Two 12.0 kg boxes are connected by a massless string that passes over a massless frictionless pulley as shown above. The boxes remain at rest, with the one on the right hanging vertically and the one on the left d = 2.9 m from the bottom of an inclined plane that makes an angle of θ = 33° with the horizontal.

(a) What is the tension T in the string?

______ N

(b) Determine the magnitude of the frictional force between the box and the plane.

______N

You then polish the plane surface, let the blocks go and they accelerate at 3.0 m/s2

(c) The rope tension is now equal to

________N

(a) T=mg =12•9.8 =...

(b) F(fr)=T-mgsinα= ...
(c) ma =mg-T
T=m(g-a)

two mass 10 kg and 20 kg are connected with a massless string. a force pf 200 N is acting on the mass 20 kg . the acceleration of 10 kg is 12m/s^2 then the acceleration of 20 kg mass is

To solve this problem, we need to apply the principles of Newton's laws of motion and the concept of forces acting on objects. We'll go step-by-step to find the answers to each part of the question.

(a) What is the tension T in the string?
To find the tension in the string (T), we'll start by calculating the net force acting on the system of boxes.

1. Calculate the gravitational force acting on the hanging box:
The weight (W) of the hanging box is given by W = mass x gravity, where mass = 12.0 kg and gravity = 9.8 m/s^2.
So, W = 12.0 kg x 9.8 m/s^2.

2. Calculate the component of gravitational force parallel to the inclined plane:
The component of the weight acting parallel to the inclined plane is given by W_parallel = W x sin(theta), where theta = 33°.

3. Calculate the net force acting on the system:
Since the boxes are at rest, the net force acting on the system must be zero. This means the tension in the string must balance out the horizontal component of the weight acting on the left box:
Net force = T - W_parallel = 0.

4. Solve for T:
Rearranging the equation from the previous step, we find:
T = W_parallel.

Substitute the values calculated previously to find the tension T:
T = W_parallel = (12.0 kg x 9.8 m/s^2) x sin(33°).

Now, calculate the value of T.

(b) Determine the magnitude of the frictional force between the box and the plane.
The frictional force (F_friction) between the box and the plane can be determined by solving for the net vertical force acting on the left box.

1. Calculate the net vertical force:
Since the boxes are at rest, the net vertical force acting on the left box must be zero. This means the vertical component of the weight acting on the left box must balance out the vertical component of the tension in the string:
Net vertical force = T x cos(theta) - Weight of the left box.

2. Solve for the frictional force:
The frictional force is equal in magnitude but opposite in direction to the net vertical force:
F_friction = - Net vertical force.

Substitute the values calculated previously to find the magnitude of the frictional force F_friction.

Now, calculate the value of F_friction.

(c) The rope tension is now equal to:
If the blocks are now accelerating at 3.0 m/s^2, the net horizontal force acting on the system should be equal to the mass of the system multiplied by the acceleration.

1. Calculate the net horizontal force:
Net horizontal force = mass x acceleration.

2. Determine the tension in the string:
Since the net horizontal force equals the tension in the string, the rope tension is now equal to the net horizontal force.

Now, calculate the value of the rope tension.

To solve this problem, we will break it down into multiple steps.

Step 1: Calculate the weight of the two boxes
The weight of an object is given by the formula W = m * g, where m is the mass of the object and g is the acceleration due to gravity (approximately 9.8 m/s^2).

For the box on the right:
W1 = m1 * g = 12.0 kg * 9.8 m/s^2

Step 2: Calculate the vertical component of the weight of the box on the left
Since the box on the left is on an inclined plane, we need to find the vertical component of the weight. This can be calculated using the formula W2_vert = m2 * g * cos(θ), where m2 is the mass of the box and θ is the angle of the inclined plane.

W2_vert = 12.0 kg * 9.8 m/s^2 * cos(33°)

Step 3: Calculate the horizontal component of the weight of the box on the left
The horizontal component of the weight will determine the tension in the string. It can be calculated using the formula W2_horiz = m2 * g * sin(θ).

W2_horiz = 12.0 kg * 9.8 m/s^2 * sin(33°)

Step 4: Determine the tension in the string
The tension in the string is equal to the difference between the horizontal component of the weight of the box on the left and the weight of the box on the right.

T = W2_horiz - W1

Step 5: Calculate the frictional force between the box and the inclined plane
The frictional force can be calculated using the formula f = μ * N, where μ is the coefficient of friction and N is the normal force exerted on the box by the plane. In this case, the normal force N is equal to the vertical component of the weight of the box on the left.

f = μ * W2_vert

Step 6: Determine the rope tension when the blocks accelerate
Since the blocks are accelerating, the tension in the rope will be greater than when they were at rest. To calculate the rope tension, we use the formula T = m * (g + a), where m is the total mass of the system (sum of the masses of both boxes) and a is the acceleration.

T = (m1 + m2) * (g + a) = (12.0 kg + 12.0 kg) * (9.8 m/s^2 + 3.0 m/s^2)

Now, you can substitute the values and calculate the answers for parts (a), (b), and (c).