A truck is driving down a steep incline when the driver realizes that there is a problem with the brakes (oh no!). Luckily the driver reaches a runaway truck ramp on the side of the road. The ramp goes up the side of a mountain that has an incline of 25° above the horizontal. The truck has a mass of 45,000 kg and is traveling at a speed of 32.0 m/s when it enters the bottom of the runaway truck ramp. (The truck is in neutral at this time.) (a) When the truck goes up the runaway truck ramp, the driver pulls the emergency brake and all the wheels lock, causing the truck to slide up the ramp. The coefficients of friction between the tires and the ramp are s = 0.7 and k = 0.6. What distance along the ramp does the truck travel before coming to a stop? Derive a symbolic answer below. Don't plug in any numbers yet. (b) Plug in the numbers in the problem statement to get a numerical value for the distance the truck travels up the ramp.
A truck is driving down a steep incline when the driver realizes that there is a problem with the brakes (oh no!). Luckily the driver reaches a runaway truck ramp on the side of the road. The ramp goes up the side of a mountain that has an incline of 25° above the horizontal. The truck has a mass of 45,000 kg and is traveling at a speed of 32.0 m/s when it enters the bottom of the runaway truck ramp. (The truck is in neutral at this time.) (a) When the truck goes up the runaway truck ramp, the driver pulls the emergency brake and all the wheels lock, causing the truck to slide up the ramp. The coefficients of friction between the tires and the ramp are s = 0.7 and k = 0.6. What distance along the ramp does the truck travel before coming to a stop? Derive a symbolic answer below. Don't plug in any numbers yet. (b) Plug in the numbers in the problem statement to get a numerical value for the distance the truck travels up the ramp.
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Transcribed Image Text:Problem 2
A truck is driving down a steep incline when the driver realizes that there is a problem with
the brakes (oh no!). Luckily the driver reaches a runaway truck ramp on the side of the road.
The ramp goes up the side of a mountain that has an incline of 25° above the horizontal.
The truck has a mass of 45,000 kg and is traveling at a speed of 32.0 m/s when it enters the
bottom of the runaway truck ramp. (The truck is in neutral at this time.)
(a) When the truck goes up the runaway truck ramp, the driver pulls the emergency brake
and all the wheels lock, causing the truck to slide up the ramp. The coefficients of
friction between the tires and the ramp are s = 0.7 and k = 0.6. What distance
along the ramp does the truck travel before coming to a stop? Derive a symbolic
answer below. Don't plug in any numbers yet.
(b) Plug in the numbers in the problem statement to get a numerical value for the distance
the truck travels up the ramp.
(c) How would your answers above change if the truck had half the mass (but everything
else in the problem remained the same)? Explain your reasoning.
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