need to analyze the forces acting on the system.
1. Start by resolving the force applied at an angle into its horizontal and vertical components.
- The horizontal component of the force is F*cos(θ), where F is the magnitude of the force and θ is the angle.
- The vertical component of the force is F*sin(θ).
2. Next, consider the forces acting on each block individually:
- For block 1:
- The weight of block 1 is m1 * g, where g is the acceleration due to gravity (approximately 9.8 m/s²).
- The tension in the string is T, acting in the opposite direction.
- The frictional force opposing the motion of block 1 is μ1 * N1, where μ1 is the coefficient of kinetic friction and N1 is the normal force.
- For block 2:
- The weight of block 2 is m2 * g.
- The tension in the string is T, acting in the same direction.
- The frictional force opposing the motion of block 2 is μ2 * N2, where μ2 is the coefficient of kinetic friction and N2 is the normal force.
3. Use Newton's second law, F = ma, for each block:
- For block 1: F_net1 = m1 * a1
- The net force acting in the horizontal direction is T - μ1 * N1 = m1 * a1.
- The net force acting in the vertical direction is N1 - m1 * g = 0 (since block 1 is not accelerating vertically).
- For block 2: F_net2 = m2 * a2
- The net force acting in the horizontal direction is T - F*cos(θ) - μ2 * N2 = m2 * a2.
- The net force acting in the vertical direction is N2 - m2 * g = -m2 * g (since block 2 is not accelerating vertically).
4. Determine the normal forces for each block:
- The normal force, N1, can be calculated by N1 = m1 * g (since block 1 is not accelerating vertically).
- The normal force, N2, can be calculated by N2 = m2 * g + F*sin(θ) (since block 2 is accelerating vertically).
5. Substitute the normal forces back into the net force equations and solve for the tension, T.
Once you have the values for the normal forces, you can use them to find the tension in the string by solving the net force equations.