# Static Friction and calculating distance

In summary, Brad, sitting on a wheeled chair with a combined weight of 540 N, catches a 15 kg medicine ball thrown horizontally by his friend at a velocity of 6 m/s. Using the conservation of momentum and accounting for the coefficient of static friction between the chair wheels and the floor (0.05), it can be determined how far Brad will travel after catching the ball. This is a combination problem involving multiple laws of physics and can be solved in different ways.
Brad is sitting at rest on a wheeled chair in a long hallway. He and the chair have a combined weight of 540 N. His friend throws a 15 kg medicine ball horizontally at Brad with a velocity of 6 m/s. Brad cataches the medicine ball. If the coefficient of static friction between the chair wheels and the floor is 0.05, how far will Bard travel after catching the ball?

My prof said that this is a combination problem meaning that multiple laws of phyics are going to be used. My problem is that I can't tell which laws I need to be using. Any help would be greatly appreciated.

Thanks!

Brad is sitting at rest on a wheeled chair in a long hallway. He and the chair have a combined weight of 540 N. His friend throws a 15 kg medicine ball horizontally at Brad with a velocity of 6 m/s. Brad cataches the medicine ball. If the coefficient of static friction between the chair wheels and the floor is 0.05, how far will Bard travel after catching the ball?

My prof said that this is a combination problem meaning that multiple laws of phyics are going to be used. My problem is that I can't tell which laws I need to be using. Any help would be greatly appreciated.

Thanks!
It is a two-step problem. First, momentum is conserved; Brad acquires a velocity in the process. He and the ball are then moving, but are slowed to a stop by a frictional force. This second part can be approached in a couple of different ways to find the distance moved.

In this scenario, we can use the laws of motion and friction to calculate the distance that Brad will travel after catching the ball. The first law of motion, also known as the law of inertia, states that an object at rest will remain at rest unless acted upon by an external force. In this case, the external force is the medicine ball being thrown at Brad.

Once the ball is caught by Brad, the second law of motion, also known as the law of acceleration, comes into play. This law states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. In other words, the greater the force and the less the mass, the greater the acceleration.

Using these laws, we can calculate the net force acting on Brad and his chair after catching the ball. The net force is equal to the force of the ball (F=ma) minus the force of static friction (Ff=μN), where μ is the coefficient of static friction and N is the normal force (equal to the weight of Brad and his chair, 540 N).

Fnet = ma - μN

Plugging in the values, we get:

Fnet = (15 kg)(6 m/s^2) - (0.05)(540 N)

Fnet = 90 N - 27 N

Fnet = 63 N

Now, using the third law of motion, also known as the law of action and reaction, we know that for every action, there is an equal and opposite reaction. In this case, the reaction force to the net force acting on Brad is the force of friction. Therefore, we can use the equation for distance (d=vi^2/2a) to calculate the distance that Brad will travel after catching the ball.

d = (6 m/s)^2 / (2)(63 N)

d = 72 m / 126 N

d = 0.57 m

Therefore, Brad will travel 0.57 meters after catching the ball. This calculation takes into account the initial velocity of the ball, the mass and weight of Brad and his chair, and the coefficient of static friction between the chair wheels and the floor.

## 1. What is static friction?

Static friction is the force that prevents an object from moving when a force is applied to it. It occurs when two surfaces are in contact with each other and have not yet started moving relative to each other.

## 2. How is static friction different from kinetic friction?

Static friction and kinetic friction are both types of frictional forces, but they act in different situations. Static friction occurs when an object is at rest, while kinetic friction occurs when an object is in motion.

## 3. How is static friction calculated?

The calculation for static friction involves multiplying the coefficient of static friction (μs) by the normal force (N) acting on the object. This can be represented by the equation F = μsN, where F is the force of static friction.

## 4. Can static friction be greater than kinetic friction?

Yes, it is possible for static friction to be greater than kinetic friction. This typically occurs when the surfaces in contact have a rough texture, increasing the coefficient of static friction and making it more difficult for the object to start moving.

## 5. How can static friction be used to calculate distance?

In order to calculate the distance an object will travel due to static friction, you would need to know the coefficient of static friction, the normal force, and the initial velocity of the object. Using the equation d = μsNv^2/2, you can solve for the distance (d) traveled by the object.

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