A 3000 kg truck is about to tow a 1250 kg car up a hill that...

A 3000 kg truck is about to tow a 1250 kg car up a hill that makes an angle of ? = 10° with respect to the horizontal. The rope attached from the truck to the car makes an angle of ? = 25° with respect to the horizontal. The coefficient of static friction between the truck tires and the road is 0.60. Ignore friction on the car's tires due to the road. Starting from rest, they move with constant acceleration until, 400 m up the hill, their speed is 11 m/s. What is the total frictional force on the truck's tires? [Hint: You'll need to apply Newton's second law to at least one of three systems—the car, the truck, or the car + rope + truck. Consider the options and choose the easiest method. You may not need all of the given information.] ? = 25° ? = 10°

Transcript

00:01 In this video, we're going to be working on looking at our problem solving skills, and we're actually going to be doing some physics as well.

00:07 But what we have is a problem of a truck towing a car up a hill.

00:12 Okay, so we have a hill here.

00:16 It's at inclined at some angle with relative to the horizontal.

00:21 I'll call that theta.

00:24 Okay, so we have a truck, and it's going to be towing a car.

00:29 Sorry for my drawing skills.

00:31 Okay, so it's towing a car up this hill.

00:38 Okay, they are connected by a rope here, and that makes some angle, a different angle, and i'll call that angle alpha.

00:49 That makes an angle alpha with respect to the horizontal.

00:53 Okay, we know that the system starts from rest, so eventually the truck and the car are stationary, okay, before the car or the truck starts accelerating and towing that car up the hill.

01:03 Okay, and they reach a final velocity of 11 meters per second.

01:08 Okay, so let's start writing down some numbers we'll need to solve this.

01:11 So our initial velocity equals zero.

01:13 Our final velocity equals 11 meters per second.

01:18 Okay, and this is achieved over a distance d of 400 meters up the hill.

01:26 Okay, so we start, let's say we start here, and then we go up the hill for a distance d of 400 meters.

01:35 We have the masses of the car and the truck.

01:38 So the mass of the truck is 3 ,000 kilograms, and the mass of the car, m sub c, we'll call that, is 1 ,250 kilograms.

01:55 And we also have the angles that the hill makes with the horizontal.

02:00 Okay, so theta, theta equals 10 degrees.

02:03 Okay, and we have the angle that the rope makes with the horizontal.

02:08 Okay, so we have alpha, alpha equals 25 degrees.

02:14 And we have a coefficient of friction between the truck's tires and the road.

02:21 Okay, mu equals 0 .6.

02:25 Right, we're going to call the friction between the road and the car's tires frictionless.

02:30 We're going to ignore that term.

02:31 And what we want to find is the total frictional force acting between the truck's tires and the surface of the road over this 400 meters of motion.

02:46 Okay, so how do we approach this? okay, this looks like a complicated problem.

02:52 We have a lot of information, but we don't really need a lot of the information.

02:57 Okay, the way i'm going to solve it is i'm going to say that the tension in this line between the two cars is constant.

03:05 Okay, the objects, the car and the truck are moving as one object.

03:09 Okay, so we don't need to worry about any of the interaction between these two.

03:12 So we don't need to worry about what the actual value of the tension is...

Question

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