# Finding two locations where power out is collision problem

• Samuelb88
In summary, the problem involves a small object being shot into a block attached to an ideal spring. The block then moves on a horizontal surface with friction. The masses of the objects, spring constant, initial velocity, and coefficient of kinetic friction are given. The task is to determine two locations of the block where the power output of the spring is 120 Watts. Using the work-energy theorem, an expression for velocity is found and substituted into the equation for power. However, there is an error in the equation due to incorrect calculation of the work done by friction. After solving for x, the correct location is found to be x = .091 m.
Samuelb88

## Homework Statement

A small object is shot into a block that is attached to an ideal spring. After the collision, the block moves over a horizontal surface for which it has friction. The masses of the two objects are given as well as the spring constant of the spring k, the initial velocity of the small object and the coeff. of kinetic friction between the block and the surface.

m (small) = .250 kg
M (big) = 3.75 kg
k = 180Nm^-1
v=145m/s
u_k = .600

(B) Determine two locations of the block (assume that it moves back to the left after it has reached its point of maximum spring compression) when the power output of the spring is 120. Watts.

## Homework Equations

Power p = (kx)(v)

## The Attempt at a Solution

This was part b of the problem. Part a was to find the max compression of the spring which is x_c (max comp) = 1.23 m.power = 120 W = kx * vx

I used the work-energy theorem to find an expression for the velocity from x_c (max comp) to the point x where the power = 120 W. I ended up with this equation

$$K_2 = k \int_{x_c}^{x} x dx - f_kx$$

$$= v = (45x^2-11.75x-68.05))^(^1^/^2^)$$

I substituted the value of v into the expression for power which gives

$$120 = 180x(45x^2-11.75x-68.05))^(^1^/^2^)$$

squaring both sides, i solve for x and get

x_1 = .59m
x_2 = 1.36
x_3 = negative value.all of which are not correct.

my professor provides one answer and that is the power output of the spring is 120 W at x = .091 m.

i don't quite understand what I'm doing wrong.

Last edited:
There's a problem with $f_k x$ in your equation for $K_2$ The work done by fricton should be 0 when $x = x_c$

I would approach this problem by first understanding the physical principles involved. In this case, we are dealing with a collision between a small object and a larger block attached to a spring. The key concept here is conservation of energy, which states that the total energy of a system remains constant in the absence of external forces.

In this problem, we are given the masses of the two objects, the spring constant, and the initial velocity of the small object. We are also given the coefficient of kinetic friction, which tells us about the frictional force acting on the block as it moves over the surface. The power output of the spring is related to the work done by the spring, which in turn is related to the change in kinetic energy of the block.

To find the locations where the power output of the spring is 120 Watts, we first need to find the velocity of the block at those locations. This can be done by using the work-energy theorem, as you did in your attempt at a solution. However, it is important to note that the work done by the spring is equal to the change in kinetic energy of the block only in the absence of external forces. In this case, there is also a frictional force acting on the block, which means that the work done by the spring is not equal to the change in kinetic energy of the block.

To account for the frictional force, we can use the work-energy theorem again, this time taking into account the work done by friction. This will give us a more accurate expression for the velocity of the block at the locations where the power output of the spring is 120 Watts.

Once we have the velocity, we can use the equation for power (P = Fv) to find the force acting on the block at those locations. This force will be equal to the force exerted by the spring, since the frictional force does not contribute to the power output of the spring.

Using the force and the given mass of the block, we can solve for the distance x traveled by the block, which will give us the two locations where the power output of the spring is 120 Watts.

In summary, to solve this problem correctly, we need to take into account the frictional force acting on the block and use the work-energy theorem twice to find the velocity and distance traveled by the block at the locations where the power output of the spring is 120 Watts.

## 1. How do I determine if a power outage is a collision problem?

To determine if a power outage is a collision problem, you will need to collect data on the power grid and analyze it. Look for patterns of power outages occurring in close proximity to each other, as well as any evidence of power surges or fluctuations in the grid. If there are multiple outages happening simultaneously in different locations, it could be a sign of a collision problem.

## 2. What causes a power outage to be a collision problem?

A collision problem occurs when two or more power outages happen at the same time due to a single event or issue. This can be caused by a variety of factors, such as severe weather conditions, equipment failures, or human error. It can also be a result of inadequate infrastructure or maintenance of the power grid.

## 3. How can I prevent a collision problem from causing a power outage?

Preventing a collision problem can be challenging, as it often involves addressing the root causes of the issue. However, implementing proper maintenance and upgrades to the power grid infrastructure can help minimize the risk of collisions. Additionally, having contingency plans in place for potential power outages can help mitigate the impact of a collision problem.

## 4. Are there any warning signs of a potential collision problem with power outages?

There are some warning signs that can indicate a potential collision problem with power outages. These include frequent power outages in the same areas, outages occurring at the same time of day, and outages affecting multiple locations at once. It is important to monitor the power grid and look for these patterns to identify potential collision problems.

## 5. How can I track and analyze power outages to identify collision problems?

Tracking and analyzing power outages can be done using various methods, such as using outage maps and data collection tools. You can also work with other experts in the field to gather and analyze data on power outages and identify any potential collision problems. Additionally, implementing advanced technologies, such as smart grids, can help track and analyze real-time data on power outages and identify any patterns or potential collision problems.

• Introductory Physics Homework Help
Replies
12
Views
2K
• Introductory Physics Homework Help
Replies
10
Views
1K
• Introductory Physics Homework Help
Replies
11
Views
2K
• Introductory Physics Homework Help
Replies
3
Views
1K
• Introductory Physics Homework Help
Replies
10
Views
3K
• Introductory Physics Homework Help
Replies
6
Views
4K
• Introductory Physics Homework Help
Replies
21
Views
2K
• Introductory Physics Homework Help
Replies
13
Views
4K
• Introductory Physics Homework Help
Replies
15
Views
2K
• Introductory Physics Homework Help
Replies
3
Views
1K