A block,mass 20kg,is pulled upwards by a force F along a plane inclined at 30 degree to the horizontal.it accelerate along the inclined plane at 2m.s-2. The surface of the inclined exert a friction force on the block calculate the component of the gravitational force exerted on the block parallel to the incline.
To solve this problem, we need to first understand the forces acting on the block on the inclined plane.
1. Gravitational force (mg): This force is acting vertically downwards due to the mass of the block. Its magnitude can be calculated using the formula F = mg, where m is the mass and g is the acceleration due to gravity (approximately 9.8 m/s^2).
2. Normal force (N): This force is perpendicular to the inclined plane and counteracts the gravitational force. It can be calculated using the formula N = mg * cosθ, where θ is the angle of inclination (in this case, 30 degrees).
3. Friction force (f): This force is parallel to the inclined plane and acts in the opposite direction to the motion of the block. Its magnitude can be determined using the formula f = μN, where μ is the coefficient of friction and N is the normal force. We will consider it to be of kinetic friction in this case since the block is accelerating.
4. Component of gravitational force parallel to the incline (F_parallel): This is the force we need to find. It is in the same direction as the motion of the block along the inclined plane.
Now, to calculate the component of the gravitational force parallel to the incline, we can follow these steps:
Step 1: Calculate the normal force.
N = mg * cosθ
N = 20 kg * 9.8 m/s^2 * cos(30°)
N ≈ 166.4 N
Step 2: Determine the friction force.
Let's assume the coefficient of kinetic friction (μ) is 0.2 (given or approximate value).
f = μN
f = 0.2 * 166.4 N
f ≈ 33.3 N
Step 3: Calculate the net force along the incline.
The net force is the force parallel to the incline and is responsible for the block's acceleration.
Net force = ma
(F_parallel - f) = m * a
(F_parallel - 33.3 N) = 20 kg * 2 m/s^2
F_parallel ≈ 20 kg * 2 m/s^2 + 33.3 N
F_parallel ≈ 40 N + 33.3 N
F_parallel ≈ 73.3 N
So, the component of the gravitational force exerted on the block parallel to the incline is approximately 73.3 N.
To calculate the component of the gravitational force exerted on the block parallel to the incline, we need to find the net force acting on the block along the incline.
Let's break down the forces acting on the block:
1. Gravitational force (Weight):
The weight of the block can be calculated using the formula:
Weight = mass * gravity
Given that the mass of the block is 20 kg and the acceleration due to gravity is approximately 9.8 m/s^2, the weight of the block can be calculated as:
Weight = 20 kg * 9.8 m/s^2 = 196 N
2. Normal force (perpendicular to the incline):
The normal force is the force exerted by the surface of the inclined plane perpendicular to the incline. It is equal in magnitude and opposite in direction to the component of weight perpendicular to the incline.
Normal force = Weight * cos(angle of inclination)
Where the angle of inclination is 30 degrees.
Normal force = 196 N * cos(30°) = 196 N * (√3 / 2) = 196 N * 0.866 = 169.936 N (approximately)
3. Friction force (parallel to the incline):
The friction force opposes the motion of the block on the inclined plane. It can be calculated using the formula:
Friction force = coefficient of friction * Normal force
The value of coefficient of friction is not provided, so we cannot calculate the exact value of friction force.
With the given information, we now have the weight (196 N) and the normal force (approximately 169.936 N). To find the component of the weight parallel to the incline, we can use trigonometry:
Component of weight parallel to the incline = Weight * sin(angle of inclination)
Component of weight parallel to the incline = 196 N * sin(30°) = 196 N * (1/2) = 98 N
So, the component of the gravitational force exerted on the block parallel to the incline is approximately 98 N.