A block of mass m is pushed along a horizontal table by a force f=70 N at an angle 55 degrees with the horizontal. Yhe coefficient of kinetic friction is 0.3
Find the normal force.
My work:
I know that there is 3 forces present: force of gravity, normal and applied.
I think the equation for finding normal force is Fa cos55 degrees + Fn - Fg = 0 but i think it is wrong....
You're on the right track, but there's a slight mistake in your equation.
Let's break down the forces acting on the block:
1. The force of gravity (Fg): This force is always acting straight down and it can be calculated as Fg = m * g, where m is the mass of the block and g is the acceleration due to gravity (approximately 9.8 m/s²).
2. The normal force (Fn): This force is exerted by the table on the block and it acts perpendicular to the surface of the table. It counteracts the force of gravity and keeps the block from sinking into the table. The magnitude of the normal force is equal to the weight of the block, so Fn = m * g.
3. The force applied (Fa): This is the force that you are applying to the block at an angle of 55 degrees with the horizontal. However, since the block is not moving vertically, only the horizontal component of this force affects the normal force. The horizontal component of the applied force can be calculated as Fa * cos(55°).
Now, we need to account for the force of friction. The force of kinetic friction (Fk) can be calculated as the coefficient of kinetic friction (μk) multiplied by the normal force, so Fk = μk * Fn.
Since the block is being pushed horizontally at a constant velocity (which means it is in equilibrium), the sum of the horizontal forces is zero. Therefore, we have:
Fa * cos(55°) - Fk = 0
Plugging in the values, we can write the equation as:
Fa * cos(55°) - μk * Fn = 0
Now, we can substitute Fn with m * g:
Fa * cos(55°) - μk * (m * g) = 0
To solve for the normal force (Fn), rearrange the equation:
Fn = (Fa * cos(55°)) / μk
Substituting the given values, we get:
Fn = (70 N * cos(55°)) / 0.3
Now, you can calculate the numerical value of the normal force by evaluating the right side of the equation.