A mass of 20 kg on a plane inclined at 40 degrees. A string attached to that mass goes up the plane, passed over a pullley and is attached to mass of 30 kg that hangs verticalyy. a) find the acceleration and it's dirction b) the tension in the string. Assume no friction.

I first drew the picture. How would I find the equation since F=ma doesn't include everything?

Benji. You are randi are apparently the same person. Please quit posting duplicates.

To find the acceleration and its direction, as well as the tension in the string, we can apply Newton's second law of motion to both masses separately.

For the mass on the inclined plane (20 kg), we need to consider the force acting parallel to the inclined plane, which is the component of the gravitational force. The force can be calculated as follows:

Force parallel = mass * gravitational acceleration * sine(angle of inclination)
= 20 kg * 9.8 m/s^2 * sin(40 degrees)
≈ 127.36 N

Since there is no friction, this force will be responsible for accelerating the mass. Therefore:

Force parallel = mass * acceleration
127.36 N = 20 kg * acceleration

By rearranging the equation, we can find the acceleration:

acceleration = 127.36 N / 20 kg
acceleration ≈ 6.37 m/s^2

The direction of acceleration will be parallel to the inclined plane, so we can take it as positive in our calculation.

Next, let's consider the hanging mass (30 kg). The tension in the string will act upward and oppose the gravitational force on this mass. Since the mass is in vertical equilibrium, the tension will be equal to the gravitational force acting on it:

Tension = mass * gravitational acceleration
Tension = 30 kg * 9.8 m/s^2
Tension ≈ 294 N

So, the tension in the string is approximately 294 N.

Therefore, the answers to the given questions are:
a) The acceleration is approximately 6.37 m/s^2, directed up the inclined plane.
b) The tension in the string is approximately 294 N.