A minimum horizontal force of 10 N is needed to keep a 500 g book in place against a wall as shown.What maximum mass of book could be supported by the 10 N force if it were directed upwards at an angle of 60° instead of at right angles to the wall?
When the force F is normal to the wall the projections of the forces acting on the book are
x: N = F,
y: mg =F(fr).
F(fr) = k•N = k••F = m•g,
k = m•g/F =0.5•9.8/10 = 0.49.
When the force F is at 60o to horizontal the projections of the forces acting on the book are
x: N1 = F•cosα
y: m1•g =F(fr)+F•sinα
F(fr) = k•N1= k•F•cosα,
F(fr) = m1•g - F•sinα,
k•F•cosα= m1•g - F•sinα,
m1=F•( k• cosα +sinα)/g =
= 10(0.49•0.5 + 0.866)/9,8 = 1.13 kg.
To solve this problem, we need to break down the forces acting on the book.
First, let's consider the situation where the force is directed at right angles to the wall. In this case, the only force acting on the book is the force of gravity, which is equal to the weight of the book.
The weight of the book can be calculated using the formula:
Weight = mass x gravity
Given that the weight of the book is equal to 10 N, we can use this information to determine the mass of the book.
Rearranging the formula, we have:
Mass = Weight / gravity
Plugging in the values, we get:
Mass = 10 N / 9.8 m/s^2 ≈ 1.02 kg
So, the maximum mass of the book that could be supported by the 10 N force when directed at right angles to the wall is approximately 1.02 kg.
Now, let's consider the situation where the force is directed upwards at an angle of 60°. In this case, we have two forces acting on the book: the force of gravity acting downwards and the vertical component of the applied force acting upwards.
To calculate the maximum mass of the book that could be supported by the 10 N force in this case, we need to find the vertical component of the force of 10 N.
The vertical component of the force can be calculated using the formula:
Vertical Force = Total Force x sin(angle)
Given that the total force is 10 N and the angle is 60°, we can calculate the vertical component.
Vertical Force = 10 N x sin(60°) ≈ 8.66 N
Now, we can use the same formula as before to calculate the maximum mass of the book that could be supported by the 8.66 N vertical force:
Mass = Weight / gravity
Weight = Vertical Force
Mass = 8.66 N / 9.8 m/s^2 ≈ 0.88 kg
So, when the 10 N force is directed upwards at an angle of 60°, the maximum mass of the book that could be supported is approximately 0.88 kg.