Work and energy in spring, kinematics, friction, and incline problems

[mOreNa405]

Hi i just need some help on how to get started with these problems because I am behind already so I'm not sure where to begin let alone how to get to the answer so I'll really appreciate any type of help to get started..thanks

1)A spring with a spring constant k = 50N/m has an unstretched length of 20cm. Find the work required to stretch the spring to a length of 30 cm.
I know the spring is being streched by 10 cm and that the work needed is equal to potential energy but I'm still stuck

2) A ball of mass 4 kg is thrown straight up in the Earth's gravitational field with an initial speed v0 = 19 m/s.
a) What is the initial kinetic energy of the ball?
b) How much work does the gravitational force do on the ball if it goes up to a height h = 1.9 m?
c) c) What is the speed of the ball at a height h = 1.9 m?
for this last part I think it's KEfinal - KEinitial = Workg but I am not sure


3)A box slides across a frictionless floor with an initial speed v = 2.2 m/s. It encounters a rough region where the coefficient of friction is µk = 0.3.
a) What is the shortest length of rough floor which will stop the box?
b) If instead the strip is only 0.32 m long, with what speed does the box leave the strip?

4)An object of mass M = 4 kg slides from rest a distance d = 4 m down a frictionless inclined plane where it encounters a spring. It compresses the spring a distance D = 1.6 m before stopping. The inclined plane makes an angle q = 30° with the horizontal.
a) When the block just touches the spring, how much gravitational potential energy has it lost?
b) After the mass has fully compressed the spring, what is its total loss of gravitational potential energy? Give your answer as a positive number.
c) What is the value of the spring constant?

5)A man pulls a block of mass m = 15 kg up an incline at a slow constant velocity for a distance of d = 3.5 m. The incline makes an angle q = 28° with the horizontal. The coefficient of kinetic friction between the block and the inclined plane is µk = 0.1.
a) What is the work Wm done by the man?
At the top of the incline, the string breaks and the block, assumed to be at rest when the string breaks, slides down a distance d = 3.5 m before it reaches a frictionless horizontal surface. A spring is mounted horizontally on the frictionless surface with one end attached to a wall. The block hits the spring, compresses it a distance L = 0.7 m, then rebounds back from the spring, retraces its path along the horizontal surface, and climbs up the incline.
b) What is the speed v of the block when it first reaches the horizontal surface?
c) What is the spring constant k of the spring?
d) How far up the incline d1 does the block rebound?

 

[Gokul43201]

1)A spring with a spring constant k = 50N/m has an unstretched length of 20cm. Find the work required to stretch the spring to a length of 30 cm.
I know the spring is being streched by 10 cm and that the work needed is equal to potential energy but I'm still stuck

There's a formula in your text for the potential energy of a stretched spring. Look it up. After that, it's a direct substitution.

2) A ball of mass 4 kg is thrown straight up in the Earth's gravitational field with an initial speed v0 = 19 m/s.
a) What is the initial kinetic energy of the ball?
b) How much work does the gravitational force do on the ball if it goes up to a height h = 1.9 m?
c) c) What is the speed of the ball at a height h = 1.9 m?
for this last part I think it's KEfinal - KEinitial = Workg but I am not sure

What you need are the formulae for : KE, PE, Work done by a force; and the a clear understanding of the Conservation of Energy principle. All these are found in the same chapter of your text.

3)A box slides across a frictionless floor with an initial speed v = 2.2 m/s. It encounters a rough region where the coefficient of friction is µk = 0.3.
a) What is the shortest length of rough floor which will stop the box?
b) If instead the strip is only 0.32 m long, with what speed does the box leave the strip?

4)An object of mass M = 4 kg slides from rest a distance d = 4 m down a frictionless inclined plane where it encounters a spring. It compresses the spring a distance D = 1.6 m before stopping. The inclined plane makes an angle q = 30° with the horizontal.
a) When the block just touches the spring, how much gravitational potential energy has it lost?
b) After the mass has fully compressed the spring, what is its total loss of gravitational potential energy? Give your answer as a positive number.
c) What is the value of the spring constant?

5)A man pulls a block of mass m = 15 kg up an incline at a slow constant velocity for a distance of d = 3.5 m. The incline makes an angle q = 28° with the horizontal. The coefficient of kinetic friction between the block and the inclined plane is µk = 0.1.
a) What is the work Wm done by the man?
At the top of the incline, the string breaks and the block, assumed to be at rest when the string breaks, slides down a distance d = 3.5 m before it reaches a frictionless horizontal surface. A spring is mounted horizontally on the frictionless surface with one end attached to a wall. The block hits the spring, compresses it a distance L = 0.7 m, then rebounds back from the spring, retraces its path along the horizontal surface, and climbs up the incline.
b) What is the speed v of the block when it first reaches the horizontal surface?
c) What is the spring constant k of the spring?
d) How far up the incline d1 does the block rebound?

For all these you need to :

1. First read your text,
2. Make sure you understand the concepts,
3. Look at the worked examples and work them out yourself,
4. Come here and ask us if you have specific doubts with certain concepts or have gotten part way through a problem and are stuck in the middle.

 

[thepatientmental]

For these types of introductory mechanics problems, it is important to start by understanding the concepts and equations involved. Make sure you have a good understanding of the relevant equations and how they relate to the problem at hand.

1) To find the work required to stretch the spring, you can use the equation W = (1/2)kx^2, where k is the spring constant and x is the displacement. In this case, x = 10 cm (or 0.1 m). So, W = (1/2)(50 N/m)(0.1 m)^2 = 0.25 J.

2) a) The initial kinetic energy of the ball can be found using the equation KE = (1/2)mv^2, where m is the mass and v is the initial velocity. So, KE = (1/2)(4 kg)(19 m/s)^2 = 722 J.
b) The work done by the gravitational force can be found using the equation W = mgh, where m is the mass, g is the acceleration due to gravity (9.8 m/s^2), and h is the height. In this case, h = 1.9 m. So, W = (4 kg)(9.8 m/s^2)(1.9 m) = 74.48 J.
c) To find the speed of the ball at a height h = 1.9 m, you can use the equation v^2 = v0^2 + 2gh, where v0 is the initial velocity and g is the acceleration due to gravity. So, v = √(19 m/s)^2 + 2(9.8 m/s^2)(1.9 m) = 17.46 m/s.

3) a) To find the shortest length of rough floor that will stop the box, you can use the equation W = µkNΔx, where µk is the coefficient of friction, N is the normal force, and Δx is the displacement. In this case, W = (0.3)(mg)(Δx) = (0.3)(4 kg)(9.8 m/s^2)(Δx) = 11.76 J. Since the work done by the frictional force is equal to the kinetic energy of the box, we can set these two equal to each other and solve for Δ