Select the correct answer.
A car with a mass of $1.2 \times 10^3$ kilograms is moving at a speed of 18 meters/second. It is hit by a truck from behind and its speed after the collision increases to 20 meters/second. What is the value of impulse?
A. $1.2 \times 10^3$ kilogram meters/second
B. $2.4 \times 10^3$ kilogram meters/second
C. $3.6 \times 10^3 kilogram$ meters/second
D. $4.8 \times 10^3 kilogram$ meters/second
Answer (1)
The impulse is equal to the change in momentum.
Calculate the change in momentum using the formula: Δ p = m ( v f − v i ) .
Substitute the given values: Δ p = ( 1.2 × 1 0 3 ) ( 20 − 18 ) .
The impulse is J = 2.4 × 1 0 3 kg m/s, so the answer is 2.4 × 1 0 3 kg m/s .
Explanation
Understanding the Problem We are given a car with a mass of 1.2 × 1 0 3 kg moving at 18 m/s. After a collision, its speed increases to 20 m/s. We need to find the impulse imparted to the car.
Change in Momentum The impulse is equal to the change in momentum of the car. The change in momentum is given by the formula: Δ p = m ( v f − v i ) where m is the mass of the car, v f is the final velocity, and v i is the initial velocity.
Calculating the Impulse We are given: m = 1.2 × 1 0 3 kg v i = 18 m/s v f = 20 m/s Substituting these values into the formula, we get: Δ p = ( 1.2 × 1 0 3 ) ( 20 − 18 ) Δ p = ( 1.2 × 1 0 3 ) ( 2 ) Δ p = 2.4 × 1 0 3 kg m/s Since the impulse J is equal to the change in momentum Δ p , we have: J = 2.4 × 1 0 3 kg m/s
Final Answer Therefore, the value of the impulse is 2.4 × 1 0 3 kg m/s.
Examples
The concept of impulse is crucial in understanding collisions and impacts in sports. For example, when a baseball bat hits a ball, the impulse delivered to the ball determines its change in momentum and, consequently, its final velocity and distance traveled. Similarly, in car crashes, understanding impulse helps engineers design safer vehicles by minimizing the force experienced by passengers during a collision. Impulse also plays a role in designing protective gear, such as helmets and padding, which aim to reduce the impact force and prevent injuries.
