Question

Part A: A ball of mass 3.5 kg rolls all the way down a slope inclined at 40° to the horizontal, with a base of length 4.8 m. How much GPE does the ball lose?

Part B: If the average frictional forces are 4.0 N, work out how much work the ball does against friction.

Answer 1

To calculate the GPE lost by the ball, find the change in height and subtract the final GPE from the initial GPE. To calculate the work done against friction, multiply the frictional force by the distance.

Step-by-step explanation:

Part A: To calculate the GPE lost by the ball, we need to determine the change in height. The vertical height of the slope can be found by multiplying the base length by the sine of the angle between the slope and the horizontal:

Vertical height = base length * sin(angle)

Once we have the height, we can calculate the initial GPE and subtract the final GPE to find the GPE lost by the ball:

GPE lost = initial GPE - final GPE

Part B: To calculate the work done against friction, we can use the formula:

Work = force * distance

In this case, the force of friction is given as 4.0 N and the distance is the length of the slope. Therefore, we can calculate the work done against friction by:

Work = 4.0 N * base length

Answer 2

In a high school physics problem, the gravitational potential energy lost by a ball rolling down an incline and the work done against friction are calculated using formulas GPE = mgh and Work = force × distance, respectively.

Step-by-step explanation:

The problem describes a scenario involving a ball rolling down an inclined plane, requiring the use of gravitational potential energy (GPE) and work done against friction calculations. The slope and the forces acting on the ball can be analyzed using principles of classical mechanics, a core subject area of high school physics.

Part A: To find the amount of GPE lost by the ball, we use the formula GPE = mgh, where 'm' is the mass of the ball, 'g' is the acceleration due to gravity (9.81 m/s²), and 'h' is the vertical height which can be determined using trigonometry (sin(40°) × 4.8 m).

Part B: The work done against friction can be found with the formula Work = force × distance, where the force is the average frictional force and the distance is the length of the slope along which the ball rolls. In this case, Work = 4.0 N × 4.8 m.