25 gram mass is given an upward acceleration of 30 m/s^2 by a rope.
need help finding tension in the rope?
not sure how to set up the problem??
Tension is the reaction force. Clearly you have two forces in opposite directions.
Let T be the tension in the rope. The net force acting is T - W, where
W = M g is the weight.
Newton's Second Law says
T - Mg = Ma
which can be rewritten
T = M (g + a), where
a is the acceleration. Solve for T
To find the tension in the rope, you can use Newton's Second Law, which states that the net force acting on an object is equal to its mass multiplied by its acceleration.
In this case, the net force is the tension in the rope minus the weight of the object. The weight can be calculated by multiplying the mass of the object by the acceleration due to gravity (9.8 m/s^2).
Let T be the tension in the rope.
Let M be the mass of the object.
Let a be the acceleration of the object.
Let g be the acceleration due to gravity (9.8 m/s^2).
The net force can be written as:
T - Mg = Ma
Rearranging the equation, we can solve for T:
T = Mg + Ma
Now, plug in the values given in the question:
M = 25 grams = 0.025 kg (since 1 gram = 0.001 kg)
a = 30 m/s^2
g = 9.8 m/s^2
Substitute these values into the equation:
T = (0.025 kg)(9.8 m/s^2 + 30 m/s^2)
Calculate the values inside parentheses and multiply:
T = (0.025 kg)(39.8 m/s^2)
Finally, calculate the tension in the rope:
T ≈ 0.995 N (rounded to three decimal places)
Therefore, the tension in the rope is approximately 0.995 Newtons.