Anna pushes horizontally on a 52-kg penguin with force of 10 N, but the penguin does not budge. Find the force of static friction between the penguin’s feet and the ground.
I have no idea where to start. Any help is appreciated. Thanks.
If the penguin isn't budging, the friction force equals the opposing force, 10 N.
This may be much less than the maximum static friction force possible, which is
52*g*mu(static).
Oh ok. Thanks this makes much more sense now.
To find the force of static friction between the penguin's feet and the ground, we can use Newton's laws of motion.
1. First, let's recall Newton's second law, which states that the net force acting on an object is equal to the product of its mass and acceleration. The formula for this is F = m * a, where F is the net force, m is the mass, and a is the acceleration.
2. In this scenario, the penguin is not moving, which means it is in equilibrium. This implies that the net force acting on the penguin is zero. Therefore, we can rewrite Newton's second law as follows: F_net = 0 = F_applied + F_friction.
3. In this case, the only force acting horizontally on the penguin is the applied force by Anna, which is 10 N. So, we have: F_applied = 10 N. The force of static friction between the penguin and the ground will be equal in magnitude but in the opposite direction to the applied force.
4. To find the force of static friction, we need to determine the maximum value of static friction (F_static_max). This maximum value can be calculated using the formula F_static_max = μ_static * N, where μ_static is the coefficient of static friction, and N is the normal force.
5. The normal force (N) is the force exerted by the ground on the penguin perpendicular to the surface. In this scenario, since the penguin is on a flat horizontal surface and not accelerating vertically, the normal force will be equal in magnitude but opposite in direction to the force of gravity acting on the penguin. Therefore, we have: N = m * g, where g is the acceleration due to gravity (approximately 9.8 m/s^2)
6. Finally, once we determine the maximum value of static friction (F_static_max), we can conclude that the force of static friction between the penguin's feet and the ground (F_friction) is equal to F_static_max since the penguin does not budge.
Now, let's calculate the force of static friction:
Step 1: F_net = F_applied + F_friction
Step 2: 0 = 10 N + F_friction
Since the penguin is not moving, F_net = 0.
Rearranging the equation to solve for F_friction, we have:
F_friction = -10 N
Since F_friction is equal in magnitude but opposite in direction to F_applied. Therefore, the force of static friction between the penguin's feet and the ground is 10 N.