a 15.5 kg block is pulled by two forces. The first is 11.8 N at a 53.7 angle and the second is 22.9 at a -15.8 angle. What is the magnitude of the acceleration
add the two forces to get the resultant force F. Then, as usual, |F| = m|a|
Given: F1 = 11.8N[53.7o],
F2 = 22.9N[-15.8o].
M = 15.5 kg.
Fr = 11.8(53.7o] + 22.9[-15.8],
Fr = (11.8*Cos53.7+22.9*Cos(-15.8)) + (11.8*sin53.7+22.9*sin(-15.8))I,
Fr = 29 + 3.2i,
Fr = sqrt(29^2+3.2^2) = Resultant force.
Fr = M*a.
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To find the magnitude of the acceleration, we can use Newton's second law of motion, which states that the acceleration of an object is directly proportional to the net force acting on it, and inversely proportional to its mass.
The net force acting on the block can be found by adding the components of the individual forces in the horizontal and vertical directions.
First, let's calculate the horizontal components of the two forces:
Horizontal component of the first force = 11.8 N * cos(53.7°)
Horizontal component of the second force = 22.9 N * cos(-15.8°) (Note: cosine of a negative angle is the same as the cosine of the positive angle)
Next, let's calculate the vertical components of the two forces:
Vertical component of the first force = 11.8 N * sin(53.7°)
Vertical component of the second force = 22.9 N * sin(-15.8°) (Note: sine of a negative angle is the same as the negative sine of the positive angle)
Now, we can sum up the horizontal and vertical components of the total force:
Horizontal component of the total force = Sum of the horizontal components of the two forces
Vertical component of the total force = Sum of the vertical components of the two forces
Finally, we can use Newton's second law to find the magnitude of the acceleration:
Acceleration = Net force / Mass
Substituting the calculated values, we can find the magnitude of the acceleration.