A taut massless string connects two boxes. The boxes are placed on an incline plane at θ = 32.00. What is the acceleration of boxes as they move down the incline, given m2 = 1.0 kg, m1 = 7.2 kg, μ2 = 0.10 and μ1 = 0.20.
total forces of friction:
(.2*m1*g + .1*m2*g)cosTheta
work that out.
gravity down the plane:
force=sinTheta(m1*g+m2*g)
acceleration=netforce/totalmass
where net force =sinTheta(m1*g+m2*g)-.2*m1*g + .1*m2*g)cosTheta
calculate acceleration
could you show how you got that equation for the total friction and gravity down the plane
To determine the acceleration of the boxes as they move down the incline, we need to consider the forces acting on each box and apply Newton's second law of motion.
First, let's analyze the forces acting on box 1:
1. Gravitational force (mg1): The weight of box 1 acts vertically downward and can be calculated by multiplying the mass of box 1 (m1) by the acceleration due to gravity (g = 9.8 m/s^2).
Weight of box 1 (mg1) = m1 * g
2. Normal force (N1): The normal force acts perpendicular to the incline plane and cancels out the vertical component of the weight of box 1.
Normal force (N1) = mg1 * cos(θ)
3. Frictional force (f1): The frictional force acts parallel to the incline plane and opposes the motion of box 1. It can be calculated by multiplying the normal force by the coefficient of friction (μ1).
Frictional force (f1) = μ1 * N1
4. Net force on box 1: The net force on box 1 is the difference between the gravitational force acting down the incline and the frictional force acting up the incline.
Net force on box 1 = mg1 * sin(θ) - f1
Next, let's analyze the forces acting on box 2:
1. Gravitational force (mg2): The weight of box 2 acts vertically downward and can be calculated by multiplying the mass of box 2 (m2) by the acceleration due to gravity (g = 9.8 m/s^2).
Weight of box 2 (mg2) = m2 * g
2. Normal force (N2): The normal force acts perpendicular to the incline plane and cancels out the vertical component of the weight of box 2.
Normal force (N2) = mg2 * cos(θ)
3. Frictional force (f2): The frictional force acts parallel to the incline plane and opposes the motion of box 2. It can be calculated by multiplying the normal force by the coefficient of friction (μ2).
Frictional force (f2) = μ2 * N2
4. Net force on box 2: The net force on box 2 is the difference between the gravitational force acting down the incline and the frictional force acting up the incline.
Net force on box 2 = mg2 * sin(θ) - f2
The acceleration of both boxes moving down the incline can be calculated using Newton's second law of motion:
Acceleration = (net force on box 1 + net force on box 2) / (m1 + m2)
Plug in the values of m1, m2, μ1, μ2, and θ into the equations above, and solve for the acceleration.