3 questions about Impulse equation

1. A car with a mass of 250 kg is moving with a speed of 72 km/hour, then accelerated with a constant force so that in 5 seconds its speed becomes 80 km/hour. Determine the impulse for 5 seconds

__Known:__

The mass of the car (m) = 250 kg

Initial speed (v_{o}) = 72 km/h = 20 m/s

Final speed (v_{t}) = 80 km/h = 22 m/s

Time interval (t) = 5 seconds

__Wanted:__ Determine impulse (I)

__Solution:__

Impulse formula: Impulse = Change in momentum

I = Δp

I = m (v_{t} – v_{o}) = (250)(22 – 20) = (250)(2)

I = 500 kg m/s

2. An object with a mass of 0.4 kg initially moving with a speed of 20 m/s is stopped by a constant force of 50 N in a certain time. How big is the impulse?

__Known____:__

Mass (m) = 0.4 kg

Velocity (v_{o}) = 20 m/s

Final velocity (v_{t}) = 0 m/s

Force (F) = 50 N

__Wanted:__ Impulse (I)

__Solution:__

Impulse formula: Impulse = Change in momentum

I = Δp

I = m (v_{t} – v_{o}) = (0,4)(0 – 20) = (0,4)(-20)

I = 8 kg m/s

3. An object with mass m is moving at a constant speed v, so the impulse of the object is…

Solution

Impulse = change in momentum. Momentum changes when mass or velocity changes. So if the speed and mass are constant then there is no change in momentum. So that there are no impulses.

**20 conceptual questions and answers related to impulse.**

**Question:**What is impulse?**Answer:**Impulse is the change in momentum of an object when a force is applied over a period of time.**Question:**How is impulse calculated?**Answer:**Impulse is calculated by multiplying the force applied to the object by the time period during which the force is applied.**Question:**What is the unit of impulse?**Answer:**The SI unit of impulse is Newton second (Ns), which is equivalent to kg x m/s.**Question:**How does impulse relate to momentum?**Answer:**Impulse is equal to the change in momentum of an object. This relationship is described by the impulse-momentum theorem.**Question:**Can impulse be negative?**Answer:**Yes, impulse can be negative. A negative impulse occurs when the final momentum of the object is less than its initial momentum, such as when a force acts to slow an object down.**Question:**What is the impulse-momentum theorem?**Answer:**The impulse-momentum theorem states that the impulse on an object is equal to the change in its momentum. Mathematically, it is expressed as FΔt = Δp.**Question:**How does increasing the time of impact affect the impulse on an object?**Answer:**Increasing the time of impact while keeping the force constant will increase the impulse on an object. This is because impulse is the product of force and time.**Question:**How does impulse apply in a collision?**Answer:**In a collision, the impulse experienced by an object is equal to the change in its momentum. The forces involved in the collision, and the duration of the collision, determine the impulse.**Question:**What role does impulse play in safety design, such as airbags in cars?**Answer:**In safety design, the goal is often to decrease the force experienced by a person during an accident. By increasing the time of impact, such as with an airbag in a car, the same impulse (and therefore the same change in momentum) can be achieved with a smaller force.**Question:**Is impulse a vector or a scalar quantity?**Answer:**Impulse is a vector quantity. It has both magnitude (the value of the impulse) and direction (the direction of the force).**Question:**How is impulse related to work done on an object?**Answer:**Impulse and work are both measures of the effect of a force over time. However, while impulse is related to a change in momentum, work is related to a change in kinetic energy.**Question:**How does impulse change with mass for a constant force and time?**Answer:**The impulse on an object is independent of its mass. It depends only on the force and the time during which the force is applied.**Question:**What happens to the impulse on a ball if it bounces back after hitting a wall?**Answer:**If a ball bounces back after hitting a wall, it experiences a larger impulse compared to a ball that simply stops. This is because the change in momentum is greater for the bouncing ball.**Question:**How is the impulse different in elastic and inelastic collisions?**Answer:**In both elastic and inelastic collisions, the total impulse, or change in momentum, is conserved. However, in an elastic collision, kinetic energy is also conserved, while in an inelastic collision, some kinetic energy is lost.**Question:**What happens to the impulse on a rocket if it ejects gas at a higher speed?**Answer:**If a rocket ejects gas at a higher speed, it experiences a larger impulse. This is because the ejected gas has more momentum, and by conservation of momentum, the rocket must experience a larger change in momentum (i.e., a larger impulse).**Question:**How does impulse relate to force and time in the case of a constant force?**Answer:**For a constant force, the impulse is simply the product of the force and the time during which it is applied. So if either the force or the time is increased, the impulse will increase.**Question:**How does impulse change for a constant force but varying time intervals?**Answer:**If the force is constant and the time interval varies, the impulse is directly proportional to the time. So if the time interval is doubled, the impulse is also doubled.**Question:**Can an object have momentum without an impulse?**Answer:**Yes, an object can have momentum without an impulse. An object has momentum as long as it has mass and velocity. An impulse is required only to change the momentum of an object.**Question:**What does it mean when the impulse on an object is zero?**Answer:**If the impulse on an object is zero, it means the object’s momentum has not changed. The object could still be moving, but its velocity (speed and/or direction) remains the same.**Question:**What is the effect of impulse on the speed of an object?**Answer:**The impulse on an object changes its momentum, which can change its speed, direction, or both. If the impulse is in the same direction as the motion, the speed of the object increases. If the impulse is in the opposite direction, the speed decreases.