Answer :
Final Answer:
(a) When the tension in the rope is 250 N, the acceleration of the crate is approximately 12.5 m/s².
(b) When the tension in the rope is 150 N, the acceleration of the crate is approximately 7.5 m/s².
(c) When the tension in the rope is zero, the acceleration of the crate is equal to the acceleration due to gravity, which is approximately 9.8 m/s².
(d) When the tension in the rope is 196 N, the acceleration of the crate is zero, as it's in equilibrium.
Explanation:
To calculate the acceleration of the 20 kg crate in each scenario, we can use Newton's second law of motion, which states that the force (F) acting on an object is equal to its mass (m) multiplied by its acceleration (a) or F = ma.
Given:
Mass of the crate (m) = 20 kg
Acceleration due to gravity (g) = 9.8 m/s² (approximately)
(a) When the tension in the rope is 250 N:
Using F = ma, we find:
250 N = (20 kg) * a
a = 250 N / 20 kg = 12.5 m/s²
(b) When the tension in the rope is 150 N:
Using F = ma, we find:
150 N = (20 kg) * a
a = 150 N / 20 kg = 7.5 m/s²
(c) When the tension in the rope is zero:
In this case, the only force acting on the crate is gravity, so it falls freely with an acceleration of approximately 9.8 m/s².
(d) When the tension in the rope is 196 N:
The tension exactly balances the force of gravity (mg), resulting in no net force and zero acceleration; the crate remains at rest.
In summary, the acceleration of the crate depends on the net force acting on it, which is the difference between the tension in the rope and the force of gravity.
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