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
wx = w sin 30 = (19.6)(0.5) = 9.8 Newton
wy = 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 wx.
∑F = wx
∑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
wx = w sin 30 = (29.4)(0.5) = 14.7 Newton
wy = 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 – wx = 0
F = wx
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
wx – 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 – wx = m a
F – 14.7 = (3)(2)
F – 14.7 = 6
F = 14.7 + 6
F = 20.7 Newton
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- Newton’s second law of motion
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- The motion of two bodies with the same acceleration on the rough horizontal surface with the friction force
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- Motion on the rough inclined plane with the friction force
- Motion in an elevator
- The motion of bodies connected by cord and pulley
- Two bodies with the same magnitude of accelerations
- Rounding a flat curve – dynamics of circular motion
- Rounding a banked curve – dynamics of circular motion
- Uniform motion in a horizontal circle
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