A 30kg box of vegetable moves down a 35 degree frictionless inclined. Find the resultant force down the inclined and the acceleration down the inclined
"inclined" is a past tense verb. You probably mean the noun "incline".
The weight force is W = M*g.
The force component down the incline is W sin 35 = M*g*sin35.
Divide that by M for the acceleration
To find the resultant force down the inclined plane, we need to resolve the weight (force due to gravity) into its components parallel and perpendicular to the inclined plane.
1. Resolving Weight:
The weight of the box can be calculated using the formula: Weight = mass * gravitational acceleration.
Given that the mass of the box is 30 kg and the gravitational acceleration is 9.8 m/s^2, the weight (W) of the box would be W = 30 kg * 9.8 m/s^2 = 294 N.
2. Resolving Components:
We need to find the components of the weight perpendicular and parallel to the inclined plane.
The component of the weight perpendicular to the inclined plane can be calculated using the formula: Weight perpendicular = Weight * cos(θ), where θ is the angle of the incline.
Weight perpendicular = 294 N * cos(35°) ≈ 241.95 N.
The component of the weight parallel to the inclined plane can be calculated using the formula: Weight parallel = Weight * sin(θ).
Weight parallel = 294 N * sin(35°) ≈ 168.12 N.
3. Resultant Force:
Since the inclined plane is frictionless, there is no force opposing the box's motion parallel to the incline. Thus, the resultant force down the inclined plane would be equal to the parallel component of the weight.
Therefore, the resultant force (F) down the inclined plane is 168.12 N.
4. Acceleration:
The acceleration of the box down the inclined plane can be calculated using Newton's second law of motion: F = m * a, where F is the net force and m is the mass of the object.
Since we have the net force (resultant force) as 168.12 N and the mass of the box is 30 kg, we can rearrange the equation to solve for acceleration (a):
168.12 N = 30 kg * a
a = 168.12 N / 30 kg ≈ 5.604 m/s^2.
Therefore, the acceleration (a) down the inclined plane is approximately 5.604 m/s^2.