Question Number 188937 by Tawa11 last updated on 09/Mar/23
A body of mass 20kg lies on a horizontal floor and is acted on by constant forces of magnitude 100N and mN in the directions 180° and 060° respectively, where m is a constant. The body begins to move in the direction 090°. If there's also a resistance of 1N/5 per kilogram to the motion of the body;
(a) calculate the value of m and the magnitude of the resultant force acting on the body
(b) find the acceleration of the body.
Commented by ARUNG_Brandon_MBU last updated on 09/Mar/23
Here is what Chat GPT says:
(a) To calculate the value of m and the magnitude of the resultant force acting on the body, we need to resolve the forces acting on the body into their components in the direction of 090°.
The force of magnitude 100N acting in the direction 180° is opposing the motion of the body in the direction 090°. Therefore, its component in the direction of 090° is -100N.
The force of magnitude mN acting in the direction 060° is at an angle of 30° to the direction of 090°. Therefore, its component in the direction of 090° is mN x cos(30°) = mN/2.
The resistance to the motion of the body is 1N/5kg x 20kg = 4N.
The resultant force acting on the body in the direction of 090° is given by:
Resultant force = -100N + mN/2 - 4N
For the body to begin moving in the direction of 090°, the net force acting on it must be greater than or equal to zero. Therefore:
-100N + mN/2 - 4N ≥ 0
Simplifying this inequality, we get:
mN/2 ≥ 96N
mN ≥ 192N
m ≥ 192N / N = 192
Therefore, the value of m is 192.
The magnitude of the resultant force acting on the body is:
Resultant force = -100N + mN/2 - 4N = -100N + 96N - 4N = -8N
Therefore, the magnitude of the resultant force acting on the body is 8N.
(b) To find the acceleration of the body, we need to use Newton's second law of motion which states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass.
The net force acting on the body is -8N.
The mass of the body is 20kg.
The resistance to the motion of the body is 4N.
Therefore, the net force acting on the body after accounting for resistance is -8N + 4N = -4N.
The acceleration of the body is given by:
Acceleration = (Net force acting on the body) / (Mass of the body)
Acceleration = (-4N) / (20kg)
Acceleration = -0.2 m/s^2
Therefore, the acceleration of the body is -0.2 m/s^2.
Commented by Tawa11 last updated on 09/Mar/23
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