A water-skier is being pulled at a steady speed in a straight line. her mass plus the mass of the ski is 65 kg. the pull of the tow rope on her is 520 N.
a...i) What is the vertical component Y of the push of the water on the ski??
....ii) What is the horizontal component X of the push of the water on the ski.( ignore air resistance)
....iii) Component X and the 520 N towing force form a clockwise couple acting on the water skier. explain how can she remain in equilibrium as she is towed along?
i) F(y) = mg
ii)F(x) = 520 N
iii)
F(y) =mg (upward); mg (downward)
F=520 N ( to the right)
F(fr) = 520 N (to the left)
Net force =0 => Steady speed => equilibrium
To answer these questions, we need to consider the forces acting on the water-skier and the ski.
i) The vertical component Y of the push of the water on the ski can be determined by considering the forces in the vertical direction. Since the skier is being pulled at a steady speed in a straight line, the vertical forces must be balanced.
The only vertical force acting on the skier is the weight, which can be calculated using the formula:
Weight = mass * acceleration due to gravity
Given that the mass of the skier and ski combined is 65 kg, and taking the acceleration due to gravity as 9.8 m/s^2, we can substitute the values into the formula:
Weight = 65 kg * 9.8 m/s^2 = 637 N
Therefore, the vertical component Y of the push of the water on the ski is equal to the weight, which is 637 N.
ii) The horizontal component X of the push of the water on the ski can be determined by considering the forces in the horizontal direction. Since the skier is being pulled at a steady speed in a straight line, the horizontal forces must also be balanced.
The only horizontal force acting on the skier is the tension force from the tow rope, which is given as 520 N.
Therefore, the horizontal component X of the push of the water on the ski is equal to the tension force, which is 520 N.
iii) The component X (520 N) and the 520 N towing force form a clockwise couple acting on the water skier. Despite the couple, the skier remains in equilibrium because the net torque acting on the system is zero.
When an object is in equilibrium, the sum of all the torques acting on it is zero. In this case, although there is a couple formed by the horizontal component X and the towing force, the torque produced by this couple is counteracted by the torque produced by other forces, such as the water resistance on the skier and the friction between the ski and water.
As long as the net torque is zero, the skier will maintain rotational and translational equilibrium — that is, the skier will neither rotate nor accelerate in any direction.