Question

In: Physics

A mass of 0.5 kg sits on a horizontal frictionless patch of ice. It is connected...

A mass of 0.5 kg sits on a horizontal frictionless patch of ice. It is connected to a spring with a with a spring constant of k=5 N/m. The spring is initially relaxed. It is then pulled to the right and stretched by 0.1 meters. It is released afterwards to return to its equilibrium position at x=0 meters. "x" is the amount of displacement. Please use conservation of energy to find the velocity of the mass at 0.08 meters.

Solutions

Expert Solution

Given:

Mass,

Spring constant of the spring,

Maximum displacement of spring,

===============

Find the velocity of the mass at 0.08 meters.

Consider the spring

When the spring is fully stretched, potential energy is stored in the spring. As spring is released potential energy of the spring is converted to kinetic energy of the mass.

When the displacement of the mass is 0.08m, only some portion of initial elastic potential energy of the spring is converted to kinetic energy of the mass.

Initial potential energy of the spring = Potential energy of the spring + Kinetic energy of the mass

ANSWER:

===============================

genius_generous answered 1 year ago

Next > < Previous

Related Solutions

A block of mass m1 = 0.500 kg sits on a frictionless surface and is connected...

A block of mass m1 = 0.500 kg sits on a frictionless surface and is connected by a weightless string to a weight of mass m2 = 0.200 kg that hangs from a pulley. The system is initially at rest. If the mass m2 is released and drops for 1.00 m, what is the speed of the system? Assume that mass m1 does not reach the edge of the surface. Use energy considerations, not force considerations. What is the speed...

A mass; m1 = 64 g, sits on a frictionless horizontal surface, and is attached to...

A mass; m1 = 64 g, sits on a frictionless horizontal surface, and is attached to a spring of spring constant k = 51 N/m. The other end of the horizontal spring is attached to a wall; the system is in equilibrium. Another mass; m2 = 18 g, strikes the stationary mass m1, and sticks to it. As a result, the spring is compressed by a distance of 24.5 cm before the masses come to a momentary stop. a) How...

A 24 kg mass is connected to a nail on a frictionless table by a massless...

A 24 kg mass is connected to a nail on a frictionless table by a massless string 1.1 m long. There is no appreciable friction between the nail and the string. If the tension in the string is 54 N while the mass moves in a uniform circle on the table, how long does it take for the mass to make one complete revolution? (Give answer to the nearest 0.1 s)

A 5.0 kg mass is initially at rest on a horizontal frictionless surface when a horizontal...

A 5.0 kg mass is initially at rest on a horizontal frictionless surface when a horizontal force along an x axis is applied to the block. The force is given by ? ⃗(?) = (6.0?2 − 2?3)?̂, where the force in in newtons, x is in meters, and the initial position of the block is x = 0. (a) What is the work done in moving the block from x = 1.0 m to x = 3.0 m? (b) What...

A box of mass 18.0 kg sits at rest on a horizontal surface. The coefficient of...

A box of mass 18.0 kg sits at rest on a horizontal surface. The coefficient of kinetic friction between the surface and the box is 0.300. The box is initially at rest, and then a constant force of magnitude FF and direction 39.0 ∘∘ below the horizontal is applied to the box; the box slides along the surface. A. What is F if the box has a speed of 6.00 m/s after traveling a distance of 8.00 mm? Express your...

A mass m1 = 5.6 kg rests on a frictionless table and connected by a massless...

A mass m1 = 5.6 kg rests on a frictionless table and connected by a massless string to another mass m2 = 5.7 kg. A force of magnitude F = 44 N pulls m1 to the left a distance d = 0.88 m. Initally both blocks are at rest. 1) How much work is done by the force F on the two block system? J 2) How much work is done by the normal force on m1 and m2? J...

A mass m1 = 4.4 kg rests on a frictionless table and connected by a massless...

A mass m1 = 4.4 kg rests on a frictionless table and connected by a massless string over a massless pulley to another mass m2 = 3.8 kg which hangs freely from the string. When released, the hanging mass falls a distance d = 0.7 m. 1)How much work is done by gravity on the two block system? 2)How much work is done by the normal force on m1? 3)What is the final speed of the two blocks? 4)How much...

A mass m1 = 4.7 kg rests on a frictionless table and connected by a massless...

A mass m1 = 4.7 kg rests on a frictionless table and connected by a massless string over a massless pulley to another mass m2 = 4.3 kg which hangs freely from the string. When released, the hanging mass falls a distance d = 0.76 m. 1. How much work is done by gravity on the two block system? 2. How much work is done by the normal force on m1? 3. What is the final speed of the two...

M1 has a mass of 6.330 kg. It is on a horizontal surface connected by a...

M1 has a mass of 6.330 kg. It is on a horizontal surface connected by a massless string to a hook where M2 can be increased smoothly. The pulley has a negligible mass & no friction. When M2= 3.266 kg it begins to accelerate downward at a rate of 2.110 m/s2. Calculate us - uk between M1 and the surface.

(question1- )A 5 kg mass is attached to a spring on a horizontal frictionless surface. the...

(question1- )A 5 kg mass is attached to a spring on a horizontal frictionless surface. the elastic constant of the spring is 48.7 n/m if the mass is 31.6 cm right (+) of the equilbrium point and moving at speed 4.8 m/s find the total mechanical energy.? ( question2-) A 5 kg mass is attached to a spring on a horizontal frictionless surface. the elastic constant of the spring is 30.3 n/m .if the mass is 24.5 cm right (+)...

Subjects