A truck driver slams on the brakes and skids to a stop through a displacement of delta x.
(a) IF the truck has twice the mass, by what factor does the stopping distance change?
1) 0.25
or
2) 1
or
3) 4
(b) If the initial velocity of the truck were halved, by what factor would the stopping distance change?
1) 2
or
2) none of these
or
3) 4
or
4) 0.25
or
5) 1
(a) If the truck has twice the mass, the stopping distance would change by a factor of 4. Why? Because the truck now has more "mass" to "stop", so it would take more effort to bring it to a complete stop. It's like doubling the number of donuts you need to eat before feeling guilty... it just takes more time and effort!
(b) If the initial velocity of the truck were halved, the stopping distance would also change by a factor of 4. Why? Well, if the truck is moving slower, it has less momentum, which means it will take less distance to come to a stop. Just like when you're trying to stop yourself from spilling your coffee while walking slowly compared to sprinting... it's easier to stop when you're moving slower!
To answer these questions, we need to understand the factors that affect the stopping distance of a truck when the brakes are applied.
(a) The stopping distance of a truck is directly proportional to the square of its initial velocity (v0) and inversely proportional to its mass (m).
1) If the truck has twice the mass, the stopping distance is affected by the change in mass only. Since the stopping distance is inversely proportional to the mass, doubling the mass would decrease the stopping distance by a factor of 2.
Therefore, the answer to (a) is 2.
(b) The stopping distance of a truck is directly proportional to the square of its initial velocity (v0) and inversely proportional to its mass (m).
2) If the initial velocity of the truck is halved, the stopping distance is affected by the change in initial velocity only. Since the stopping distance is directly proportional to the square of the velocity, halving the initial velocity would decrease the stopping distance by a factor of (1/2)^2 = 1/4 = 0.25.
Therefore, the answer to (b) is 0.25.
To answer these questions, we need to understand the relationship between stopping distance and the factors given (mass and initial velocity).
(a) According to Newton's second law of motion, the stopping distance of an object is directly proportional to its mass. So, if the truck has twice the mass, the stopping distance would also increase by the same factor. The correct answer is 2.
To understand this conceptually, recall that the force required to stop an object is directly proportional to its mass. When the mass increases, more force is required to bring the object to a stop, thus increasing the stopping distance.
(b) The stopping distance is also influenced by the initial velocity of the truck. If the initial velocity is halved, the stopping distance will decrease by a factor determined by the square of the initial velocity.
To calculate this, let's assume the initial velocity is "v" and the stopping distance is "d". We know that the stopping distance is inversely proportional to the square of the initial velocity (d ∝ 1/v^2).
If the initial velocity is halved, the new initial velocity becomes "v/2". Now, we can compare the two scenarios: (d1)/(d2) = (v2/v1)^2 = ((v/2)/v)^2 = 1/4.
So, the stopping distance would decrease by a factor of 1/4. The correct answer is 4.
In summary:
(a) The stopping distance changes by a factor of 2.
(b) The stopping distance changes by a factor of 1/4 or 0.25.
(a) The answer is (2)(a factor of 1). The stopping distance does not change. That is because both the kinetic energy and the friction force double.
(b) 4) 0.25