Question

In: Physics

a 4.00 kg mass is moving in a circular path of radius 3.20 m with a...

a 4.00 kg mass is moving in a circular path of radius 3.20 m with a constant linear speed of 6.29 m/s. The radial force on the mass is

Expert Solution

Information provided- mass=m=4.00 kg

Radius=R=3.20 m

linear speed=v=6.29 m/s

concept to be used-curvilinear motion.

When a body moves in a curved path its velocity changes both in magnitude and direction giving rise to two components of acceleration namely and .

is the component of acceleration due to change in direction of velocity.

=v²/R in magnitude and acts radially towards the centre.

= dv/dt in magnitude and acts in the direction of v (if velocity increases with time)

In this question the body is moving with a constant linear velocity v so making the =0 (as derivative of a constant is zero)

let be the total acceleration .

as =0

=v²/R and directed towards the centre.

=6.29²/3.2=12.364 m/s²

we know F=ma=m=4.00x12.364=49.456 N and direction of the force is towards the centre.(in the direction of acceleration)

The radial force on the mass is 49.456 N.

genius_generous answered 2 years ago

A rocket with mass 4.00×103 kg is in a circular orbit of radius 7.40×106 m around...

A rocket with mass 4.00×103 kg is in a circular orbit of radius 7.40×106 m around the earth. The rocket's engines fire for a period of time to increase that radius to 8.90×106 m, with the orbit again circular. a) What is the change in the rocket's kinetic energy? Does the kinetic energy increase or decrease? b) What is the change in the rocket's gravitational potential energy? Does the potential energy increase or decrease? c) How much work is done...

A particle of mass m orbits around the origin (0,0) in a circular path of radius...

A particle of mass m orbits around the origin (0,0) in a circular path of radius r. (a) Write the classical Hamiltonian (energy) of this system in terms of angular momentum of the particle. (b) Write the Schrodinger equation for this system. (c) Find the energy eigenvalues and their corresponding (normalized) wavefunctions.

a) Consider an object of mass m=0.527kg rotates on circular path of radius r=1.82 m. Object...

a) Consider an object of mass m=0.527kg rotates on circular path of radius r=1.82 m. Object starts at rest and slowly increase its angular velocity at constant angular acceleration of 0.128 rad/s2. I. Find the angular velocity of the object after 35 seconds? II. Find the magnitude and direction of resultant linear acceleration after 35 seconds? III. Find the net force acting on the object after 35 seconds? b) Consider the same above object of mass m=0.527kg rotates around its...

A spherical satellite of radius 4.8 m and mass M = 210 kg is originally moving...

A spherical satellite of radius 4.8 m and mass M = 210 kg is originally moving with velocity satellite,i = < 2800, 0, 0 > m/s, and is originally rotating with an angular speed ω1 = 2 radians/second, in the direction shown in the diagram. A small piece of space junk of mass m = 3.9 kg is initially moving toward the satellite with velocity junk,i = < -2600, 0, 0 > m/s. The space junk hits the edge of...

A railroad car of mass 35000 kg moving at 4.00 m/s collides and couples with two...

A railroad car of mass 35000 kg moving at 4.00 m/s collides and couples with two coupled railroad cars, each of the same mass as the single car and moving in the same direction at 2.00 m/s. a) What is the speed of the three coupled cars after the collision? b) How much kinetic energy is lost in the collision?

A flat uniform circular disk (radius = 2.90 m, mass = 1.00 ✕ 102 kg) is...

A flat uniform circular disk (radius = 2.90 m, mass = 1.00 ✕ 102 kg) is initially stationary. The disk is free to rotate in the horizontal plane about a frictionless axis perpendicular to the center of the disk. A 40.0 kg person, standing 1.75 m from the axis, begins to run on the disk in a circular path and has a tangential speed of 2.80 m/s relative to the ground. Find the resulting angular speed of the disk (in...

A rocket with mass 5.00×103 kg is in a circular orbit of radius 7.30×106 m around...

A rocket with mass 5.00×103 kg is in a circular orbit of radius 7.30×106 m around the earth. The rocket's engines fire for a period of time to increase that radius to 8.70×106 m , with the orbit again circular. A)What is the change in the rocket's gravitational potential energy? Does the potential energy increase or decrease? B) How much work is done by the rocket engines in changing the orbital radius

Constants A 3.20 kg box is moving to the right with speed 8.00 m/s on a...

Constants A 3.20 kg box is moving to the right with speed 8.00 m/s on a horizontal, frictionless surface. At t = 0 a horizontal force is applied to the box. The force is directed to the left and has magnitude F(t)=(6.00 N/s2 )t2 What distance does the box move from its position at t=0 before its speed is reduced to zero? Express your answer with the appropriate units. If the force continues to be applied, what is the velocity...

A flywheel comprises a uniform circular disk with a mass of 97.0 kg and a radius...

A flywheel comprises a uniform circular disk with a mass of 97.0 kg and a radius of 1.1 m. It rotates with an angular velocity of 1420 rev/min. A constant tangential force is applied at a radial distance of 0.5 m. What is the initial kinetic energy of the wheel? (b) If the wheel is brought to rest in 133.0 s, what is the tangential force?

A planet of mass 6 × 1025 kg is in a circular orbit of radius 4...

A planet of mass 6 × 1025 kg is in a circular orbit of radius 4 × 1011 m around a star. The star exerts a force on the planet of constant magnitude 1.8 × 1023 N. The speed of the planet is 3.4 × 104 m/s. (a) In half a "year" the planet goes half way around the star. What is the distance that the planet travels along the semicircle? (b) During this half "year", how much work is...