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
So I substituted 1 for acceleration
90-m10 = 1m
I still don't know what to do now.
Another question -
A 30 N force is pushing the 10kg object down the slope. The coefficient of friction between the object and the surface is 0.625. The slope is 37 degrees to the horizontal.
Calculate the acceleration of the object.
Perpendicular - balanced forces
EF = 0
Fn - Fgperp = 0
Fn - 100cos37 = 0
Fn = 79.86N
Parallel motion - unbalanced forces
EF = ma
Fa - Ffr + Fg// = ma
30 - (0.625)*(79.86) + 100Sin37 = 10a
a = 4.03m/s^2
Is that right?
I don't know what to do next. Help?
You have it.
Solve that last equation for the mass.
I would strongly recommend that you keep the units in your equations--especially ones that are challenging.
90N - m *(10 m/s^2) = m * (1 m/s^2)
90N = m (11 m/s^2)
(90N)/(11 m/s^2) = 8.18kg
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Your answer to the second question look OK.
For the first question, you have correctly calculated the acceleration of the system as 1 m/s^2. Now, to calculate the mass of the second object, you can use the equation Ft - Fg = ma, where Ft is the tension in the rope and Fg is the force due to gravity acting on the second object.
You already know the tension in the rope (90 N) and the acceleration (1 m/s^2). The force due to gravity acting on the second object can be calculated as mass times acceleration due to gravity (Fg = mg), where g is approximately 9.8 m/s^2 on Earth.
Substituting the given values into the equation, we have:
90 - m * 9.8 = 1 * m
To solve for the mass of the second object, you can rearrange the equation:
90 = m * (9.8 + 1)
Now, divide both sides of the equation by (9.8 + 1) to isolate the mass:
m = 90 / (9.8 + 1)
Calculating this expression, we find:
m ≈ 8.18 kg
Therefore, the mass of the second object is approximately 8.18 kg.
For the second question, you correctly calculated the acceleration of the object as 4.03 m/s^2.
If you need further assistance, please let me know.