A light rope passing over a frictionless pulley connects two objects. One object has a mass of 10kg. The tension in the rope is 90N. Calculate the acceleration and the mass of the second object.
Object 1
Fg-Ft = ma
100 - 90 - 10*a
10/10 = a
a = 1m/s^2
Object 2
Ft-Fg = ma
90-m10 = ma
I don't know what to do next. Help?
To calculate the mass of the second object, you can rearrange the equation Ft - Fg = ma to solve for mass (m):
Ft - Fg = ma (equation 1)
From the given information, the tension in the rope (Ft) is 90N, and the mass of the first object (m1) is 10kg. The acceleration (a) is already calculated as 1m/s^2.
Substituting the values into equation 1, you get:
90N - (10kg * 9.8m/s^2) = m * 1m/s^2
After calculating the right side of the equation, it becomes:
90N - 98N = m * 1m/s^2
Simplifying further:
-8N = m * 1m/s^2
To isolate the mass (m), divide both sides of the equation by 1m/s^2:
m = -8N / (1m/s^2)
The negative sign indicates that the direction of the force is opposite to the gravitational force. However, mass should always be positive, so you can simply take the magnitude:
m = 8kg
The mass of the second object is 8kg.
To summarize:
- The acceleration of both objects is 1m/s^2.
- The mass of the first object is 10kg.
- The tension in the rope is 90N.
- The mass of the second object is 8kg.