To find the mass of block m2, we can start by analyzing the forces acting on the system.
For block m1, the forces acting on it are:
- The force of gravity pulling it downward with a magnitude of m1 * g, where g is the acceleration due to gravity.
- The normal force exerted by the ramp, which is perpendicular to the surface of the ramp.
- The force of kinetic friction opposing the motion of m1 up the ramp, which can be calculated as μk * (m1 * g * cos(θ)), where μk is the coefficient of kinetic friction and θ is the angle of inclination of the ramp.
The net force acting on m1 is given by the equation:
Net Force = m1 * a + μk * (m1 * g * cos(θ))
Now, let's consider block m2. Since the string is light and ideal, the tension in the string is the same throughout. The tension in the string is also equal to the force pulling m1 up the ramp.
So, the force pulling on m2 is m2 * g, where g is the acceleration due to gravity.
Since the two blocks are connected by the string and the tension is the same, we can equate the forces:
m2 * g = m1 * a + μk * (m1 * g * cos(θ))
Now we can solve for m2:
m2 = (m1 * a + μk * (m1 * g * cos(θ))) / g
Plugging in the given values for m1, a, μk, θ, and g, we can calculate the mass of block m2.
I hope this helps! Let me know if you have any further questions.