Question

A mass m slides upward along a rough plane surface inclined at an angle of 0.11 radians to the horizontal. Initially, the mass has a speed of 2.59 m/s before it slides a distance of 1.0 m up the incline. After sliding this distance, the new speed of the mass is ______ m/s. What is the acceleration of the sliding mass? (Positive denotes acceleration up the incline; negative denotes acceleration down the incline.)

Answer 1

To find the new speed of the mass after sliding up the incline, use the work-energy principle. The acceleration of the sliding mass can be calculated using the formula: acceleration = change in velocity / time taken.

Step-by-step explanation:

To find the new speed of the mass after it slides a distance of 1.0 m up the incline, we can use the work-energy principle. The work done on the mass is equal to the change in its kinetic energy.

The work done is given by the formula:

Work = Force * Distance * Cos(angle)

Since the force of friction opposes the motion of the mass, the work done by friction is:

Work_friction = Force_friction * Distance * Cos(angle)

Since the object starts with a speed of 2.59 m/s and comes to rest at the end of the incline, its change in kinetic energy is:

Change in KE = KE_final - KE_initial = 0 - (1/2 * m * (2.59)^2)

Setting these two equations equal to each other, we can solve for the new speed of the mass:

Work_friction = Change in KE

Finally, we can calculate the acceleration of the sliding mass using the following formula:

Acceleration = Change in velocity / Time taken