Question

A solid disk of radius 9.50 cm and mass 1.15 kg, which is rolling at a speed of 1.40 m/s, begins rolling without slipping up a 6.00

∘
slope. How long will it take for the disk to come to a stop?

Answer 1

To determine how long it takes for the disk to come to a stop, calculate the deceleration of the disk using the equation a = g * sin(θ) - (μ * g * cos(θ)), where a is the deceleration, g is the acceleration due to gravity, θ is the angle of the incline, and μ is the coefficient of kinetic friction. Then, use kinematic equations to determine the time.

Step-by-step explanation:

To determine how long it takes for the disk to come to a stop, we need to calculate the deceleration of the disk. When a disk is rolling without slipping up an incline, the force of gravity can be broken down into two components: the component parallel to the incline and the component perpendicular to the incline. The component parallel to the incline causes the deceleration of the disk.

The deceleration can be calculated using the equation:

a = g * sin(θ) - (μ * g * cos(θ))

Where:

a is the deceleration

g is the acceleration due to gravity (9.8 m/s^2)

θ is the angle of the incline (6.00 degrees)

μ is the coefficient of kinetic friction (0.3)

Using this equation, we can solve for the deceleration, and then use kinematic equations to determine the time it takes for the disk to come to a stop.

Answer 2

To calculate the time it takes for the solid disk to come to a stop, we use the formula: t = (2Iω)/(gRf), where I is the moment of inertia, ω is the initial angular velocity, g is the acceleration due to gravity, R is the disk radius, and f is the coefficient of kinetic friction.

Step-by-step explanation:

To calculate the time it takes for the solid disk to come to a stop, we need to consider both the rotational motion and the translational motion of the disk. The disk will experience a decelerating torque due to friction while rolling up the slope. The formula to calculate the time is given by:

t = (2Iω)/(gRf)

where I is the moment of inertia of the disk, ω is the initial angular velocity, g is the acceleration due to gravity, R is the radius of the disk, and f is the coefficient of kinetic friction.

Plugging in the given values, we can calculate the time it takes for the disk to come to a stop.