A dynamics cart m1 attached to has a hanging mass m2 m1 = 0.20 kg, and m2 = 1.3 kg. The magnitude of the acceleration of this system will be what approximately?
To determine the magnitude of acceleration for this system, we can first analyze the forces acting on the system.
1. The force due to the mass hanging vertically is given by: F = m2 * g
where m2 represents the mass of the hanging mass and g is the acceleration due to gravity (approximately 9.8 m/s^2).
2. The tension force in the string connecting the two masses is the same for both masses. Since the string is taut, it acts as if it were a single mass.
3. The net force acting on the system is the force due to the hanging mass minus the force due to friction between the dynamics cart and the surface it's on.
Since we need to find the magnitude of the acceleration, we can set up the equation:
Fnet = (m1 + m2) * a
In this case, Fnet is equal to the force due to the hanging mass minus the force of friction. However, if we assume that the friction is negligible, we can simplify the equation to:
Fnet = (m1 + m2) * a = m2 * g
Now we can substitute in the given values:
m1 = 0.20 kg
m2 = 1.3 kg
g = 9.8 m/s^2
(m1 + m2) * a = m2 * g
(0.20 + 1.3) * a = 1.3 * 9.8
Simplifying the equation:
1.50 * a = 12.74
Finally, to find the magnitude of acceleration (a), we'll divide both sides of the equation by 1.50:
a = 12.74 / 1.50 ≈ 8.49 m/s^2
Therefore, the magnitude of acceleration for this system is approximately 8.49 m/s^2.