a body of mass 20kg slides down on a plane inclined of 30 degree to the horizontal. if a constant resisting force of 40N act on the body, it's a acceleration down the plane is?
To determine the acceleration of the body sliding down the inclined plane, we need to consider the forces acting on the body.
1. Determine the gravitational force (weight) acting on the body.
The weight of an object can be calculated using the formula:
weight = mass * gravity
Given: mass = 20 kg and gravity approximately 9.8 m/s^2 (acceleration due to gravity)
weight = 20 kg * 9.8 m/s^2 = 196 N
2. Resolve the weight of the body into two components: one parallel to the inclined plane and one perpendicular to it.
The component of weight parallel to the incline (F_parallel) can be calculated using the equation:
F_parallel = weight * sin(theta)
theta is the angle of inclination, which is 30 degrees.
F_parallel = 196 N * sin(30 degrees) = 98 N
3. Determine the net force acting on the body.
The net force is the difference between the parallel force component and the resisting force.
net force = F_parallel - resisting force
Given: resisting force = 40 N
net force = 98 N - 40 N = 58 N
4. Finally, calculate the acceleration of the body using Newton's second law:
F_net = mass * acceleration
Given: mass = 20 kg and net force = 58 N
58 N = 20 kg * acceleration
acceleration = 58 N / 20 kg = 2.9 m/s^2
Therefore, the acceleration of the body sliding down the inclined plane is 2.9 m/s^2.
To find the acceleration of the body, we can use Newton's second law of motion, which states that the net force acting on an object is equal to its mass multiplied by its acceleration.
In this case, the net force acting on the body is the component of the gravitational force acting down the incline, minus the resisting force. The gravitational force can be calculated using the formula:
Force_gravity = mass * gravitational acceleration,
where the gravitational acceleration is approximately 9.8 m/s^2.
The component of the gravitational force acting down the incline can be found by multiplying the gravitational force by the sine of the angle of inclination, which is 30 degrees in this case:
Force_gravity_component = Force_gravity * sin(angle of inclination).
The net force can be calculated by subtracting the resisting force from the component of the gravitational force:
Net force = Force_gravity_component - resisting force.
Since the net force is equal to the mass times the acceleration, we can rearrange the equation to solve for the acceleration:
acceleration = Net force / mass.
Plugging in the given values, we can calculate the acceleration:
mass = 20 kg,
resisting force = 40 N,
angle of inclination = 30 degrees,
gravitational acceleration = 9.8 m/s^2.
First, calculate the force of gravity:
Force_gravity = mass * gravitational acceleration.
Force_gravity = 20 kg * 9.8 m/s^2 = 196 N.
Next, calculate the component of the gravitational force:
Force_gravity_component = Force_gravity * sin(angle of inclination).
Force_gravity_component = 196 N * sin(30 degrees) = 98 N.
Now, calculate the net force:
Net force = Force_gravity_component - resisting force.
Net force = 98 N - 40 N = 58 N.
Finally, calculate the acceleration:
acceleration = Net force / mass.
acceleration = 58 N / 20 kg = 2.9 m/s^2.
Therefore, the acceleration of the body down the plane is 2.9 m/s^2.