Question

A 4 kg block hangs by a light string that passes over a massless, frictionless pulley and is connected to a block that rests on a shelf. The coefficient of kinetic friction is 0.20. The 6 kg block is pushed against a spring, compressing it 30 cm. The spring has a force constant of 180N/m. (Assume the 6:0kg block is initially 40 cm or more from the pulley.)

1. What is the work done by the spring force on mass m1?
2. What is the work done by the kinetic friction on mass m2?
3. What is the work done by the gravitational force on mass m2?
4. What is the work done by the tension on masses m1 and m2?
5. What is the speed of the blocks after the 6 kg block is released and the 4 kg block has fallen a distance of 40 cm?

Answer 1

The work-energy principle helps to relate forces acting on an object to the changes in its kinetic or potential energy, providing insight into the work done by spring force, kinetic friction, and gravitational force, as well as determining the final speed of the objects in a mechanical system.

Step-by-step explanation:

Work and Energy in Physics

The work-energy principle is a key concept in physics that relates work done on or by an object to changes in its energy. In this problem, the student is asked to analyze the work done by various forces on two masses connected by a light string. The key concepts illustrated in this problem include work done by spring force, kinetic friction, gravitational force, and tension, as well as the conversion of potential energy into kinetic energy.

• Work done by the spring force is found using the spring force constant and the distance the spring is compressed.
• Work done by kinetic friction is calculated by multiplying the frictional force (which is the product of the coefficient of kinetic friction and the normal force) by the distance the block moves.
• The work done by the gravitational force on an object is zero when there is no vertical displacement of the centre of mass of the system.
• The work done by tension is zero if the pulley is massless and frictionless since the tension force does not result in displacement in the direction of the force.
• The speed of the blocks can be found by applying conservation of energy principles, accounting for the work done by the non-conservative frictional force.

To solve for the specific values of work and speed, the student would need to follow the steps outlined above using the provided parameters.

Answer 2

To find the work done by various forces and the eventual speed of two blocks involved in a classical mechanics problem, key principles such as Hooke's Law, the work-energy theorem, and energy conservation must be applied.

Explanation:

To solve the problem set regarding forces and motion which involves concepts in kinetic and potential energy, work, and friction, one needs to apply principles of classical mechanics, specifically Newton's laws and the work-energy theorem. In question 1, the work done by the spring on mass m1 relates to the spring force which follows Hooke's Law, where the spring force F=-kx and the work done by spring W=springs=(1/2)kx^2. In question 2, the work done by friction on mass m2 can be found using the formula W=friction=-μkmgd, where μk is the coefficient of kinetic friction, m is the mass, g is the acceleration due to gravity, and d is the displacement. In question 3, the work done by gravity is W=gravity=mgd, where d is the vertical displacement. In question 4, the work done by tension is zero if the pulley is massless and frictionless. For question 5, energy conservation can be used to find the speed of the blocks by equating the potential energy lost by the falling block with the kinetic energy gained by both blocks.