A block of mass m = 3.40kg and charge q = 1.50C is on an incline plane that makes an angle è = 33.0o with the horizon. An applied electric field is parallel with the incline as shown in the above diagram. What must the value of the applied electric field be to keep the block from sliding down the ramp?
To find the value of the applied electric field that keeps the block from sliding down the ramp, we need to calculate the maximum electric field that can be applied.
First, let's analyze the forces acting on the block. Along the incline, we have the gravitational force acting downwards and the normal force acting perpendicular to the incline. There is also a friction force opposing the motion.
Let's break down the forces along the ramp:
1. Gravitational force (mg): The gravitational force can be calculated using the mass of the block (m) and the acceleration due to gravity (g). Since the ramp makes an angle with the horizon, only the component along the ramp (mg*sin(θ)) affects the motion parallel to the incline.
2. Friction force (f): The friction force opposes the motion of the block and is dependent on the coefficient of friction (μ) and the normal force (N). The friction force can be calculated as f = μ*N. Since the ramp makes an angle with the horizon, the normal force can be calculated as N = mg*cos(θ).
3. Applied electric force (E): The applied electric field (E) creates an electric force (qE), where q is the charge of the block. If the applied electric force is greater than or equal to the component of the gravitational force along the ramp (mg*sin(θ)), it will prevent the block from sliding down.
Now we can set up the equation:
qE ≥ mg*sin(θ) + μ*N
Substituting the values given in the problem:
qE ≥ mg*sin(θ) + μ*mg*cos(θ)
Let's calculate the values:
m = 3.40 kg
q = 1.50 C
θ = 33.0°
μ (coefficient of friction) is not provided in the information given.
Once you have the value of the coefficient of friction (μ), you can substitute it into the equation and solve for E.