Two packing crates of masses m1 = 10.0 kg and m2 = 6.60 kg are connected by a light string that passes over a frictionless pulley as in the figure. The 6.60-kg crate lies on a smooth incline of angle 37.0°.
You failed to ask a question. All you have done is describe a situation.
35=a
7.94=t
i have no cluce
To determine the tension in the string and the acceleration of the system, we need to analyze the forces acting on each crate separately.
Let's start with the crate on the incline (m2 = 6.60 kg). We'll assume the positive x-direction is along the incline and the positive y-direction is perpendicular to the incline, pointing upwards.
1. Determine the weight force of m2: The weight force (mg) acting on m2 can be split into two components: mg*cos(37°) along the incline and mg*sin(37°) perpendicular to the incline.
Weight force along the incline: F_ax = m2 * g * cos(37°)
Weight force perpendicular to the incline: F_ay = m2 * g * sin(37°)
2. Calculate the net force acting on m2 along the incline: The net force acting on m2 is the component of the force parallel to the incline. Since the crate is on a smooth incline with no friction, the only force acting on it is the component of its weight along the incline, so:
F_net_x = F_ax
3. Calculate the acceleration of m2 using Newton's second law: The net force acting on m2 is equal to the mass of m2 multiplied by its acceleration (F_net_x = m2 * a). So we have:
m2 * a = F_net_x
a = F_net_x / m2
Next, let's move on to the second crate (m1 = 10.0 kg).
4. Determine the weight force of m1: The weight force (mg) acting on m1 only has a component parallel to the incline.
Weight force parallel to the incline: F_bx = m1 * g * sin(37°)
5. Calculate the net force acting on m1 along the incline: The net force acting on m1 is the component of the force parallel to the incline. Since the crate is on a smooth incline with no friction, the only force acting on it is the component of its weight along the incline, so:
F_net_x = F_bx
6. Calculate the acceleration of m1 using Newton's second law: The net force acting on m1 is equal to the mass of m1 multiplied by its acceleration (F_net_x = m1 * a). So we have:
m1 * a = F_net_x
a = F_net_x / m1
Finally, we can determine the tension in the string connecting the crates:
7. Calculate the tension in the string: The tension in the string is the same for both crates since they are connected. We can find it by analyzing the vertical forces acting on m2.
The vertical forces on m2 are its weight force (mg) and the tension force (T) in the string. These forces must cancel each other out since there is no vertical acceleration:
T - F_ay = 0
T = F_ay
Now you have the expressions for the acceleration of the system (a), the net forces on each crate, and the tension in the string. Plug in the known values for m1, m2, the angle, and the acceleration due to gravity (g = 9.8 m/s²) to calculate the values.