Problem 34 - College Physics

Question

A factory worker pushes horizontally on a 250 \(\mathrm{N}\) crate with a force of 75 \(\mathrm{N}\) on a horizontal rough floor. \(\mathrm{A} 135 \mathrm{N}\) crate rests on top of the one being pushed and moves along with it. Make a free-body diagram of each crate if the friction force exerted by the floor is less than the worker's push.

Step-by-Step Solution

Answer

Draw forces on each crate: 250 N crate has push, friction, gravity, normal; 135 N crate has gravity, normal, and small friction.

Step 1: Understand the Problem

We have two crates, with weights of 250 N and 135 N. The worker pushes the 250 N crate horizontally with a force of 75 N, and both crates move together. There's friction from the floor that acts against this motion but is less than 75 N.

Step 2: Draw Forces for the 250 N Crate

For the 250 N crate, the forces to consider are: 1. The horizontal pushing force of 75 N. 2. The friction force, which opposes the push and acts to the left. 3. The gravitational force acting downwards: 250 N. 4. The normal force from the ground acting upwards to balance the gravitational force.

Step 3: Draw Forces for the 135 N Crate

For the 135 N crate, since it sits on top of the 250 N crate, consider: 1. The gravitational force acting downwards: 135 N. 2. The normal force from the lower crate pushing upwards, which equals 135 N in magnitude. 3. The force exerted by the friction from the upper crate on the lower crate, which acts forward parallel to the ground surface.

Step 4: Combine Forces for Each Crate

In a free-body diagram for the 250 N crate, show: - An upward normal force from the ground, - A downward gravitational force (250 N), - A forward push of 75 N, - A backward friction force less than 75 N, balanced by the forward force of friction by the upper crate. For the 135 N crate, show: - An upward normal force exerted by the 250 N crate of 135 N, - A downward gravitational force (135 N). - A friction force caused by the movement against the lower crate.

Key Concepts

Forces and Motion

When we talk about forces and motion, we're diving into the basic principles that explain how objects move or stay still. Imagine the factory worker pushing the crates - that's a perfect example of forces at play. These forces include:

• Pushing forces exerted by the worker.
• Friction forces from the floor, acting against movement.
• Gravitational pull, pulling the crates downward due to their weight.
• Normal forces that act perpendicular to the surface, balancing the gravitational pull.

When two objects, like the crates, move in response to a force, they're demonstrating Newton's first law. This law tells us that they won't start moving unless a force makes them, and similarly, they will keep going until another force stops them. As you can see, all these forces are essential to keeping everything in balance and determining the motion, like the way the crates slide over the floor.

Newton's Laws of Motion

Newton's laws are key to understanding the movement of objects like the crates. There are three laws to get familiar with: 1. **First Law** (Law of Inertia): An object will remain at rest or in uniform motion unless acted upon by an external force. This is shown in the problem as the crates move only when pushed by the worker. 2. **Second Law**: This law states that force equals mass times acceleration ( F = ma ). This relationship helps explain how different forces, such as the 75 N push, cause the crates to move. Each crate's acceleration depends on the net force after accounting for friction. 3. **Third Law** (Action and Reaction): This law tells us that for every action, there's an equal and opposite reaction. As the worker pushes the crate, the floor pushes back with a normal force. Likewise, the friction between crates acts in the opposite direction of movement, trying to hold things still. By examining these laws, you'll appreciate how each force impacts the crates' movement and how balanced forces result in no change in motion.

Friction

Friction is the force that resists the relative motion of surfaces sliding past one another. In the crate example, friction is the unsung hero trying to keep things from moving too easily. There are a few points to understand about friction:

• **Static Friction**: This prevents objects from moving. It's the initial friction when the worker starts to push the crate. If the friction was equal to or greater than the push, the crate wouldn't budge.
• **Kinetic Friction**: This takes over once the crates start moving. It's weaker than static friction, which is why the worker's push can keep the crates in motion.
• **Direction**: Friction always works opposite to the direction of motion or intended motion. In this case, it resists the worker's 75 N push.

Understanding friction helps explain why it's harder to start moving an object than to keep it moving. Grasping these concepts allows better predictions of motion and control, just like when the factory worker pushes those crates across the floor.