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Elastic and Plastic Behaviour

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Elastic Energy for A-Levels

1. Work done by the force when stretching a spring

2. Energy equation

3. Forum

↓ Show theory [1] ↓

Detailed solution steps are available at:

https://en.openprof.com/wb/chapter:elastic_and_plastic_behaviour/4049/

Example 1.

Which of the following bodies are elastic?

Ball,
Stone,
Plasticine,
Elastic band,
Sheet of paper,
Eraser,
Metal ball.

Example 2.

Which of the following elastic bodies have elastic energy:

A ball on which a child sits.
A spring lying on a table.
An elastic band that holds the hair in a ponytail.
A sponge that a student presses hard against the board while wiping the board.
A catapult which my father has in his pocket.
A tarpaulin taut on a trampoline.

In the listed cases, the events in which elastic bodies occur are described. For each event, determine whether the body’s elastic energy increases, decreases, or does not change.

A ball rolling on the floor.
A balloon inflated by a child.
A taut bowstring that an archer lowers and shoots an arrow.
A bed grandma sits on.
An elastic band that falls from the table to the floor.
A spring balance on which the teacher hangs a weight.
A compressed spring that a student lowers to fly off the table.

Two identical springs are pinned to the ceiling. A weight of 200 g is hung on the first spring and a weight of 150 g on the second. Which spring has more elastic energy?

An archer did 2 J of work while pulling a bowstring. What is the elastic energy of the stressed string?

We slowly and uniformly hang a body of mass 80 g on a spring. The spring is stretched by 10 cm. Calculate the elastic energy of the stretched spring.

Jasper first shoots a ball with an elastic band on his catapult. The ball travels 3 m away from him. He then shoots the same ball with the same catapult and the ball moves 4.5 m away. If he shoots the balls at the same angle, in which case does the elastic band on the catapult have more elastic energy? Explain the answer.

A hockey puck slides to the wall of the rink and bounces off it. Answer the following questions:

What form of energy does the puck have when it slides to the wall of the rink?
What form of energy does this energy convert into when it hits the wall?
What form of energy does the puck have when it bounces off the wall?

When a catapult is stretched, it receives elastic energy. How high can we shoot a stone with mass ? Round off the value to the nearest whole number.

10.

A weight of is hung on a spring. In doing so, the spring is stretched by .

How much is the potential energy of the weight reduced?
What spring energy accompanies the reduction and the magnitude of the energy?

11.

A block of mass is placed on a duster to wipe a board. In doing so, the duster is compressed by . Does the elastic energy of the duster increase or decrease due to the block on top of it and by how much?

A block on top of a duster on a board

12.

A spring is compressed with the finger by applying a force so that it contracts through a distance . By how much does the elastic energy of the spring change?

13.

Mary with a mass of jumps on a trampoline. Calculate the elastic energy transferred to Mary by the trampoline before the jump in each of the two cases below if Mary bounces high.

Assume that there are no energy losses in the jump.
Assume the trampoline transfers of its elastic energy to Mary.

14.

A ball with a mass of is dropped from a height of . What is the elastic energy of the ball when bouncing off the ground if no energy is lost during the collision?

15.

When pulling a bow, the string is pulled with an average force with an extension of from equilibrium. What is the velocity of the mass of the arrow immediately after launch if the bow gives it its elastic energy? Express the speed in and round it off to the nearest whole number.

16.

In a catapult shooting competition, an elastic band of length is stretched with an average force of .

By how many joules does the elastic energy increase when the rubber is stretched?
How much energy does the elastic band give to the pebble that is shot with the catapult when we pull it?
Which energy does the pebble have due to the energy received from the elastic band after launch and what is its value?
How much work can the pebble do when it hits an obstacle?

17.

A spiral spring with elastic constant is compressed by 1.0 cm.

How much work is done when compressing the spring?
By how much, at least, must the spring be compressed in order for it to shoot a 100 g mass to a vertical height of 3.0 m when released?
Neglect air resistance, and also the change in potential energy during the stretching of the spring.

18.

A mountain climber is protected by a 25 m-long rope with a spring constant of 400 N/m. If the mountaineer weighs 70 kg, by how much does the rope extend when he falls?

19.

