Energy, Friction, and Velocity

In summary, the system is set up with a block M (15 kg) attached to a string across a pulley and a smaller mass m (8 kg) dangling over the edge of the table. The block M is initially moving to the left at a speed of 2.8 m/s. The goal is to find the velocity of M when m has fallen 2.5 m. The approach is to treat both masses as one object and use an energy equation, taking into account the work done by kinetic friction. After solving for the velocity, the answer is approximately 3 m/s.
  • #1
Selerinus
3
0
I've been struggling over this homeword question for hours now, and have made little, or no progress figuring out the exact steps for it.

The system is set up with block M, on a table, attached on the left side of the block is a string, which is holding, across a pulley, little mass m, which dangles over the edge of the table. The exact difference in angles would be 90'.

In the system shown, block M (15 kg), is initially moving to the left, with a speed v(i) = 2.8 m/s. The mass of m, which dangles in the air is 8 kg. There is no mass in the string, and no friction in the pulley. The coefficent of friction betweek M and the surface are kinetic friction = .3, and static friction = .4.

Find the velocity of M when m has fallen 2.5 m

Any help would be appreciated.
 
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  • #2
Selerinus said:
I've been struggling over this homeword question for hours now, and have made little, or no progress figuring out the exact steps for it.

The system is set up with block M, on a table, attached on the left side of the block is a string, which is holding, across a pulley, little mass m, which dangles over the edge of the table. The exact difference in angles would be 90'.

In the system shown, block M (15 kg), is initially moving to the left, with a speed v(i) = 2.8 m/s. The mass of m, which dangles in the air is 8 kg. There is no mass in the string, and no friction in the pulley. The coefficent of friction betweek M and the surface are kinetic friction = .3, and static friction = .4.

Find the velocity of M when m has fallen 2.5 m

Any help would be appreciated.
There are a couple of approaches to this problem. One approach will permit you to find the tension in the string, the other will not. Since you are not asked for the tension, you can consider it to be an "internal force" and treat the two blocks as one object. You can do the problem as if both masses were on the table (if you assume no friction acts on the small mass) and you were pulling the little mass horizontally with a force equal to its weight. The string and pulley only serve to change the directions of motion. Both masses move the same distance with the same speed and the same magnitude of acceleration.
 
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  • #3
there are several ways to solve this problem, but since it gave you distance for mass m, I would attack it with an energy approach.

you want to find the acceleration of the system with no friction. Multiply by mass M to get the force acting on mass M excluding friction (what is this force by the way)? Now it's easy. Work=force *distance and work is the change in kinetic energy, right?

Don't forget about friction and the initial speed!
 
  • #4
So how do the forces of kinetic and static friction factor in. I've already tried solving it, every which way I can. The actual mass of the object seems independent of the system, because it seems to me, that they cancel out.

Solving for them as one mass doesn't seem to work, as I keep getting a velocity way off.

K(i) = K(f) + U(f)

I divided out the masses, and solves for the velocity, but its way too high.

v(i)^2 = v(f)^2 + 2gh

(2.8 m/s)^2 = v(f)^2 + 2 (9.8 m/s^2)(2.5m)
v(f) = about 6 m/s, but the book shows the answer more at about 3.

I assumed that the acceleration of the object would be dependent on gravity, since the dangling mass m, has a mass of 8 kg, and a force of 9.8 m/s^2 pulling down on it
So the force pulling down on it, and subsequently on M, is 78.4N, but I can't figure out where to go from here, except that I have already connected on the concept of the force, and such, not really being dependent on the angle.
 
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  • #5
Selerinus said:
So how do the forces of kinetic and static friction factor in. I've already tried solving it, every which way I can. The actual mass of the object seems independent of the system, because it seems to me, that they cancel out.

Solving for them as one mass doesn't seem to work, as I keep getting a velocity way off.

K(i) = K(f) + U(f)

I divided out the masses, and solves for the velocity, but its way too high.

v(i)^2 = v(f)^2 + 2gh

(2.8 m/s)^2 = v(f)^2 + 2 (9.8 m/s^2)(2.5m)
v(f) = about 6 m/s, but the book shows the answer more at about 3.
My mistake. I lost track of the friction. I will go back and correct my post. You can treat the small mass as I said if you assume it is frictionless.

You have taken a completely different approach to the problem, using energy instead of just looking at forces. This will work if you include the work done by friction in the calculations. Since the mass is moving initially, and continues to move, only kinetic friction is relevant. Can you compute the work done by friction? Can you incorporate that into your equation?

You need to be careful with the masses. Mass is not going to divide out of a correct energy equation.
 
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  • #6
Woo, got it. Thanks for the help.
 

Related to Energy, Friction, and Velocity

1. What is energy and how is it related to velocity?

Energy is the ability to do work. In physics, it is defined as the capacity of an object to do work, which is the product of its mass and the square of its velocity. This means that the more mass an object has, the more energy it will have, and the faster it moves, the more energy it will possess.

2. How does friction affect an object's velocity?

Friction is the force that opposes the motion of an object. It acts in the opposite direction of the object's movement and decreases its velocity. The amount of friction depends on factors such as the surface roughness, the weight of the object, and the force pushing the object forward. Therefore, the higher the friction, the lower the velocity of the object will be.

3. What are the different forms of energy and how do they relate to each other?

The different forms of energy include kinetic, potential, thermal, electrical, chemical, and nuclear energy. Kinetic energy is the energy an object possesses due to its motion, while potential energy is the energy an object has due to its position or state. Thermal energy is the energy that comes from heat, electrical energy is the energy of moving electrons, chemical energy is stored in bonds between atoms, and nuclear energy is the energy stored in the nucleus of an atom. These forms of energy can be converted into one another, but the total amount of energy in a system remains constant.

4. How is energy conserved in a closed system?

In a closed system, energy cannot be created or destroyed; it can only be transferred or converted from one form to another. This is known as the law of conservation of energy. This means that the total amount of energy in a closed system will remain constant, even if it changes forms. For example, if a ball is dropped from a height, its potential energy will be converted into kinetic energy, but the total energy remains the same.

5. How can friction be reduced to increase an object's velocity?

Friction can be reduced by using materials that have a lower coefficient of friction, which means they have less resistance to motion. Additionally, lubricants can be used to reduce friction between two surfaces. By reducing friction, less energy is lost to heat, allowing an object to maintain a higher velocity. Other factors that can help increase an object's velocity include reducing its weight and minimizing the force acting against its movement.

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