Question

Franklin is driving some test laps at Daytona. The track has a radius of 300 m and is tilted at 30 degrees at the turns. The car has a mass of 700 kg.

1. How fast can he drive in m/s if there is no friction?
2. How fast can he go if she doubled the mass of the car?
3. If his tires had a coefficient of friction of 0.40 and there was friction, how fast could he go in m/s?
4. What angle in degrees should the track be tilted at, if he only plans to drive at 25 m/s with no friction?

Answer 1

To calculate the speed at which Franklin can drive in m/s with no friction, we can use the formula for centripetal acceleration. If there is no friction, the speed remains the same regardless of the mass of the car. With a coefficient of friction of 0.40, the speed is given by v = sqrt(mu * g * r). To find the angle at which the track should be tilted for a specific speed with no friction, we can use the equation theta = arctan(v^2 / (g * r)).

Step-by-step explanation:

To calculate the speed at which Franklin can drive in m/s with no friction, we can use the formula for centripetal acceleration. The centripetal acceleration is given by the equation a = v^2 / r, where a is the acceleration, v is the speed, and r is the radius of the curve. Plugging in the values, we get v = sqrt(a * r), where a = g * tan(theta) and theta is the angle of the curve in radians. For the given track tilt of 30 degrees, the angle in radians is pi/6. So the speed at which Franklin can drive with no friction is v = sqrt(g * r * tan(theta)), where g is the acceleration due to gravity.

• The mass of the car is not relevant to the speed at which Franklin can drive with no friction. So the speed remains the same, which is v = sqrt(g * r * tan(theta)).
• If Franklin doubles the mass of the car, the speed at which he can drive with no friction remains the same, which is v = sqrt(g * r * tan(theta)).
• To find the speed at which Franklin can drive with a coefficient of friction of 0.40, we need to calculate the maximum frictional force. The maximum frictional force is given by mu * N, where mu is the coefficient of friction and N is the normal force. The normal force is equal to the weight of the car, which is mg. So the maximum frictional force is mu * mg. The maximum frictional force provides the centripetal force, which is given by F = m * a = m * v^2 / r. Plugging in the values, we get mu * mg = m * v^2 / r. Solving for v, we get v = sqrt(mu * g * r).
• To find the angle in degrees at which the track should be tilted to drive at 25 m/s with no friction, we can rearrange the equation for v = sqrt(g * r * tan(theta)) to solve for theta. So theta = arctan(v^2 / (g * r)). Plugging in the values, we get theta = arctan(25^2 / (9.8 * 300)).