A block of mass m is placed on a triangular block of mass M Which in turn Placed on a horizontal frictionless Surface find the velocity of the triangular block when the smaller block reaches the bottom end
42 cm/s
To find the velocity of the triangular block when the smaller block reaches the bottom end, we can use the principle of conservation of energy.
1. We first determine the potential energy of the smaller block when it reaches the bottom end. The potential energy (PE) of an object is given by the formula PE = mgh, where m is the mass of the object, g is the acceleration due to gravity, and h is the height.
2. Assuming that the triangular block is an isosceles triangle, we can calculate its height using the Pythagorean theorem. Let's assume the length of the base of the triangle is L, then the height (h) can be found as h = (L/2) * sqrt(3).
3. When the smaller block reaches the bottom end, the height of the triangle (h) will be equal to the distance it has traveled. Therefore, we can substitute the value of h in the potential energy equation as PE = mg(L/2) * sqrt(3).
4. The potential energy of the smaller block will be transferred to the triangular block as kinetic energy when it reaches the bottom end. Therefore, the kinetic energy (KE) of the triangular block will be equal to the potential energy of the smaller block, i.e., KE = mg(L/2) * sqrt(3).
5. The kinetic energy (KE) of an object is given by the formula KE = (1/2) * M * V^2, where M is the mass of the object and V is its velocity.
6. Equating the expressions for kinetic energy, we have (1/2) * M * V^2 = mg(L/2) * sqrt(3).
7. Now we can solve the equation for V. Rearranging the equation, we get V^2 = (2mg(L/2) * sqrt(3)) / M.
8. Simplifying further, V^2 = (mgsqrt(3)L) / M.
9. Finally, taking the square root of both sides, we find the velocity of the triangular block when the smaller block reaches the bottom end as V = sqrt((mgsqrt(3)L) / M).
By following this procedure and substituting the values of m, g, L, and M, you can find the velocity of the triangular block.