The mass of an object C is 100kg, the acceleration measured by the observer in the inertial system A is 100 m/s², while the observer
in the system B measures the
acceleration as 90 m/s². What is the fictitions force? What is the acceleration of the non inertial system B? What could B do to achieve a true inertial system?
Answers
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Answer:
Non-inertial frames
Motion in a non-inertial frame
Linear acceleration
Problem:
At t = 0 a 100 g ball is thrown upward with initial speed v = 2 m/s in an open-platform elevator which at that time is moving downward with v = 3 m/s and accelerating downward with an acceleration of magnitude a = 3 m/s2. A drag force with magnitude Fdrag = 0.8 N acts on the ball.
(a) What is the net force Fnet acting on the ball in the frame of the elevator just after it has been thrown?
(b) What is the net force Fnet acting on the ball in the frame of a person standing on the ground just after it has been thrown?
Solution:
Concepts:
Motion in an accelerating frame
Reasoning:
Fictitious forces appear in an accelerating frame.
In the inertial frame the ball moves downward just after it is thrown, the drag force which opposes the relative motion of the ball and the air therefore points upward.
Details of the calculation:
Let the upward direction be the positive y -direction.
(a) Fnet = mg - ma + Fdrag = (-mg + ma + Fdrag) j = (-0.1*6.8 N + 0.8 N) j
= 0.12 N j. The ball accelerates upward in the frame of the elevator.
(b) Fnet = mg + Fdrag = (-mg + Fdrag) j = (-0.1*9.8 N + 0.8 N) j = 0.18 N j.
The ball accelerates downward in the frame of the person on the ground.
Problem:
A hauling truck is traveling on a level road. The driver suddenly applies the brakes, causing the truck to decelerate by an amount g/2. This causes a box in the rear of the truck to slide forward. If the coefficient of sliding friction between the box and the truck bed is (1/3), find the acceleration of the box relative to
(a) the truck and
(b) the road.
Solution:
Concepts:
Motion in an accelerating frame.
Reasoning:
In an accelerating frame fictitious forces appear. The net force in such a frame is
F = Finertial - ma, where a is the acceleration of the frame.
Details of the calculation:
This is a one-dimensional problem. Let the positive direction be the direction of the trucks initial velocity.
(a) F = -mg/3 + mg/2 = +mg/6. The acceleration of the box relative to the truck is g/6.
(b) F = -mg/3. The acceleration of the box relative to the road is -g/3.