Tom (65 kg) is standing on a scale in an elevator holding an apple. The elevator begins to accelerate downwards at 2.4 m/s2.
(c) What is the acceleration of the apple with respect to Tom, after he drops the apple while accelerating?
(d) What is the acceleration of the apple if an outsider would look onto the scenario?
(e) What would the scale read if the elevator accelerated upward at 2.4 m/s2?
Would it be N=m(g+a) = 793N
To find the acceleration of the apple with respect to Tom when he drops the apple while accelerating downwards, we need to consider the relative motion between Tom and the apple.
(c) When Tom drops the apple, it will experience the same acceleration as him due to gravity, regardless of the acceleration of the elevator. This is because both objects are in free fall, and their motion is solely influenced by gravity. So, the acceleration of the apple with respect to Tom will be equal to the acceleration due to gravity, which is approximately 9.8 m/s^2.
To calculate the acceleration of the apple if an outsider were to look onto the scenario, we need to consider the net force acting on the apple. This will be the sum of the gravitational force and the force due to the elevator's acceleration.
(d) The gravitational force acting on the apple is given by F_gravity = m * g, where m is the mass of the apple (not provided) and g is the acceleration due to gravity (approximately 9.8 m/s^2). The force due to the elevator's acceleration is F_elevator = m * a_elevator, where m is the mass of the apple and a_elevator is the acceleration of the elevator. Since the apple is no longer supported by Tom after being dropped, the net force acting on the apple will be the same as the force due to the elevator's acceleration, so:
Net force = F_elevator = m * a_elevator
Therefore, the acceleration of the apple if an outsider looks onto the scenario will be the same as the acceleration of the elevator, which is given as 2.4 m/s^2.
(e) If the elevator were accelerating upward at 2.4 m/s^2, the scale reading would be the sum of the normal force and the force due to the elevator's acceleration. According to Newton's second law, the net force acting on the person standing on the scale is equal to the product of their mass and their acceleration:
Net force = m * (g + a_elevator)
Since the person's weight is given by the product of their mass and the acceleration due to gravity (W = m * g), we can rewrite the equation as:
Net force = W + m * a_elevator
The scale reading would be equal to the net force acting on the person. Therefore, the scale reading would be N = m * (g + a_elevator) = 65 kg * (9.8 m/s^2 + 2.4 m/s^2) = 65 kg * 12.2 m/s^2 = 793 N. So, you are correct, the scale reading would be 793 N.