Solving Mass in Horizontal Pulley System: 99 kg?

In summary, the conversation discusses a problem involving a mass on a smooth surface connected to another block hanging vertically through a pulley. The problem is to determine the mass (m1) needed to maintain a given acceleration of .098 m/s^2 when m1 is 1.0 kg. The solution involves drawing free-body diagrams and applying Newton's second law. The final answer is 99 kg, but the person is unsure if it is correct and asks for confirmation.
  • #1
pointintime
166
0

Homework Statement



a mass (m1) on a smooth horizontal surface, connected by a thin cord that passes over a pulley to a second block (m2), which hangs vertically.

If the acceleration is .098 m/s^2 and m1 is 1.0 kg how much must m1 must be to keep it at this acceleration

Homework Equations



net force = ma

The Attempt at a Solution



i got 99 kg
please help me... it's really late at night and I'm tired...
 
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  • #2
Do what you always should do with mechanics problems: draw free-body diagrams, then write out Newton's second law for each body. Remember that the tension in a massless rope hung over a massless pulley is constant throughout the rope.
 
  • #3
Draw free-body diagrams of each object and the forces acting on them. If two objects are connected by a single string, then they have the same tension.
 
  • #4
Do you know if I got it right?
 
  • #5
your asking for m1? It's already given. Am I right?
 

1. How do you calculate the mass in a horizontal pulley system?

To calculate the mass in a horizontal pulley system, you will need to use the equation F=ma, where F is the net force acting on the system, m is the mass of the object, and a is the acceleration. In a horizontal pulley system, the net force is equal to the tension in the rope, so you can set F equal to the tension and solve for m.

2. Is the mass in a horizontal pulley system affected by friction?

Yes, friction can affect the mass in a horizontal pulley system. Friction is a force that acts in the opposite direction of the motion, so it can decrease the acceleration and therefore affect the mass calculated using the F=ma equation.

3. Can you explain the difference between static and kinetic friction in a horizontal pulley system?

Static friction is the force that prevents an object from moving when a force is applied to it. In a horizontal pulley system, this would refer to the initial force needed to get the system in motion. Kinetic friction, on the other hand, is the force that acts on an object in motion. In a horizontal pulley system, this would refer to the force that must be overcome to maintain a constant acceleration.

4. How does the angle of the pulley affect the mass in a horizontal pulley system?

The angle of the pulley can affect the mass in a horizontal pulley system by changing the direction of the net force acting on the system. This can affect the acceleration and therefore the mass calculated using the F=ma equation.

5. Can you provide an example of a real-life situation where a horizontal pulley system is used?

A common example of a real-life horizontal pulley system is a clothesline. The weight of the wet clothes pulls down on one side, while the tension in the rope pulls up on the other side. This allows the clothes to be hung and dried in a horizontal position. The mass in this system would be equal to the weight of the clothes, as this is the force acting on the system.

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