Two forces act on a 10-kg mass. The first force has a magnitude of 15 N and pushes the
mass due North. The second force has a magnitude of 25 N and pushes the force due West.
What is the magnitude and direction of the acceleration of the mass?
net force is <-25,10> = 18.03 @ W31N
acceleration is thus 1.8 in the same direction
oops. The net force is 26.9, so a = 2.69
To find the magnitude and direction of the acceleration of the mass, 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.
First, let's calculate the net force acting on the 10-kg mass by considering both forces. Since the first force pushes the mass due North and the second force pushes it due West, these forces are acting perpendicular to each other. To find the net force, we can use the Pythagorean theorem.
The force due North has a magnitude of 15 N, and the force due West has a magnitude of 25 N.
Using the Pythagorean theorem, the net force (F_net) can be calculated as:
F_net = sqrt(F1^2 + F2^2)
F_net = sqrt(15^2 + 25^2)
F_net = sqrt(225 + 625)
F_net = sqrt(850)
F_net ≈ 29.15 N
Now, to find the acceleration (a), we can use Newton's second law:
F_net = m * a
where m is the mass (10 kg) and a is the acceleration. Rearranging the equation, we can solve for a:
a = F_net / m
a = 29.15 N / 10 kg
a ≈ 2.92 m/s^2
Therefore, the magnitude of the acceleration of the mass is approximately 2.92 m/s².
To find the direction of the acceleration, we can consider the angles formed by the two forces. Since the force due North and the force due West are perpendicular to each other, the acceleration will be along the diagonal between the North and West directions.
Using trigonometry, we can find the angle (θ) between the acceleration and due North:
θ = arctan(F2 / F1)
θ = arctan(25 N / 15 N)
θ ≈ arctan(1.67)
θ ≈ 58.29 degrees
Therefore, the direction of the acceleration is approximately 58.29 degrees relative to the North direction.