I = FΔt = Δp = mv – mu
Since hailstones bounce back off an umbrella, compared to water droplets from rain, there is a greater impulse on an umbrella in hail than in rain
A 58 g tennis ball moving horizontally to the left at a speed of 30 m s–1 is struck by a tennis racket which returns the ball back to the right at 20 m s–1.(a) Calculate the impulse delivered to the ball by the racket(b) State the direction of the impulse
Part (a)
Step 1: Write the known quantities
Step 2: Write down the impulse equation
Impulse I = Δp = m(v – u)
Step 3: Substitute in the values
I = (58 × 10–3) × (–20 – 30) = –2.9 N s
Part (b)
Direction of the impulse
When the force is not constant, the impulse is the area under a force–time graph
Impulse = FΔt
A ball of mass 3.0 kg, initially at rest, is acted on by a force F which varies with t as shown by the graph.
Calculate the magnitude of the velocity of the ball after 16 s.
Step 1: List the known quantities
Step 2: Calculate the impulse
Area = Impulse = 32 × 103 N s
Step 3: Write the equation for impulse
Impulse, I = Δp = m(v – u)
Step 4: Substitute in the values
I = mv
32 × 103 = 3.0 × v
v = (32 × 103) ÷ 3.0
v = 10 666 m s–1 = 11 km s–1
Step 5: State the final answer
v = 11 km s–1
Remember that if an object changes direction, then this must be reflected by the change in sign of the velocity. As long as the magnitude is correct, the final sign for the impulse doesn't matter as long as it is consistent with which way you have considered positive (and negative)For example, if the left is taken as positive and therefore the right as negative, an impulse of 20 N s to the right is equal to −20 N sSome maths tips for this section:Rate of Change
Areas
A cricket fielder moves their hands backwards when catching a cricket ball to reduce the force it will exert on their hands
The follow through action of a football kick increases the change in momentum of the ball
A tennis ball hits two rackets with a change in momentum of 0.5 kg m s−1. The first racket has a contact time of 2 s. The second racket has a contact time of 0.1 s.For the different contact times, which tennis racket experiences more force from the tennis ball?
The seat belt, airbag and crumple zones help reduce the risk of injury on a passenger
The increase in contact time Δt decreases the force for the same impulse
A 7 kg bowling ball has an impulse of 84 N s act upon it. The bowling ball was initially at rest and sitting on a flat frictionless surface.Predict the distance moved by the bowling ball in the first 3 seconds after the impulse was delivered.
Step 1: List the known quantities
Step 2: Find the velocity caused by the impulse
Impulse, I = Δp = m(v – u)
Step 3: Rearrange and solve for v
I = m × v (since u = 0 m s−1)
v = I ÷ m = 84 ÷ 7 = 12 m s−1
Step 4: Find the distance travelled
v = d ÷ t
d = v × t
d = 12 × 3 = 36 m
Step 5: State the final answer
转载自savemyexams
© 2023. All Rights Reserved. 沪ICP备2023009024号-1