two blocks are connected over a pulley. The mass of block A is 10 kg and the coefficient of kinetic friction between A and the incline is 0.24. Angle èof the incline is 30°. Block A slides down the incline at constant speed. What is the mass of block B?
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To find the mass of block B, we first need to understand the forces acting on block A.
Let's break down the forces acting on block A:
1. Gravity force (FgA): This force pulls block A downward and is equal to the mass of A (10 kg) multiplied by the acceleration due to gravity (9.8 m/s^2). So, FgA = 10 kg * 9.8 m/s^2 = 98 N.
2. Normal force (FnA): This force is perpendicular to the incline and prevents block A from sinking into the incline. It is equal in magnitude and opposite in direction to the perpendicular component of the gravitational force. So, FnA = FgA * cos(30°) = 98 N * cos(30°).
3. Friction force (FfA): This force opposes the motion of block A and is parallel to the incline. Its magnitude is given by the coefficient of kinetic friction (0.24) multiplied by the normal force (FnA). So, FfA = 0.24 * FnA.
Since block A slides down the incline at a constant speed, the net force in the horizontal direction must be zero. This means that the friction force equals the component of the gravitational force parallel to the incline.
FfA = component of FgA in the direction of the incline
0.24 * FnA = 98 N * sin(30°)
Now, we can solve for the normal force FnA:
FnA = (98 N * sin(30°)) / 0.24
Next, let's move on to block B. The only force acting on block B is the tension force in the string (T). This tension force is the same throughout the string.
Since block B is connected to block A by a pulley, the tension force is equal to the force required to lift block A, which is the gravitational force acting on A.
T = FgA = 10 kg * 9.8 m/s^2 = 98 N
Finally, the mass of block B can be calculated using the following equation:
T = mB * g,
where mB is the mass of block B and g is the acceleration due to gravity.
Rearranging the equation, we have:
mB = T / g = 98 N / 9.8 m/s^2
Therefore, the mass of block B is equal to 10 kg.