Final answer:
To find the deceleration of a snowboarder going up a slope, we use the modified equation of motion that includes the effects of gravity and kinetic friction. By substituting the angle of the slope and the known coefficient of kinetic friction into the equation, we can calculate the deceleration.
Step-by-step explanation:
To calculate the deceleration of a snowboarder going up a 4.7° slope with the coefficient of friction for waxed wood on wet snow, we can use the following equation derived from Newton's second law:
a = g(sin θ - μ_k cos θ)
Where:
- a is the acceleration or deceleration,
- g is the acceleration due to gravity (9.8 m/s²),
- θ is the angle of the slope (4.7°),
- μ_k is the coefficient of kinetic friction.
We know that the motion is against gravity and friction always acts in the opposite direction of the motion. So, when the snowboarder is going uphill, the gravitational component (g sin θ) and the friction ( μ_k g cos θ) are both acting to decelerate the snowboarder. Assuming we have a value for μ_k from previous exercises or tables, we can plug in the values into the equation to find the deceleration ('a'). It's important to note that if the snowboarder were moving downhill, we would subtract the friction term from the gravitational component, but since they're moving uphill, we actually add them because both forces are resisting the motion.