A 5kg object is to be given an upward acceleration of 3m/s2 by a rope pulling straight upward on it. The tension in the rope is (g = 10m/s2).
Question
A 5kg object is to be given an upward acceleration of 3m/s2 by a rope pulling straight upward on it. The tension in the rope is (g = 10m/s2).
Solution
To solve this problem, we need to use the second law of motion, which states that the force acting on an object is equal to its mass times its acceleration (F = ma).
Step 1: Calculate the force due to gravity The force due to gravity (weight) can be calculated using the formula F = mg, where m is the mass of the object and g is the acceleration due to gravity.
F = 5kg * 10m/s² = 50N
Step 2: Calculate the force needed to accelerate the object upwards The force needed to accelerate the object upwards can be calculated using the formula F = ma, where m is the mass of the object and a is the acceleration.
F = 5kg * 3m/s² = 15N
Step 3: Calculate the total tension in the rope The total tension in the rope is the sum of the force due to gravity and the force needed to accelerate the object upwards.
Tension = 50N + 15N = 65N
So, the tension in the rope is 65N.
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