A block of metal, of 25g mass moves down without acceleration when the plane is inclined at an angle of 30^ . When the inclination is increased by 30^ , find the downward acceleration of the block.

Step-by-step solution

When the block moves down without acceleration at an angle = 30^ , the net force is zero. mg 30^ = _k mg 30^ _k = 30^ = 1 3 When the inclination is increased by 30^ , the new angle is ' = 60^ . The downward acceleration a is given by: ma = mg 60^ - _k mg 60^ a = g ( 60^ - _k 60^ ) Substituting the values of _k and g = 9.8 ms⁻² : a = 9.8 ( 3 2 - 1 3 ( 1 2 ) ) a = 9.8 ( 3 - 1 2 3 ) = 9.8 3 a = 9.8 1.732 5.66 ms⁻² Answer: 5.66 ms⁻²