An inquisitive physics student, wishing to combine pleasure with scientific inquiry, rides on a rollercoaster sitting on a bathroom scale. (Do not try this yourself on a rollercoaster that forbids loose heavy packages.) The bottom of the seat in the rollercoaster car is in a plane parallel to the track. The seat has a perpendicular back and a seat belt that fits around the student's chest in a plane parallel to the bottom of the seat. The student lifts his feet from the floor, so that the scale reads his weight, 150 lb, when the car is horizontal. At one point during the ride, the car zooms with negligible friction down a straight slope inclined at 26.0° below the horizontal. What does the scale read at that point?

Question

An inquisitive physics student, wishing to combine pleasure with scientific inquiry, rides on a rollercoaster sitting on a bathroom scale. (Do not try this yourself on a rollercoaster that forbids loose heavy packages.) The bottom of the seat in the rollercoaster car is in a plane parallel to the track. The seat has a perpendicular back and a seat belt that fits around the student's chest in a plane parallel to the bottom of the seat. The student lifts his feet from the floor, so that the scale reads his weight, 150 lb, when the car is horizontal. At one point during the ride, the car zooms with negligible friction down a straight slope inclined at 26.0° below the horizontal. What does the scale read at that point?

Answer 1

To figure out what the scale reads at the point when the car is zooming down the inclined slope, we need to consider the forces acting on the student sitting on the rollercoaster.

1. First, we need to find the component of the student's weight that acts perpendicular to the inclined slope.
- The total weight of the student is 150 lb, which is the force acting downward.
- We can find the perpendicular component of this weight by multiplying the total weight by the cosine of the angle between the weight and the direction perpendicular to the slope.
- The angle between the weight and the perpendicular direction is (90° + 26.0°) because the slope is inclined 26.0° below the horizontal.
- So the perpendicular component of the weight is: perpendicular weight = 150 lb * cos(90° + 26.0°).

2. Next, we need to determine the net force acting on the student in the perpendicular direction.
- Since the student is not accelerating in the perpendicular direction, the net force is zero according to Newton's second law (F = ma).
- The net force is the difference between the force exerted by the scale upward and the perpendicular weight of the student.
- So we have: net force = scale reading - perpendicular weight = 0.

3. Using the information from step 2, we can solve for the scale reading.
- Rearranging the equation, we find: scale reading = perpendicular weight = 150 lb * cos(90° + 26.0°).

Now, we can calculate the scale reading by plugging the values into the equation:

scale reading = 150 lb * cos(90° + 26.0°)

To figure out what the scale reads at the point when the car is zooming down the inclined slope, we need to consider the forces acting on the student sitting on the rollercoaster.

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