Question

A four-person bobsled (total mass = 524 kg) comes down a straightaway at the start of a bobsled run. The straightaway is 80.0 m long and is inclined at a constant angle of 8.80° with the horizontal. Assume that the combined effects of friction and air drag produce on the bobsled a constant force of 62.0 N that acts parallel to the incline and up the incline. Answer the following questions to three significant digits.

(a) If the speed of the bobsled at the start of the run is 5.77 m/s, how long does the bobsled take to come down the straightaway?

(b) Suppose the crew is able to reduce the effects of friction and air drag to 42.0 N. For the same initial velocity, how long does the bobsled now take to come down the straightaway?

Answer 1

To determine the time it takes for the bobsled to come down the straightaway, we can use the equations of motion. The bobsled is moving down the incline, so we can break the motion into two components: one along the incline and one perpendicular to the incline. Using the net force, we can apply Newton's second law to find the acceleration of the bobsled. Since we are given the initial velocity of the bobsled, we can use the equations of motion to find the time it takes for the bobsled to come down the straightaway.

Step-by-step explanation:

To determine the time it takes for the bobsled to come down the straightaway, we can use the equations of motion. The bobsled is moving down the incline, so we can break the motion into two components: one along the incline and one perpendicular to the incline. The force due to friction and air drag opposes the motion down the incline. The force due to gravity is split into two components: one parallel to the incline and one perpendicular to the incline. The net force acting on the bobsled is the component of the force due to gravity parallel to the incline minus the force due to friction and air drag. Using this net force, we can apply Newton's second law to find the acceleration of the bobsled. Since we are given the initial velocity of the bobsled, we can use the equations of motion to find the time it takes for the bobsled to come down the straightaway.

(a) Using the given information, the force due to friction and air drag is 62.0 N and the initial velocity of the bobsled is 5.77 m/s. The net force acting on the bobsled is the component of the force due to gravity parallel to the incline minus the force due to friction and air drag.

Net force = m * a(component of force due to gravity parallel to the incline) - (force due to friction and air drag) = m * a

(mass * g * sin(θ)) - (force due to friction and air drag) = m * a

Where m is the mass of the bobsled, g is the acceleration due to gravity, and θ is the angle of the incline.

Using this equation and the known values, we can solve for the acceleration of the bobsled:

a = ((mass * g * sin(θ)) - (force due to friction and air drag)) / mass

Once we have the acceleration, we can use the equation of motion, s = ut + 0.5at^2, to find the time it takes for the bobsled to come down the straightaway. In this equation, s is the distance traveled, u is the initial velocity, a is the acceleration, and t is the time.

s = 80.0 m

u = 5.77 m/s

a = ((mass * g * sin(θ)) - (force due to friction and air drag)) / mass

t = sqrt((2s) / a)

Using this equation and the known values, we can solve for the time it takes for the bobsled to come down the straightaway.

b) If the force due to friction and air drag is reduced to 42.0 N, we can repeat the above calculations to find the new time it takes for the bobsled to come down the straightaway.