A skier is pulled up a slope at a constant velocity by a tow bar. The slope is inclined at 27.2 ° with respect to the horizontal. The force applied to the skier by the tow bar is parallel to the slope. The skier's mass is 53.7 kg, and the coefficient of kinetic friction between the skis and the snow is 0.137. Find the magnitude of the force that the tow bar exerts on the skier.

Question

A skier is pulled up a slope at a constant velocity by a tow bar. The slope is inclined at 27.2 ° with respect to the horizontal. The force applied to the skier by the tow bar is parallel to the slope. The skier's mass is 53.7 kg, and the coefficient of kinetic friction between the skis and the snow is 0.137. Find the magnitude of the force that the tow bar exerts on the skier.

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Answer 1

Oh, don't worry! Clown Bot is here to save the day and add some humor to your physics question.

To find the magnitude of the force that the tow bar exerts on the skier, we'll have to break it down step by step.

First, let's identify the forces acting on the skier. We have the force applied by the tow bar, the weight of the skier, and the force of kinetic friction.

Now, since the skier is moving at a constant velocity, we know that the net force acting on the skier is zero (otherwise, the skier wouldn't have a constant velocity). This means the force applied by the tow bar must be equal in magnitude to the force of kinetic friction.

Applying some trigonometry magic, we can find that the component of the skier's weight acting down the slope is (mass * gravity * sin(angle of slope)).

Using the coefficient of kinetic friction, we can find the force of kinetic friction by multiplying it with the skier's weight (mass * gravity).

Finally, since the force applied by the tow bar is equal to the force of kinetic friction, we can solve for it.

So, the magnitude of the force that the tow bar exerts on the skier is... drumroll, please... equal to the force of kinetic friction!

I hope that adds a little laughter to your physics journey. Good luck!

Answer 2

To find the magnitude of the force that the tow bar exerts on the skier, we need to consider the forces acting on the skier in the vertical and horizontal directions.

In the vertical direction, we have the weight of the skier pulling downward. The weight can be calculated using the formula:

Weight = mass × acceleration due to gravity

Given that the mass of the skier is 53.7 kg and the acceleration due to gravity is approximately 9.8 m/s^2, we can calculate the weight:

Weight = 53.7 kg × 9.8 m/s^2 = 526.26 N

In the horizontal direction, the force applied by the tow bar is balanced by the force of kinetic friction between the skis and the snow. The force of kinetic friction can be calculated using the formula:

Force of kinetic friction = coefficient of kinetic friction × normal force

The normal force is the perpendicular force exerted by the surface (snow) on the skis. It is equal in magnitude but opposite in direction to the force component of the weight perpendicular to the slope. The normal force can be calculated using the equation:

Normal force = weight × cos(θ)

Where θ is the angle of inclination of the slope with respect to the horizontal. In this case, θ = 27.2°.

Normal force = 526.26 N × cos(27.2°) = 460.37 N

Now we can find the force of kinetic friction:

Force of kinetic friction = 0.137 × 460.37 N = 63.07 N

Since the skier is moving at a constant velocity, the force applied by the tow bar must be equal in magnitude to the force of kinetic friction. Therefore, the magnitude of the force that the tow bar exerts on the skier is:

Magnitude of the force = 63.07 N