a 15 kg bucket is raised to paint a ladder with an acceleration of 3 m/s.^2 what is the tension in the rope?
To calculate the tension in the rope, we need to consider the forces acting on the bucket. In this case, there are two forces: the weight (mg) of the bucket acting downwards and the tension force (T) in the rope acting upwards.
The formula to calculate the net force on an object is given by Newton's second law of motion:
Net force (F) = mass (m) * acceleration (a)
In this case, the net force is equal to the tension force minus the weight of the bucket:
F = T - mg
We know the mass of the bucket (m = 15 kg) and the acceleration (a = 3 m/s^2). The weight of the bucket can be calculated using the formula:
Weight (mg) = mass (m) * acceleration due to gravity (g)
The acceleration due to gravity is approximately 9.8 m/s^2. Substituting the values, we can calculate the weight:
Weight (mg) = 15 kg * 9.8 m/s^2 = 147 N
Now we can substitute the values back into the equation for the net force:
F = T - mg
F = T - 147 N
Since the bucket is being raised, the net force is equal to the mass multiplied by the acceleration (F = ma). Substituting the values:
F = ma
T - 147 N = 15 kg * 3 m/s^2
T - 147 N = 45 N
Now, to find the tension (T), we can rearrange the equation:
T = 45 N + 147 N
T = 192 N
Therefore, the tension in the rope is 192 N.