Motion on the inclined plane without the friction force – application of Newton’s law of motion problems and solutions

1. Box’s mass = 2 kg, acceleration due to gravity = 9.8 m/s². Find (a) the net force which accelerates the box downward (b) magnitude of the box’s acceleration.

Solution

Known :

Mass (m) = 2 kg

Acceleration due to gravity (g) = 9.8 m/s²

Weight (w) = m g = (2)(9.8) = 19.6 Newton

w_x = w sin 30 = (19.6)(0.5) = 9.8 Newton

w_y = w cos 30 = (19.6)(0.5√3) = 9.8√3 Newton

Solution :

(a) The net force which accelerates the box

Inclined plane is smooth, so there is no friction force. The only force which acts on the object is w_x.

∑F = w_x

∑F = 9.8 Newton

(b) magnitude of the acceleration

∑F = m a

9.8 = (2) a

a = 9.8 / 2

a = 4.9 m/s²

Magnitude of the acceleration is 4.9 m/s², direction of the acceleration is downward.

2. Inclined plane is smooth so there is no friction force. Object’s mass is 3 kg, acceleration due to gravity is 9.8 m/s². Determine the magnitude of the force F if (a) object is at rest (b) object is moving downward with constant acceleration 2 m/s² (c) object is moving upward with a constant acceleration of 2 m/s².

Solution

Known :

Mass (m) = 3 kg

Acceleration due to gravity (g) = 9.8 m/s²

Weight (w) = m g = (3)(9.8) = 29.4 Newton

w_x = w sin 30 = (29.4)(0.5) = 14.7 Newton

w_y = w cos 30 = (29.4)(0.5√3) = 14.7√3 Newton

Solution :

(a) The magnitude of the force F if an object is at rest

Newton’s first law of motion states that if an object is at rest, the net force acts on the object is zero.

∑F = 0

F – w_x = 0

F = w_x

F = 14.7 Newton

(b) The magnitude of the force F if an object is moving downward at a constant 2 m/s²

∑F = m a

w_x – F = m a

14.7 – F = (3)(2)

14.7 – F = 6

F = 14.7– 6

F = 8.7 Newton

(c) The magnitude of the force F if an object is moving upward at a constant 2 m/s²

∑F = m a

F – w_x = m a

F – 14.7 = (3)(2)

F – 14.7 = 6

F = 14.7 + 6

F = 20.7 Newton

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1. Mass and weight
2. Normal force
3. Newton’s second law of motion
4. Friction force
5. Motion on the horizontal surface without friction force
6. The motion of two bodies with the same acceleration on the rough horizontal surface with the friction force
7. Motion on the inclined plane without friction force
8. Motion on the rough inclined plane with the friction force
9. Motion in an elevator
10. The motion of bodies connected by cord and pulley
11. Two bodies with the same magnitude of accelerations
12. Rounding a flat curve – dynamics of circular motion
13. Rounding a banked curve – dynamics of circular motion
14. Uniform motion in a horizontal circle
15. Centripetal force in uniform circular motion