A body whose weight is W1=75N is tied to another
body whose weight is W2=45N .If the coefficient of
kinetic friction between W1 and the inclined plane
(25°)AB is 0.15,calculate the coefficient of kinetic
between W2 and the inclined plane(15°) BC when the
two masses slide down at constant velocity. (answer
0.23)
I don't get the picture of the arrangement of the inclined planes at different angle.
To calculate the coefficient of kinetic friction between W2 and the inclined plane BC, we need to use the principles of forces, friction, and the angle of inclination.
First, let's break down the problem into different components:
1. Calculate the force of gravity acting on each body:
- W1 (weight of the first body) = 75N
- W2 (weight of the second body) = 45N
2. Determine the net force acting on each body:
- For W1, we need to consider the force of gravity, the normal force, and the force of friction.
- For W2, we need to consider the force of gravity and the normal force.
3. Set up the equilibrium condition for both bodies:
- When the two masses slide down at constant velocity, the net force acting on each body is zero.
Now, let's calculate the coefficient of kinetic friction between W2 and the inclined plane BC.
1. Determine the net force acting on W1:
- Net force on W1 = Force of gravity - Force of friction
- The force of gravity acting on W1 is W1 = 75N
- The angle of inclination of the inclined plane AB is given as 25°.
- The normal force, N1, acting on W1 is given by N1 = W1 * cos(25°).
- The force of friction, Fk1, acting on W1 is given by Fk1 = μk * N1, where μk is the coefficient of kinetic friction (given as 0.15).
- Therefore, the net force on W1 is: F_net1 = W1 - Fk1.
2. Determine the net force acting on W2:
- Net force on W2 = Force of gravity - Force of friction
- The force of gravity acting on W2 is W2 = 45N
- The angle of inclination of the inclined plane BC is given as 15°.
- The normal force, N2, acting on W2 is given by N2 = W2 * cos(15°).
- We need to find the force of friction, Fk2, acting on W2.
- Let's assume the coefficient of kinetic friction between W2 and BC as μk2.
- Therefore, the net force on W2 is: F_net2 = W2 - Fk2.
3. Set up the equilibrium condition for both bodies:
- Since both bodies are sliding down at a constant velocity, the net forces acting on them are zero.
- Therefore, F_net1 = 0 and F_net2 = 0.
4. Solve for the coefficient of kinetic friction (μk2):
- From F_net1 = 0, we have W1 - Fk1 = 0, which gives Fk1 = W1.
- From F_net2 = 0, we have W2 - Fk2 = 0, which gives Fk2 = W2.
- Substituting the values of Fk1 and Fk2, we have W1 = μk * N1 and W2 = μk2 * N2.
- Rearranging the equation for W2, we get μk2 = W2 / N2.
5. Calculate the coefficient of kinetic friction (μk2):
- Substitute the values of W2 and N2 into the equation: μk2 = W2 / N2.
- μk2 = 45N / (W2 * cos(15°)).
- Simplify the equation and calculate the value of μk2.
By following these steps and substituting the given values, we can calculate the coefficient of kinetic friction between W2 and the inclined plane BC.