If a block of mass 10.0 kg rests on a horizontal surface, and the coefficient of static friction is 0.300, what is the maximum static friction that can act on the block?
If you could walk me step by step on completing this problem, I would be extremely grateful and it would be helpful! Thank you!
weight = 10 * 9.81 = 98.1 Newtons
= normal force
max friction force = .3 * 98.1 Newtons
Of course we are not allowed to push down on it :)
So the answer is 29.4?
Our mass is 10.0 kg right?
that is what you said. A mass of 10 kg is a weight of 98.1 Newtons
does the mass always have to be in kilograms? If it is not, do we convert it to kg?
Certainly! Let's walk through the steps to solve this problem.
Step 1: Identify the given values and the desired unknown.
Given:
- Mass of the block (m) = 10.0 kg
- Coefficient of static friction (μ) = 0.300
Unknown:
- Maximum static friction (F_static)
Step 2: Understand the concept of static friction.
Static friction is the force that prevents an object from moving when it's at rest on a surface. It acts parallel to the surface and opposes the motion. The maximum static friction occurs just before the object starts to move and is given by the equation F_static = μ * N, where μ is the coefficient of static friction and N is the normal force.
Step 3: Determine the normal force (N).
The normal force is the force exerted by the surface on the object perpendicular to the surface. In this case, the object is resting on a horizontal surface, so the normal force (N) is equal in magnitude and opposite in direction to the force of gravity acting on the object. Therefore, N = m * g, where m is the mass of the object and g is the acceleration due to gravity (approximately 9.8 m/s²).
Substituting the given values, we get N = 10.0 kg * 9.8 m/s² = 98.0 N.
Step 4: Calculate the maximum static friction (F_static).
Using the formula F_static = μ * N, where μ is the coefficient of static friction and N is the normal force, we substitute the given values:
F_static = 0.300 * 98.0 N
Evaluating this expression, we find that the maximum static friction on the block is:
F_static = 29.4 N
So, the maximum static friction that can act on the block is 29.4 N.
I hope this guide was helpful! Let me know if you have any further questions.