Three masses are arranged on a flat surface as shown. Two of the masses are as follows: m2 = 16.3 kg and m3 = 66.5 kg. A horizontal force of 519 N applied to m2 accelerates the masses across the floor, which has a coefficient of friction of μ = 0.312, at 1.77 m/s2.
What is the mass of m1?
To find the mass of m1, we can use Newton's second law of motion, which states that the net force acting on an object is equal to the product of its mass and acceleration (F = m * a).
In this case, the net force acting on the masses is the horizontal force applied to m2, minus the force of friction (F_net = F_applied - F_friction).
Therefore, we need to calculate the force of friction. The force of friction can be determined using the equation F_friction = μ * N, where μ is the coefficient of friction and N is the normal force.
The normal force is the force exerted by a surface to support the weight of an object resting on it. In this case, since the masses are on a flat surface and not accelerating up or down, the normal force is equal to the weight of the masses.
Now, let's calculate the force of friction and the normal force:
For m2:
Weight of m2 = m2 * g (where g is the acceleration due to gravity)
Weight of m2 = 16.3 kg * 9.8 m/s^2 = 159.74 N
Normal force on m2 = Weight of m2 = 159.74 N
Force of friction on m2 = μ * N = 0.312 * 159.74 N = 49.83 N
Now, let's calculate the net force:
Net force = F_applied - F_friction
Net force = 519 N - 49.83 N = 469.17 N
Finally, let's calculate the mass of m1 using Newton's second law:
Net force = m1 * a
469.17 N = m1 * 1.77 m/s^2
Dividing both sides of the equation by 1.77 m/s^2:
m1 = 469.17 N / 1.77 m/s^2
m1 ≈ 264.56 kg
Therefore, the mass of m1 is approximately 264.56 kg.