A 1050 kg sports car is moving westbound at 13.0 m/s on a level road when it collides with a 6320 kg truck driving east on the s
ame road at 14.0 m/s . The two vehicles remain locked together after the collision.
a. What is the velocity (magnitude and direction) of the two vehicles just after the collision?
b. At what speed should the truck have been moving so that both it and the car are stopped in the collision?
c. Find the change in kinetic energy of the system of two vehicles for the situations of part (a) and part (b). For which situation is the change in kinetic energy greater in magnitude?
a. What is the velocity (magnitude and direction) of the two vehicles just after the collision?
b. At what speed should the truck have been moving so that both it and the car are stopped in the collision?
c. Find the change in kinetic energy of the system of two vehicles for the situations of part (a) and part (b). For which situation is the change in kinetic energy greater in magnitude?
1 answer:
Answer:
(A) V = 9.89m/s
(B) U = -2.50m/s
(C) ΔK.E = –377047J
(D) ΔK.E = –257750J
Explanation:
The full solution can be found in the attachment below. The east has been chosen as the direction for positivity.
This problem involves the principle of momentum conservation. This principle states that the total momentum before collision is equal to the total momentum after collision. This problem is an inelastic kind of collision for which the momentum is conserved but the kinetic energy is not. The kinetic energy after collision is always lesser than that before collision. The balance is converted into heat by friction, and also sound energy.
See attachment below for full solution.
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Complete Question
Q. Two go-carts, A and B, race each other around a 1.0km track. Go-cart A travels at a constant speed of 20m/s. Go-cart B accelerates uniformly from rest at a rate of 0.333m/s^2. Which go-cart wins the race and by how much time?
Answer:
Go-cart A is faster
Explanation:
From the question we are told that
The length of the track is
The speed of A is
The uniform acceleration of B is
Generally the time taken by go-cart A is mathematically represented as
=>
=>
Generally from kinematic equation we can evaluate the time taken by go-cart B as
given that go-cart B starts from rest u = 0 m/s
So
=>
=>
Comparing we see that
is smaller so go-cart A is faster
Answer:
The angle of banked curve that makes the reliance on friction unnecessary is
Explanation:
In order the car to stay on the curve without friction, the net force in the direction of radius should be equal or smaller than the centripetal force. Otherwise the car could slide off the curve.
The only force in the direction of radius is the sine component of the weight of the car
The cosine component is equivalent to the normal force, which we will not be using since friction is unnecessary.
Newton’s Second Law states that
Also, the car is making a circular motion:
Combining the equations:
Finally the angle is