# How Does a Man Sliding on a Cart Affect Their Combined Speed and Energy?

• AznBoi
In summary: Impulse = Force * Time. The time can be found by dividing the impulse by the force acting on the man.
AznBoi
I'm stuck on a lot of parts in this problem. I've been able to solve for some though. Any help is appreciated! =] Thanks!

Problem: A 60 kg man running at an initial speed of 4 m/s jumps onto a 120 kg cart initially at rest. He sildes on the cart's top surface and finally comes to rest relative to the cart. The coefficient of kinetic friction between the man and the cart is 0.400. Friction between the cart and ground can be neglected. a) Find the final speed of the man and cart relative to the ground. b) Find the frictional force acting on the man while he is sliding across the top surface of the cart. c) How long does the frictional force act on him? d) Find the change in momentum of the man and the change in momentum of the cart. e) Determine the displacement of the man relative to the ground while he is sliding on the cart. f) Determine the displacement of the cart relative to the ground while he is sliding. g) Find the change in the man's kinetic energy. h) Find the change in kinetic energy of the cart.

So far I have gotten:

b) Friction force= (mu)*(Normal force)
Ff=(0.4)(588N)
Ff=235N

a) How do you find the final speed of the man relative to the ground?? I don't get what it means by "relative to the ground" Would you use the
KE(initial)=KE(final) ?

I did it but I didn't get the right answer of 1.33m/s

.5(60)(4)^2=.5(180)(Velocity of combined masses)' ^2

and I got V=sqrt.(5.333) but that equals 2.31m/s

What am I doing wrong??

c) how do you find the time of the friction force that acts on him?? I know that he is travel rightwards initially at 4m/s and the friction acts opposite at 235N. What equation do I need to use to find the time until he stops? Is there a way to make 4m/s into a Force??

Thats all the help I need for now, thanks!

For question (a), since the collision is inelastic one should use conservation of linear momentum.

For question (c), you should consider the impulse-momentum theorem

I would approach this problem by breaking it down into smaller parts and using equations from Newton's laws of motion. Here are some suggestions for how to solve the remaining parts of the problem:

a) To find the final speed of the man and cart relative to the ground, you can use the principle of conservation of momentum. This states that the total momentum of a system before and after a collision remains constant. In this case, the initial momentum of the man is m1v1, where m1 is the mass of the man and v1 is his initial velocity. The initial momentum of the cart is 0, since it is initially at rest. The final momentum of the combined system (man and cart) is (m1+m2)v2, where m2 is the mass of the cart and v2 is the final velocity of the man and cart combined. Setting these two equal, you can solve for v2.

b) To find the frictional force acting on the man, you can use the equation you already have (Ff=μN), where μ is the coefficient of kinetic friction and N is the normal force. The normal force in this case is the weight of the man, which is mg. So, Ff=μmg.

c) To find the time that the frictional force acts on the man, you can use the equation F=ma, where F is the force, m is the mass, and a is the acceleration. In this case, the force is the frictional force (Ff), the mass is the mass of the man (m1), and the acceleration is the deceleration of the man as he slides on the cart. This can be calculated using the equation a=-μg, where g is the acceleration due to gravity. Once you have the acceleration, you can use the equation v=u+at, where v is the final velocity, u is the initial velocity (in this case, 4 m/s), a is the acceleration, and t is the time. You can solve for t.

d) To find the change in momentum of the man and the cart, you can use the equation Δp=mΔv, where Δp is the change in momentum, m is the mass, and Δv is the change in velocity. For the man, his initial momentum is m1v1 and his final momentum is 0, so the change in momentum is -

## 1. What causes a collision between a man and a car?

A collision between a man and a car is typically caused by the man being hit by a moving vehicle. This can happen due to a variety of factors such as distracted driving, speeding, or failure to yield to pedestrians.

## 2. What are the most common injuries sustained in a collision between a man and a car?

The most common injuries sustained in a collision between a man and a car include broken bones, head and neck injuries, and internal injuries. These injuries can range from minor bruises and cuts to more serious conditions such as concussions or organ damage.

## 3. How can collisions between men and cars be prevented?

Collisions between men and cars can be prevented by following traffic laws and safety precautions. This includes obeying speed limits, using crosswalks and sidewalks, and staying alert while driving or walking near roads. It is also important for both drivers and pedestrians to avoid distractions such as texting while driving or walking.

## 4. What factors can increase the severity of a collision between a man and a car?

The severity of a collision between a man and a car can be increased by a variety of factors such as high speeds, intoxication, and failure to wear seatbelts or other safety gear. The size and weight of the vehicle involved can also play a role in the severity of the collision.

## 5. What should I do if I am involved in a collision between a man and a car?

If you are involved in a collision between a man and a car, the first priority is to seek medical attention for any injuries. It is also important to exchange contact and insurance information with the driver of the vehicle and report the incident to the police. It may also be necessary to consult with a legal professional to understand your rights and options for seeking compensation for any damages or injuries sustained.

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