A mass of m1 = 6.00 kg is sitting on an inclined plane, which meets the horizantal at an angle of 22.0, which has a coefficient of sliding friction of 0.290, which is 3.50 m = L.

a string is attached to m1, it is strung over a pulley, and attached to mass m2 = 7.0kg which is initially a distance of h= 65.0 cm off the floor. as a result m1 accelerates up the incline at a constant rate.

a) what is magnitude of tension T in string b/w two masses?

b) what will be acceleration of the system?

c) how long will it take m2 to reach the floor?

d) what will be the speed of m2 just as it reaches the floor?

assalam terbaiklah

To find the answers to the given questions, we'll take a step-by-step approach:

a) The magnitude of the tension (T) in the string between the two masses can be found using Newton's second law and considering the forces acting on mass m1.

First, let's draw a free-body diagram for m1 on the inclined plane. The gravitational force (mg) acts vertically downward, and the component of the weight down the slope is mg.sin(θ), where θ is the angle of the inclined plane (22.0°). The normal force (N) acts perpendicular to the plane, and the frictional force (f) opposes the motion, acting up the slope.

The net force acting on m1 is the force pulling it up the plane, which is T, minus the frictional force (f). The equation is given by:
T - f = m1 * acceleration

The frictional force (f) can be calculated by multiplying the coefficient of sliding friction (μ) with the normal force (N):
f = μ * N
N = m1 * g * cos(θ)

Substituting the values and solving the equations will give us the magnitude of the tension (T) in the string.

b) The acceleration of the system can be determined using the Newton's second law for the hanging mass m2. The force pulling m2 down is T (from tension in the string), and the force resisting its motion is the gravitational force (m2 * g). The equation is given by:
m2 * g - T = m2 * acceleration

Solving this equation will give us the acceleration (a) of the system.

c) To find the time it takes for m2 to reach the floor, we need to calculate the distance m2 travels. The distance is equal to h (initial distance, given as 65.0 cm). We'll use the kinematic equation:
s = ut + (1/2) * a * t^2

Since the initial velocity (u) is 0 (as m2 is initially at rest), substituting the values into the equation will give us the time (t) taken for m2 to reach the floor.

d) The speed of m2 just as it reaches the floor can be calculated using the formula:
v^2 = u^2 + 2 * a * s

In this case, the initial velocity (u) is 0 (as m2 is initially at rest), and the distance (s) is equal to the distance traveled by m2 (which is equal to h). Substituting the values into the equation will give us the final speed (v) of m2.

Now that we have explained the appropriate steps, you can apply the formulas and calculations to find the numerical answers to the questions.