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Worksheet: Force as Rate of Momentum Change

Q1:

An average force of 12.5 N is applied by moving air to a bicycle and its rider, of total mass 80 kg, while it is windy that day. The force is applied throughout a time interval of 0.8 s as the gust of wind is very brief. The wind blows from directly behind the bicycle. What is the total momentum change?

Q2:

A man running on a road had a momentum of 360 kg⋅m/s. The road ahead of the man was covered by sand. The man ran through the sand for 12 seconds and his momentum when he had crossed the sand-covered part of the road was 330 kg⋅m/s. What average force did the sand apply to the man while he ran across it?

Q3:

A force of 10 N is applied to an object for 3 seconds, acting in the direction in which the object is moving. How much does the momentum of the object change?

Q4:

An object increases its momentum by 10 kg⋅m/s in a time of 5 seconds. What average force was applied to the object in that time?

Q5:

A tennis racquet hits a tennis ball that has a mass of 60.5 g and applies a constant 75 N force to it. The tennis ball changes its velocity by 30 m/s during the collision. For how many seconds does the collision last?

Q6:

An object is decelerated by an average force of 15 N for a time of 0.5 s. What is the change in the object’s momentum?

Q7:

A car has an initial momentum of 1 500 kg⋅m/s when the driver starts to speed it up, changing its momentum to 1 750 kg⋅m/s in a time of 0.75 s. Determine the average force that acts on the car’s wheels while it accelerates. Answer to the nearest newton.

Q8:

The graph shows how the momentum of an object changes over the time interval 𝑡 = 0 s to 𝑡 = 7 s .

What constant force is applied to the object between 𝑡 = 2 s and 𝑡 = 3 s ?

What constant force is applied to the object between 𝑡 = 3 s and 𝑡 = 4 s ?

What force is applied to the object between 𝑡 = 4 s and 𝑡 = 6 s ?

What average force is applied to the object between 𝑡 = 2 s and 𝑡 = 5 s ? Answer to one decimal place.

What average force is applied to the object between 𝑡 = 2 s and 𝑡 = 7 s ?

Q9:

A force of 8 N is applied to an object and the object’s momentum increases by 2 kg⋅m/s. How long is the force applied for?

Q10:

An object that has a momentum of 12 kg⋅m/s is acted on by a constant force for 8 seconds, after which the object’s momentum is 6 kg⋅m/s. Determine the force that acted on the object.

Q11:

An object with an initial momentum of 20 kg⋅m/s is acted on by an average force of 2.5 N and comes to rest. For how long does the force act on the object?

Q12:

Which of the following formulas correctly relates the force acting on an object, the time for which that force acts, and the change in the momentum 𝑝 of the object?

  • A 𝐹 = 1 2 Δ 𝑝 Δ 𝑡
  • B 𝐹 = Δ 𝑡 Δ 𝑝
  • C 𝐹 = 2 Δ 𝑝 Δ 𝑡
  • D 𝐹 = Δ 𝑝 Δ 𝑡
  • E 𝐹 = Δ 𝑝 Δ 𝑡

Q13:

A bicycle and its rider have a total mass of 72 kg, and they initially moved at a constant speed of 9 m/s. The bicycle was ridden in a straight line through a puddle for a time of 1.2 s and, when the bicycle had crossed the puddle, it had a momentum of 540 kg⋅m/s. What average force was applied to the bicycle by the puddle?

Q14:

A frog of mass 30 g jumping into the air from a resting position accelerates to a speed of 12 cm/s in 0.025 s. How many newtons of force did the frog’s legs exert in the jump?