Three bodies of masses , and lie in the same plane on a horizontal surface as shown in the figure below:

Bodies on a horizontal base

The surface is smooth on the left side of point 0 and rough on the right side. Between bodies A and B is a light spring with a spring constant of . Bodies A and B are tied with a rope so that the spring is compressed by 2.0 cm.

How much elastic energy does the compressed spring have?
If the rope is immediately cut to release the compressed spring. At what speed will the bodies A and B fly away?
How much distance does body A travel on the rough surface? (Coefficient of friction between body A and the surface is ).
Body B collides inelastically with body C. What is the common velocity of the combined bodies?
What percentage of kinetic energy is lost in the inelastic collision of bodies B and C?

20.

A light spiral spring with an elastic constant of is attached to the top of a slope inclined at an angle . A log of mass 200 g is attached to the spring and is held so that the spring is not deformed (see the figure below).

When the log is released, it starts to slide down the slope. By how much is the spring stretched when the log stops if the coefficient of friction between the log and the slope is 0.2?
How much work does the log receive from gravity?

A log on a slope

21.

A log of mass 1 kg slides on a horizontal rough surface and encounters a flexible spring of a force constant which is attached to a wall as shown in the figure below. After the collision of the log with the spring, the spring is compressed by 4.0 cm. What is the speed of the log at the moment it hits the spring if the coefficient of friction between the log and the surface is 0.25?

Motion of a log on a rough surface

22.

In the figure below, light elastic spiral springs with elastic constant and are connected in series.

What is the elastic constant of the combined springs?
What is the minimum work to be done in order to stretch the springs by 10 cm?

Figure 1: Connected light springs

23.

A body of mass 1 kg, connected to an elastic spiral spring, is held at point A on a circular ring of radius 0.5 m as shown in the figure below. When the body is released, it can only move on a circular track, without friction, in a horizontal plane. The length of the spring when unloaded is . A force of 32 N is required to extend the spring by 80 cm.

How much force does the spring exert on the body at point A?
What are the kinetic and elastic energies at point A?
Describe the motion of the body when it is released.
Calculate the acceleration of the body at point A.
What are the kinetic and elastic energies at point B?
What is the speed of the body at point B?

24.

A block of mass 500 g is placed on a horizontal surface near the foot of a slope and rests against a compressed spring of elastic constant . The spring is compressed by 20 cm and the slope is inclined at an angle to the horizontal. When the block is released, it slides towards and up the slope as shown in the figure below.

Figure 1: Block attached to a compressed spring.

What is the elastic energy of the compressed spring?
What is the initial kinetic energy of the block at the bottom of the slope?
With what speed does the block move away after the spring is released?
How far up the slope does the block go if friction is negligible?
How far up the slope does the block move if there is a friction of coefficient 0.1 between the block and the surface of the slope?

25.

A body of mass 200 g, attached to a light elastic spiral spring, is held on a smooth slope as shown in the figure below. The length of the unloaded spring is 40 cm and a force of 1.4 N is required to extend it by 10 cm.

Figure 1: Body on elastic spiral spring

What is the spring's elastic constant?
What is the energy of the spring-body system when the body is at the top of the slope?
If the body is released from the top of the slope, what is the elastic energy of the spring when the body is in the middle of the slope?
What is the kinetic energy of the body when the body is in the middle of the slope?
What is the speed of the body in the middle of the slope?

26.

A spring is compressed by 6 cm when 12 J of work is done on it. Calculate its spring constant.

27.

The string of a bow with an elastic constant of 4 N/cm is stretched by 15 cm to shoot an arrow of a mass of 12 g vertically upwards. How much work is done in stretching the bow? How high will the arrow fly?

28.

Two elastic helical springs, the first has a spring constant while the second has a spring constant , are stretched to the same length.

Draw a graph of the applied force against the extension of the spring (one graph for both springs).
What is the ratio of their elastic energies after stretching?

29.

An unloaded vertical light spring with elastic constant is 80 cm long. A block of mass 1.5 kg is attached to the lower end of the spring with the block resting on the ground while the spring is not deformed (see figure). The upper end of the spring is then slowly raised from a height of 80 cm to 170 cm.

How much work is done during the lifting?
Draw the graph of the force acting on the upper end of the spring against the height.
Draw the graph of the elastic energy of the spring against the height.

Figure 1: Spring weight.